|I. Newtonian Mechanics
|The Idea of the Center of Gravity
The IDEA OF CENTER OF GRAVITY plays an enormous role in the affairs of men. In this program we show a number of enchanting and dramatic DEMONSTRATIONS bearing on the IDEA.
A - In the very first demonstration we show a double-track which serves as an inclined-plane. Things that can roll - when put at the top - should roll downhill. A uniform cylinder - like a rolling-pin - does roll DOWN. A double-cone, however, rolls UP! Or so it seems. This is not true - of course - although it looks so. What does happen is this: The center of gravity of the cylinder seeks a lower potential plane; the center of gravity of the cone seeks a lower potential plane. The energy of a system tends toward least. So they both in truth DO RO LL DOWN.
B - Although definitions are dangerous - since we can not always tell all the truth in one sentence - we can say - for our purpose here - that by CENTER OF GRAVITY we mean that point in a body or system where we may IMAGINE all the weight of the body to be. We use here the terms CENTER OF GRAVITY and CENTER OF MASS inter¬changeably although they are strictly different things.
C - We now show experimentally - and this is where all proof lies - using a meter stick - that the CENTER OF MASS of the stick is indeed that point where ALL THE STICK IS. And having said this there is NO stick any¬where else! A remarkable thing to discover.
D - We show also the CENTER OF GRAVITY or CENTER OF MASS of some simple geometric shapes using a plumb line. We learn in this adventure that a strange thing can occur: The e.g. or cm. of a body (or a system) can lie - can be - where there is no "stuff" - no material! Accordingly -we can say that the CENTER OF GRAVITY of a doughnut is in the middle of the hole. This too is remarkable to discover.
E - Using the IDEA OF CENTER OF GRAVITY we show some "systems" which look very unstable but which are indeed very stable because we make use of this~GREAT IDEA:
1 - THE CASE OF THE FORKS IN THE CORK STOPPER; THE CASE OF THE LITTLE MAN ON THE STAND; THE CASE OF THE MONKEY ON THE STAND:
All these configurations are stable because the CENTER OF GRAVITY of the system lies below the point of support.
2 - THE CASE OF THE LEANING TOWER OF PISA:
This configuration is stable if a plumb line from its CENTER OF GRAVITY falls within the base.
This great and wonderful idea of CENTER OF GRAVITY was first set forth by the genius ARCHIMEDES in the 3rd century B.C. in a classic treatise called De Aequiponderantibus. Students and teachers at all levels should read this in translation.
|Newton's First Law of Motion: Inertia
The MASS of a body is a measure of its inertia. The WEIGHT of a body is the FORCE with which the Earth pulls on it. MASS is - as we say -invariant - it is the same everywhere; WEIGHT varies from place to place. NEWTON'S FIRST LAW has to do with INERTIA. It says this: A body at rest wishes to remain at rest; a body in uniform motion in a straight line wishes to do this. Allthe demonstrations in this program near on these great ideas.
A - We show a block of mass M. IT wants to remain at rest "so much" . A block of mass 2M wants to remain at rest TWICE AS MUCH. So too on April Fool's Day does a package of bricks behave!
B - The HEAVY block with the dowel-rod handle stays at rest if it is at rest; it keeps on going if THAT is what it is doing.
C - We show a sequence of simple, utterly-simple, plebeian DEMONSTRA¬TIONS bearing out the strength and beauty of this "apparently" trivial FIRST LAW. But we must remember that it took the genius of a Newton to first formulate it!
1 - A mass with two strings. We break the lower one OR the upper
one utilizing Newton.
2 - A HEAVY sphere is pulled upward on a string - first gently -
slowly — then suddenly - impulsively.
3 - A brick in the hand can be struck a severe blow and the hand
4 - The mass of air on a sheet of paper has ENORMOUS INERTIA.
5 - A glass of water can be dragged along* gently on a piece of
paper but a sudden pull on the paper leaves the glass at rest. NOTE: The glass of water stays on the very edge of the table if its CENTER OF GRAVITY is NOT beyond the edge. See Program #1 on CENTER OF GRAVITY.
6 - A vehicle is at rest. It starts suddenly forward. Your head is
jerked backwards. NO! This is not right. Your head was at rest and it wishes to stay at rest! Now the vehicle is moving for¬ward. Suddenly it is brought to rest. YOU fly forward! Very dangerous!
7 - A pint of milk has greater inertia than a pint of cream. Milk Is
heavier than cream!
8 - A stack of coins stands erect - one atop another. The very bottom
one can be driven out with a sharp flat blade without troubling the others. This is a wonderful thing to do - you can even play it like a game. The STACK has great INERTIA and wishes to remain at rest.
D - A ball is whirled in a vertical circle on the end of a string. At the top of the path the ball is at this instant moving tangentially to the path -that is - in a straight line. If now we cut the string or let go of it what does the ball do? ANSWER: The ball goes off in the direction it was going - tangent to the circle. It does NOT fly out radially! Here we see the SECOND part of Newton's First Law beautifully demonstrated.
E - We show a likeness of Newton. The work of men must always be con¬nected with the men. In this way we acquire a warmer and deeper feeling for those who made these wonderful contributions to our Know¬ledge and Understanding.
|Newton's Second Law of Motion: The Elevator Problem
It is rather obvious that the greater the MASS - the greater the INERTIA of a body - the harder it is to put it into motion. That is: if a body of MASS M requires a FORCE F to give it "so much" motion - that is, so much acceleration - than a body of MASS 2M requires a FORCE 2F to give it the same motion. These truths are tied up in NEWTON'S SECOND LAW in the mathematical form F = ma. When now a body - held in the hand, say - is dropped to fall freely, the force urging it DOWNWARD is its weight. The motion it acquires - its acceleration downward - is now g. We call this the acceleration of gravity for short. Accordingly we write W = mg. Thus it is that F = ma and W = mg are analogous expressions.
A - We show two cars - a little one and a big one - masses M and 2M say. They are connected with a "spring" which pulls them together each with a force F. The mass M is urged to move faster than the mass 2M. Obviously. We thus write
Ma = F = mA
B - A mass M hangs on a scale. The scale reads the "weight" of M. If we accelerate the system upward the scale reads more. If we ac¬celerate the system downward the scale reads less. We write this F = Mg + Ma and F = Mg - Ma. A good question to ask is this: If we drop the whole thing and let it fall freely what will the scale read during the free fall? We find the answer by writing F = Mg - Ma and since a = g in this case the equation says F = Mg - Mg - which is ZERO. So the scale reads ZERO in free fall.
C - We show an array of DEMONSTRATIONS revealing Newton's Second Law:
1 - A tiny sphere falls at the same rate - with the same acceleration
as a BIG one. Although their masses are different the forces on them are different in
the same order. 'That is, if W = Mg so 2W = 2Mg.
2 - The cartoon showing two boys jumping on to a platform scale re-
veals Newton's Second Law. So cartoons often have good physics!
3 - Two men on the free ends of a rope over a pulley: If A climbs and
B just holds on B gets a FREE RIDE since whatever A does to the rope B feels.
4 - In the PARADOX OF FORCES a weight W pulls one way and another
equal weight W pulls the other way. What does the scale read? Not zero. Not 2W. It reads just W.
5 - When you ride an elevator Newton's Second Law acts in a very
clear way: Starting upward F = Mg + Ma - so your knees buckle. Or the bag in your hand feels heavier! Starting downward F = Mg - Ma - so your belly feels empty.
Thus it is that Newton's Laws of Motion play their roles in our everyday lives.
|Newton's Third Law of Motion: Momentum
The only way I can walk forward is to have the Earth to push on! We discover this when we try to walk on sheer clear smooth ice! So - too - I can jump upward only by pushing downward on the Earth. Invoking Newton's Second Law and the Third Law we are led to say that if I go up the Earth must go down! and indeed this is so. But the Earth is so massive that ITS motion is not de¬tected. You see ME go up but you do not see the Earth go down - yet it most certainly does.
We show an array of DEMONSTRATIONS bearing on this Third Law.
A - A balloon attached to a little car is blown up. When the air comes out this way the car goes the other way.
B - A rocket goes best where "there is nothing" . The STUFF coming out be¬hind DOES NOT need the atmosphere to push against.
C - In the Case of The Two Cars (See Program *3) the force which the spring exerts on both cars is the same. We see that the little car of mass m acquires a higher velocity than the big car of mass M. Thus we can write mV - Mv which is to say that the momenta of both cars are the same. (Momenta is the plural of momentum).^
D - With the "Sputnik" demonstration the gas comes out one way and the vehicle goes the other way. We find the CO2 cartridge VERY COLD after the gas comes out! The gas, experiencing free expansion, drops in temperature. We shall learn more of this in later programs. You can discover this same thing by letting the HOT air out of a HOT tire on a HOT day. As the HOT air IN the tire emerges it feels COLD!
E - The elastic steel spheres on the track demonstrate CONSERVATION of LINEAR MOMENTUM. As many "go away" after the collision as collide before.
Toys can demonstrate in a pretty way the principles of Physics.
1 - A spinning propeller goes UP only because it PUSHES the air DOWN.
2 - The air in a blown-up balloon comes out one way; the balloon goes the
3 - Hero's Engine - known as early as the 5th century B.C. - shows the idea
of Newton's Third Law.
4 - To demonstrate that I PUSH BACKWARD when I WALK FORWARD I stand on a free-wheeling cart like a skate-board. As I move forward the cart goes backward. So does the Earth!
|Energy and Momentum
It is of great importance that the ideas of ENERGY and MOMENTUM be clearly
distinguished and understood. Mathematically, momentum is M x V or MV.
Energy - more exactly kinetic energy - is 1/2 MV^. We need not worry here
where the 1/2 comes from. Momentum is the consequence of a force acting for
a time: F x t. Energy is the consequence of a force acting over a distance: ___
Thus it is with the two cars:
The force acting on both cars is the same. The force acts for the same time on both. The force acts for a greater distance on the little car and for a lesser distance on the bigger car.
Accordingly: The F x t is the same for both.
Therefore their momenta are equal. The F x S for the little car is greater than the F x s for the bigger car. Therefore their energies are UNequal.
We show an array of DEMONSTRATIONS bearing on ENERGY and MOMENTUM.
1 - On a curved track the ball can go no higher to a remote end than the height
from which it was released.
2 - We drive a nail into a block of wood. The energy delivered to the system
by the moving hammer is spent in splitting the wood and raising the temperature of the nail and the wood. Friction always produces heat.
3 - We demonstrate acoustic energy which arises from the mechanical energy
of my moving vocal cords.
4 - Thermal energy communicated to a kernel ,of corn makes it "pop" . The
expansion of the water in the corn is enormous.
5 - We rub a rod of bakelite (hard-rubber) with a piece of fur. This mechanical
work separates the electric charges and "creates" electrostatic energy.
6 - A pile-driver delivers the potential energy of the driver to the nail.
7 - A spring is compressed; potential energy is stored. This energy can push
a ball upward when the spring "recovers" .
8 - In shooting a gun we hold it tightly against the shoulder so the "kick"
9 - A child's toy stores "elastic" energy in a wound-up rubber band. This
stored energy can drive the car backwards.
10 - A geared-wheel is turned by mechanical force. The energy thus stored can heat a metal to incandescence - that is - hot enough to emit light, Thus mechanical energy produces heat and light.
We show a likeness of Christiaan Huygens, a Dutchman, who contributed to our understanding of these things.
|Concerning Falling Bodies & Projectiles
In FREE SPACE - that is, where there is no opposition to motion - as in a vacuum -ALL BODIES near the Earth fall with the same acceleration. This is a consequence of Newton's Second Law explored in Program *3 where we learned that F = ma and W = mg. In FREE FALL a body starting at rest falls 16' in the first second; 48' in the second second; 80' in the third second. These distances are in the ratio of 1:3:5. The total distance fallen is 16' in the first second; 64' in the first two seconds; 144' in the first three seconds. These distances are in the ratio of 1:4:9 which is to say - in the ratio of n:2^:3 . These interesting things were first arrived at by Galileo. When a body has motions both vertical and horizon¬tal simultaneously these motions take place independent of each other.
A - We show the Classical Guinea and Feather Tube. With the tube highly evacuated - much of the air taken out - the light feather and the heavy coin would fall side by side.
B - We show a record of a freely-falling body - electrically recorded every 1/60 of a second. The dots on the tape show the facts enumerated above but on a smaller scale.
C - When a body A is allowed to fall vertically and another B is projected horizontally a wonderful thing is observed: Both hit the ground at the same time! The path of B is a parabola.
D - When a body is projected vertically upward from a car moving horizontally another enchanting thing is observed: The car catches the ball later on in its path. At the instant the ball is projected up it has two motions: a vertical one which is acted on by gravity as a freely falling body and a horizontal motion which remains unaltered.
E - THE MONKEY AND HUNTER DEMONSTRATION is filled with Drama. With the gun bore-sighted on the Monkey the Monkey drops from his place high up at the instant the projectile emerges from the muzzle. The Monkey is hit!
F - If an array of bodies - say billiard balls - is fixed to a string in a manner following the numbers of Galileo - that is in a ratio like 1:4:9 and the string is allowed to fall vertically - the impact of the balls on the floor below occurs in equal time intervals.
We show a photograph - a likeness - of Galileo whose DIALOGUES should be read by every student. In these we find Sagredo and Salviati and Simplicio engaged in heated but friendly discussion of many of the Events of Nature -especially those we are concerned with here.
|The Simple Pendulum and Other Oscillating Things
We learn in the Physics books that the Period - the time for one complete round-trip - of a Simple Pendulum - is given by this mathematics:
T = 2piSqrt(L/g)
This means that the time of oscillation is governed by the squareroot of the length and by g - that is - where on the Earth or on the Moon - do we clock it. ANY body can oscillate as a pendulum - say a rod - and this we call a Physical Pendulum. Every Physical Pendulum has an Equivalent Simple Pendulum - that is, a simple pendulum which keeps in phase with the motion of the Physical Pendulum. A loaded spring also oscillates with a Period governed by how stiff the spring is and what the load on it is. Oscillating bodies can be coupled with other oscillating bodies - that is - connected with them.
A- We show three Simple Pendulums of lengths 10, 40, 90 cm. We clock equal numbers of oscillations. The times come out to be very interest¬ing! In the ratio of 1:2:3.
B - Since the "formula" for the period of a simple pendulum does NOT involve the mass of the bob we show several pendulums with bobs of different size and mass.
C - We show in turn - a prismatic rod; a hoop; a disk. These all execute oscillatory motion as physical pendulums., The rod has special enchant¬ing properties: It has the same period at a point 2/3 its length as it does at its very end! And this tells us why a bat stings the hand sometimes!
D - We show an array of loaded springs - alone and coupled. The period of a loaded spring is given mathematically by
T = 2piSqrt(M/k)
where M is the load on the spring and k is its modulus - that is - a number which tells us how stiff it is.
A special interesting problem arises: If a spring of length L has a modulus k - what is the modulus of half such a spring? It turns out to be 2k -which is very exciting to know.
The genius Robert Hooke - who was a contemporary of Isaac Newton - discovered the Law of the Spring. He wrote it as an anagram in this way:
And why did he write it this way? Because he was afraid Newton would steal it! The anagram reads
Ut tensio sic vis As the extension so the force.
|II. Fluid Mechanics
|Adventures with Bernoulli: Bernoulli's Principle
When a fluid - a gas or a liquid - flows in a conduit - a pipe - of uniform cross-section - the pressure in the pipe is so much and the velocity of flow is so much. If now the fluid encounters a constriction in the pipe - a narrow-ness - TWO REMARKABLE THINGS OCCUR:
The velocity is increased The pressure is diminished
These remarkable events tell us how an airplane can fly - how a bird can soar -how a chimney has a good draft - how a flag flutters and a thousand other things. We show an array of exciting DEMONSTRATIONS bearing out these matters.
A - Two heavy croquet balls hang side by side with a little gap between.
When a stream of air is blown between them they are PUSHED TOGETHER by the greater pressure on their outer sides.
B - When a stream of air is blown across the top of a "chimney" - a vertical glass tube - the reduction in pressure is felt in the chimney and the atmospheric pressure outside drives the "soot" - the puffed rice -up the chimney. This is the principle of the atomizer.
C - When a ball is lodged in a funnel and the air is driven stoutly into the
funnel the ball is NOT driven out! This appears quite illogical until we think of Bernoulli's Principle.
D - Using a large-scale atomizer tube we blow a stream of air across the top of the spout of a closed tin can. The reduction in pressure is felt in the can. The atmosphere crushes the can! Very very dramatic!
E - A ball is supported on a vertical stream of air. We say the air pushes up -the ball pushes down. Now we deliver the stream of air off the vertical. The ball does not fall down! The secret? The ball is given a spin. This gives rise to a diminution in pressure on the UPPER side of the ball where¬upon the atmosphere below holds up the ball! Wonderful!
F - This phenomenon is demonstrated with a Toy Car.
The Bernoulli Family has had no likeness in all of history. There were over 120 bearing this illustrious name - and all were uncommon men - nearly all geniuses!
In their youngest years they showed remarkable intellectual competence in every body of knowledge - .mathematics - science - languages - philosophy medicine. An incredible thing!
|Soap Bubbles and Soap Films
Soap Bubbles and Soap Films are not for child's play alone. Their study reveals some very important principles of Nature. Principal among these is this: That the Energy of a System tends toward Least. That is - the Energy of a System left to itself goes downhill. This is why raindrops are spherical; this is why a drop of water or a drop of mercury flattens out when it gets bigger. We show an array of exciting things:
A - THE DOUBLE BUBBLE PARADOX: We blow a small soap bubble and a big_ soap bubble simultaneously. Then we allow the two to be connected with each other. And a most remarkable thing happens! The SMALL one blows the BIG one bigger! We thus discover that the pressure in the smaller bubble is the greater. Which is NOT what most people think!
B - We fill a vessel very very full with water - so full in fact that it is
"humped up" high above the edge of the vessel. The surface behaves as a tight membrane - a stretched film - and is so strong in fact that we can float a steel needle on it!
C - We show some mercury droplets on a clean glass plate. When small they
are round; when bigger they flatten out. When two bubbles are brought very near to each other they coalesce - that is - they swiftly go together and become one. This action is incredibly swift and is most certainly electrical in nature.
D - We show an array of wire frames of various geometries dipped into a vat of soap solution. The soap films formed are very beautiful to see. When any one is punctured - broken - all the rest quickly take up a form such that the Energy of the System is again a minimum.
E - A circular frame has a loose string across a diameter. A soap film is formed covering the frame and the string. When the film is punctured at any spot the string instantly goes into a circular arc since a circular shape represents least Energy.
F - When a narrow small-bore tube - like a glass-tube - is dipped into water the water climbs INSIDE the tube higher than it is outside the tube. When this is done with mercury the mercury inside the tube is lower than the mercury level outside the tube. And the surface of the water is concave upward whereas the surface of the mercury is concave downward" We show this surface curvature with two wedge-shaped vessels.
Soap Films and Soap Bubbles and Drops are wonderful to play with and exciting to explore. Everyone - young and old - should read SOAP BUBBLES by C.V. Boys. Professor Boys describes hundreds of experiments which can be done at home or in school with utterly simple apparatus.
Put out your open hand - grab hold of a handful of air - there is NOTHING there! Or so it seems! But there is - there's a powerful lot of STUFF there -an enormous array of it! The ATMOSPHERE is a massive thing. The pressure of the air is about 15 pounds per square inch at sea level. On every square inch of everything there is a load of 15 pounds - very nearly. The average human being bears a load of some TWENTY TONS! The whole blanket of atmosphere which envelops the Earth weighs some 5000 million million tons! Fantastic! We show an array of enchanting DEMONSTRATIONS on THE PUSH OF THE AIR.
A - We boil water in a tin can. We drive out all the air. We now stopper up the can. The water vapor in the can condenses - that is - it goes back into the liquid state. The pressure in the can is reduced. The atmosphere squeezes the can! The PUSH of the air is terrific.
B - We do the same thing with another can but in this case we evacuate
the can - we take out SOME of the air - with a vacuum pump. Again the great push of the air squeezes the can.
C - A funnel has its open end covered with a stout rubber sheet. We take out some of the air. The atmosphere PUSHES the sheet in — the more air we take out the more it pushes in - and suddenly BANG - the sheet is burst apart by the PUSH of the air.
D - "Suction" cups! This is bad language! There is NO SUCTION! We
squeeze the "suction" cups together; we drive out the air between them. Then what? The atmosphere OUTSIDE pushes them together! And very strongly.
E - We do the classic experiment of Otto von Guericke with the Magdeburg Hemispheres. In the original demonstration in the Public Square SIXTEEN HORSES pulled the hemispheres apart. But only eight were really necessary. See why?
F - On a sheet of newspaper about 20" by 30" - that is - on an area of 600 square inches - there rests a load of atmosphere of some 9000 pounds. Fantastic! Now we wish to put this enormous load - this massive MASS - into motion by a short-lived impulsive blow. Remember the Sack of Bricks in Inertia? Newton said: "A body at rest wishes to remain at rest". And 9000 pounds - over FOUR TONS - has just too much inertia to be put into motion suddenly. So BANG! The board is broken because the great load of air does not wish to move.
When the air is quiet the PUSH of the air is something to think about. Imagine what happens when this massive air is on the move - as in a hurricane or in a tornado. Cities are destroyed!
|Centrifugal Force and Other Strange Matters
The name "centrifugal" force given to certain events is very often badly used. Consider a car going round a curve. A book lies on the seat beside you. You are the driver. You take a curve to the left - say. As you make the curve you see the book move radially out on the seat - moving toward the door. NO! This is not right! You make the curve. The car makes the curve. The book keeps on going in a straight line - tangent to the curve. It does not move radially outward. We show some DEMONSTRATIONS on these matters.
A - We whirl a ball on a string in a vertical circle. At the top of the
circular path we let go of the string. What does the ball do? Does it go radially outward? NO. It goes off in the direction it was going -tangent to the path. This is Newton's First Law again. See Program *2.
B - A device has two spheres in it - lying in a circular trough. To get each
sphere to ITS end of the trough we spin the device about a central vertical axis. The balls get to their respective slots at the ends but they do not fly radially outward.
C - IN THE PARADOX OF THE ROTATING CANDLES we spin the apparatus about a central vertical axis - as in B above - but this time a paradox arises. The candle flames lean INWARD. HINT: The density - the "heaviness" of the flames - is less than that of the air in the protecting chimneys.
D - In the classic of whirling a bucket of water in a vertical circle it is always said: " If you don't go fast enough the water will fall out" . NO. This is not right. For when the motion is too slow to make the circle the bucket will fall along with the water! OK?
E - On the forces which arise in rotation we show: (a) Why the Earth is flattened at the Poles; (b) How a "governor" works; (c) A coin on a coat-hanger; (d) A String in a Glass Tube; (e) A limp rubber loop rolls off as a rigid body; (f) A lasso; (g) Emptying a jug of water in the quickest way.
We raise an added dilemma with a toy gun which "rolls" a hoop away and then — e -coo "rolls" back! Question: How can a hoop ROLL AWAY - rolling in one direction - and roll back - still rolling? ANSWER: It can not! So - if we look circumspectly at the Physics of this we discover an enchanting thing.
The hoop was NOT rolling away - Got it?
NOTE: This business of Centrifugal Force is very troublesome for beginners -indeed for everybody. What we see happen in circular motion really depends upon where the observer is. Which brings us to the subject of Relativity.
|The Strange Behavior of Rolling Things
When we roll things down an inclined plane we discover a strange business: The mass of the rolling body does not matter. What matters is how the mass is distributed. To explore these wonderful thing we roll disks and hoops and spheres - all sizes - all masses and very enchanting discoveries are made.
A - We first roll a solid disk and a hoop. They have the same diameter -
the same mass - the same weight. How do they roll? That is - do they roll together? Does the disk win? Does the hoop win? We discover that the disk beats the hoop.
B - Now we roll an array of disks and hoops. And what do we find? We find that ALL disks roll alike. We find that ALL hoops roll alike. AND - we find that every disk beats every hoop. Little disks - big disks - fat disks - skinny disks - ALL DISKS BEAT ALL HOOPS. Now -how can I say this? One cannot roll ALL the disks and all the hoops in the whole WoTId! ANSWER: The MATHEMATICS tells us all this in a jiffy:
FR = lot and Mgh = 1/2 MV + 1/2 \(n . So you see how very much a brief sentence in mathematics can tell us.
C - We further find that ALL SPHERES ROLL ALIKE. Little spheres - big spheres - tiny spheres - ALL SPHERES - roll alike. But they must be solid uniform spheres like steel balls.
D - Now the question: Suppose we roll disks and spheres and hoops? What now? And to sum up our wonderful discoveries we say:
1 - All disks roll alike
2 - All hoops roll alike
3 - All spheres roll alike
4 - All spheres beat all disks
5 - All disks beat all hoops.
This is really wonderful to know.
E - The bodies we have rolled are very special. They are uniform in their mass distribution. So - we ask: what happens if the bodies are "loaded"? And so we roll two disks - one loaded near the center - one loaded at the edge. The centrally-loaded one wins.
F - The Yo-Yo has interesting behavior. It is a disk with an axis and the cis* rolls down a string. The string is like an inclined plane which is vertical. The mathematics above tells us how it rolls.
G - If a wheel - a disk - a ring - rolls without slipping on a roadway a good question to ask is this: What is the path marked out - traced out -described - by a point on the edge of the rolling wheel? The answer is very dramatic. The curve is called a cycloid and it is a very pretty thing to study.
If a body is submerged in a fluid - a liquid or a gas - the body is buoyed up -lifted up - by a force equal to the weight of the fluid displaced. This is the Classic Principle of Archimedes. We show an array of DEMONSTRATIONS bearing on this Principle.
A - We weigh a body on a spring scale. It weighs "so much" . We now
submerge it in a vessel of water. The scale reads less. How much less? We discover this with another demonstration.
B - We now submerge the body in a vessel so the displaced water runs out a spout. We weigh this water which ran out - which was "pushed" out by the body. And what does it weigh? It weighs EXACTLY the very loss in weight the body experienced when submerged. A wonderful thing.
C - So the water in a vessel pushes up on a body submerged in it. Proof: We push a glass into a tank of water. The glass has a hole in the bottom. The water gushes up through the hole.
D - We show a dramatic demonstration of Archimedes' Principle with THE BUCKET AND CYLINDER.
E - As we all know: some bodies sink in water; others float. When does a body float? When it displaces a weight of water equal to its own weight BEFORE it is completely submerged. Thus it is that some wood sinks - other wood floats.
F - Mercury is fantastic stuff! It is very dense. We all know that steel will sink in water. What will steel do in mercury? Answer: Steel will float in mercury.
We show some exciting things in the Life of Archimedes.
1 - A mosaic depicting his death at the hands of a Roman soldier at the
Siege of Syracuse.
2 - A monument to him showing his Burning Mirror.
3 - The classic discovery of the relationship between the volumes of a
cylinder - a sphere - a cone.
4 - A sphere circumscribed by a cylinder - which is what Archimedes wished to have put atop his tomb.
The Life and Work of Archimedes should be read by every student.
|Pascal's Principle: The Properties of Liquids
MATTER as we know it exists in three familiar "states": Solid-Liquid-Gas. Liquids have strange and wonderful properties one of these being incompressibiiity - they cannot be squeezed together very much. We show this enchanting business in a number of DEMONSTRATIONS.
A - PASCAL'S PARADOX: Three glass vessels have different shapes but the same base. We fill these to the same depth with water. And very strangely they have the same pressure on the bottom and the same force on the bottom. Pressure we define as a Force per unit area - that is
P = F/A.
B - The Hydraulic Press utilizes the dramatic property of the incompressibiiity of liquids and Pascal's Principle which says: A force communicated to a liquid is "felt" without loss in all parts of the liquid. The press is worked by a lever so this machine is a Compound Machine and it has enormous Mechanical Advantage.
C - A hypodermic needle has a very tiny point - a point of small area. If we push the piston with the thumb with a force say of ONE pound and the point has an area of ONE THOUSANDTH of a square inch we have at the point end a PRESSURE of ONE THOUSAND POUNDS PER SQUARE INCH. No wonder the needle goes in!
D - We show an array of demonstrations of a simple ordinary sort which point up the beauty of these properties of liquids:
1 - We squeeze a flask equipped with a glass tube; the liquid goes UP
and it goes DOWN. The glass is highly ELASTIC and the water is highly incompressible.
2 - The Cartesian Diver: The water is incompressible; the air IN the
Diver very compressible.
3 - A flask filled COMPLETELY with water can be broken apart by a
sharp blow on the stopper. WHY? The water is incompressible.
4 - A flask filled COMPLETELY with water can be used as a hammer
to drive nails. WHY? The water is highly incompressible.
E - A tin can is filled with water. The can has a TINY hole in the side near the bottom. With the stopper IN the water does not run out! Pull out the stopper and the water runs out! What holds the water IN? Answer: Atmospheric Pressure.
F - A U-Tube has mercury in it to a certain level. We add water to one arm. The mercury falls in that arm and rises in the other. A measure of the mercury and water columns reveals a wonderful thing: The ratio comes out to be 13.6 - which is the specific gravity of mercury.
We show a picture of Blaise Pascal - that genius of the 17th century who lived a very short life (1623-1662) but one filled with drama. He died as is said -with seven-fold immortality: as a mathematician - a physicist - an inventor -chief creator of his nation's great prose - a theologian - a philosopher - and a fanatic. His sister wrote a biography of him.
|Levers, Inclines Planes, Geared-wheels and Other Machines
All the machines in the whole world - however complicated - are made up of combinations of the so-called SIMPLE MACHINES: The lever - the wheel and axle - the pulley - the inclined plane - the wedge - the screw. These can be further reduced to TWO: The lever and the inclined plane. All about us there are abundant illustrations of these wonderful devices:
A - The ordinary fork-and-knife at dinner: The knife is a lever AND an inclined plane! Why? When held in the hand it is used as a lever; the edge is sharp - and this is an inclined plane! The tines of the fork are also sharpened which makes them inclined planes! OK?
B - The screw-driver is a lever: We grasp the handle and twist. The
lever-arm is the radius of the handle. So it is really a lever. And a bigger screw-driver provides a bigger lever-arm!
C - The screw-thread is an inclined plane: If we wrap an inclined plane around a cylinder we get a "threaded screw" .
D - Wrenches are levers and Stillson wrenches are useful in the opening of screw-1 ids on bottles.
E - The ordinary kitchen grater is an array of inclined planes. The sharpened edges make them so.
F - A railroad spike is an inclined plane. So is a pointed nail.
G - The ordinary claw-hammer is obviously a lever. We increase the
mechanical advantage by using a block under the head as we pull a nail. AND NOTE WELL: The nail gets hot when we drive it IN and when we pull it OUT.
H - The nutcracker is a lever. The broom is a -lever. Indeed - as we show -the broom can be used as a lever of two different classes.
I - Metal shears are both levers and inclined planes.
J - A metal file - and a lady's nail file - are inclined planes.
K - A meat grinder is a compound machine - it consists of a lever and a screw. And the screw is an inclined plane.
And so we find these commonplace things possessing abundant enchantment when we explore them more thoroughly.
L - PULLEYS: The mechanical advantage of a pulley system is often calculates by counting the number of ropes supporting the load. This MAY give the right answer but it is NOT a reliable method. The point I wish to make here is this: We can.sometimes get the right answer by physically wrong means! This is bad.
We conclude this series of 15 programs with some large-scale philosophy: My ambition is NOT TO TEACH PHYSICS in these lessons - NOT TO POSE EXERCISES - NOT TO GIVE A COURSE IN PHYSICS. My singular ambition is to point up the Beauty and Drama in these Things - to stir your Curiosity -to awaken your Imagination - TO SEE HOW NATURE BEHAVES. Having always a watchful eye to THINGS ALL AROUND US and INCESSANTLY ASKING QUESTIONS will give a Fullness to Life and become a Stirring Adventure.
|The Ideas of Heat and Temperature
It is absolutely essential that we UNDERSTAND these IDEAS - that the MEANING of the terms be "loud and clear" - and so we show an array of DEMONSTRATIONS to distinguish the commonplace notions of HEAT and TEMPERATURE.
A. In the very first demonstration we show a sealed glass tube containing a bit of mercury and some tiny glass chips. We heat the tube
gently. The MOTION of the STUFF increases. Some of the mercury is vaporized - since the tube was somewhat pumped down before sealing - and the mercury vapor PUSHES the glass chips into
great agitation. The higher the TEMPERATURE the greater the agitation. As the system cools down - as we say - the system gets
quieter and quieter. HEAT|SA~M0DE OF MOTION. (You will
observe that when I represent the addition of HEAT ENERGY to a
system I show a candle flame. This is a tribute to Michael Faraday
who gave six one-hour lectures on a CANDLE.) The phrase HEAT
IS A MODE OF MOTION was first advanced by one of the BERNOULLI family - that family of one hundred or more geniuses!
B. We heat an array of various spheres of stuff in a beaker of water.
After some time we agree that they are all at the SAME TEMPERATURE - being - as we say - heated through. We now place
them on a slab of paraffin and an astonishing thing is witnessed.
They sink to different levels - to different depths. That is -
they MELT different amounts of paraffin. That is - they DO
DIFFERENT AMOUNTS OF WORK. They therefore contained
DIFFERENT AMOUNTS OF HEAT ENERGY. But they were all
at the SAME TEMPERATURE. Thus we distinguish HEAT and TEMPERATURE.
C. Again - to distinguish HEAT and TEMPERATURE: We have two
ordinary potatoes - a BIG one and a SMALL one. We have baked
these - so we IMAGINE - IMAGINATION IS A VERY NECESSARY INGREDIENT of our work - and they are therefore at the
SAME TEMPERATURE. But - clearly - there is vastly MORE
HEAT ENERGY in the bigger one.
D. We have two beakers - one with a little water - one with much
water - and a thermometer tells us that they are at the SAME
TEMPERATURE. But they have DIFFERENT HEAT ENERGIES.
E. Again we have two beakers - one with a little water - one with
much water - and a thermometer tells us that the LITTLE water is
at a HIGHER TEMPERATURE. These systems could have the same
amount of HEAT ENERGY.
By the TEMPERATURE of a system we will mean this: The average kinetic energy of the elementary parts - 1/2 mv^2 - the bar over the v meaning average v. By the HEAT - or HEAT ENERGY of a system we will mean this: the SUM of all the kinetic energies of these elementary parts.
F. We have a beaker with ice cubes in it. The thermometer reads
0°C. This is the TEMPERATURE of the system. Now let us add
some thermal energy - some HEAT ENERGY - to the system -
as by heating below with a candle flame - and what do we see
happen? The TEMPERATURE remains unchanged as long as there
is any ice. We are adding HEAT ENERGY but NOT changing the
TEMPERATURE. The heat energy being added serves only to change
the STATE - not the TEMPERATURE. The heat energy of the system is getting more but the temperature is not changed.
G. We have two beakers with water: One is cold water - one is hot
water. We drop into each a bit of red dye. The diffusion takes
place at different rates - faster in the hotter system. The motion
in the hotter system is the faster.
|Thermometric Properties and Processes
We ask: By what physical properties or processes can we investigate the nature of HEAT and TEMPERATURE? What does NATURE do to demonstrate changes in temperature?
A. Expansion is a thermometric process. Evidence: a mercury-in-
glass thermo-meter — note the spelling! - shows an expanding
length of mercury column when the thermometer is immersed in
hot water - say.
B. Electrical Resistance is a thermometric property. We show a coil
of wire connected in series with an automobile lamp and a car battery. At room temperature the coil resistance is such that the lamp
lights at normal brightness. If now we put some ice - or "dry ice"
- solid CO2 - on the coil - the lamp lights brighter. On the
other hand if we heat the coil with a flame the light goes dimmer.
The mathematical expression for the behavior of a coil - of a metallic conductor - is this:
Rt = Ml +c^) where «C is called the temperature coefficient of resistance. For most metallic conductors this has the value 0.00366 - which comes out to be very nearly 1/273. This reveals that the electrons in a wire behave very much like the molecules In a gas! A very exciting thing to discover!
C. Magnetism is a thermometric property. If a bar of magnetic material
- iron - say - is held by a magnet and the bar is heated - the
magnetic forces get less. Roughly speaking this suggests the follow¬
ing: A magnetized sample of stuff implies an orderly arrangement of
the elementary parts. When heated a state of disorder arises.
D. Thermoelectric "power" is a thermometric process. If we connect
any two different wires and have their junctions at different temperatures a difference of potential arises and an electric current
ensues. We show an array of thermocouples - one whose scale is
thermometric - that is - it reads in degrees.
E. Color is a thermometric property. If we lay out on a clean fresh snow bank an array of colored sheets of paper - in the full sun -we see an astonishing thing: the paper sinks in the snow - mean¬ing of course that the snow is being melted underneath. And the different colored sheets sink at different rates.
|How to Produce Heat Energy
There are many KINDS of ENERGY: Mechanical - Acoustic - Elec¬tric - Magnetic - Electrostatic - Chemical - Electromagnetic -
Atomic - Nuclear AND HEAT ENERGY. Strangely enough -
ALL of these can be transformed - transmuted - changed - into HEAT ENERGY. Indeed - all forms of energy do end up as heat energy! Physicists therefore refer to heat energy as a "degenerate" form.
A. Acid added to water is an exothermic process. Heat is evolved.
It is interesting to explore just why this occurs!
B. A cold cup of tea can be heated up - as we say - by stirring.
Mechanical energy is transformed into energy of motion of the
C. This cold cup of tea can be heated acoustically! Energy is required
for ordinary speech. Some people spend an awful amount of energy
just talking!! It is easy to calculate how much talk would be required to heat this cup of tea: Ordinary talk generates about TOO
ergs per second. This is about one ten-millionth watt.
D. We show an array of simple things:
1. Beat - hit - a sheet of lead with a hammer. It gets hot.
2. Beat a slab of lead with a hammer and a thermocouple imbedded in the lead block would show a rise in temperature.
3. Drive a nail into a block of wood. Pull it out. It is hot.
4. Drill a hard-wood block with an electric drill. The bit gets hot - the shavings get hot.
Here we make reference to Count Rumford - Sir Benjamin Thompson - in the 18th century - who was engaged in the boring of cannon - and his observations are a legacy to our understanding of HEAT.
E. A cardboard tube has some lead-shot in it. Let us first determine
the mass of the shot - the original temperature of the shot - the
length of the tube. Now what can we do? If we invert the tube
end-over-end the shot is now at the top of the tube and under
gravitation it falls down. Work is being done on it by gravitational forces. Its potential energy suffers conversion to kinetic. The impact forces generate heat. Now let us do this operation several
hundred times. We can therefore know the total height through which the shot falls. We can measure its final temperature. We thus can learn the Mechanical Equivalent of Heat. How much work does it take to produce so much heat!
F. Electrostatic energy can produce heat. The apparatus is called an
electrophorus. We rub or slap the lucite slab with a cat's fur.
This work separates the electric charges. We now place atop the
lucite slab a metal plate held by an insulating handle. We ground
the upper face of the metal plate. Now because of Coulomb forces
work is required to lift the plate from the slab. This work or energy
now resides in the form of electrostatic energy. A spark can be
drawn from the plate. This spark represents heat energy and light
energy . We can indeed "light" a fluorescent lamp with the new energy.
Which is an amazing thing indeed! And why is this so? Not certainly because we have a perpetual-motion machine.'.' Never that!
Never! The reason is this: that work is required to lift the plate
free of the charged slab.
G. As an interesting adventure: We show hot to extract a stubborn
glass stopper from a perfume bottle. Friction produces heat!
|Thermal Expansion of Stuff: Solids
Most of the stuff in Nature expands when heated. And we have some wonderful and exciting demonstrations of this. In some cases some enchanting questions arise
A. The classical ball-and-ring demonstration: We have a metal ring
- brass - and a metal sphere - also brass. At room temperature we show that the ball does not go through the ring. So we say the ring is too small OR the ball is too big! Now we heat the ring and presto - the ball now goes through. We say the ring got bigger OR the hole got bigger! We must UNDERSTAND exactly what is going on here!
B. We now have some metal plates - round ones - square ones -
rectangular ones - and in each is a hole - a tiny tiny hole in
some. Now we heat these plates uniformly - as we could do in
an oven - and we ask: What does the tiny hole do? There are
only three cases: The hole does nothing.
The hole gets smaller.
The hole gets bigger. And I leave it as an enchanting exercise for you all to contemplate! I might give a HINT: The ring which we first used in the ball-and-ring demonstration is really a plate with a big hole! Got it now?
C. We have a metal ring - no need to say EXACTLY CIRCULAR. And
this ring has a diameter of its own stuff. We now heat this ring uniformly - as in the oven of my stove. Question: does the ring preserve its circularity or does it warp? Good question! Suggestion!
Those of you who think one thing should try to convince those who
think another! This is real intellectual inquiry.
D. A bimetallic strip consists of two metals fixed to each other along
their length. We heat the strip. Let us say one metal is iron -
the other brass. We see the strip bend. Question: does it bend
toward the iron or toward the brass.
A question for mathematical proof: If both strips are of equal thickness d the straight bimetallic strip will bend into a circle
E. We have two rods - both look like glass. One - we say - IS
glass; the other is quartz. We heat these to red-hot in a flame.
NOTE: while heating we see a color in the flame. Color is a
thermometric process. Then we immerse them both in a beaker of
COLD water. The glass shatters. The quartz does not. The quartz
has a very small temperature coefficient of expansion.
F. We introduce an interesting question: Consider one rail of the RR
track between Los Angeles and San Francisco. Let it be 400 miles
long - in one continuous strip. No breaks. Let this rail suffer an
overall change in temperature of - say 25°C. QUESTION: How
much expansion does this 400-mile rail suffer? ANSWER: Nearly
600 feet! Hard to believe but easy to prove:
G. Why does popcorn pop? A kernel of un-popped corn looks dry -
lifeless - inert - dead! But it is not dry! and it is not dead!
When we heat it the very tiny - very minute - bit of water which
is in it EXPANDS enormously - some 1700 times! The forces are
|Thermal Expansion of Stuff: Gases & Liquids
Some strange and uncommon things occur in these adventures. For example: how can a gas which is HOT feel COLD? Let's look at some of these unusual things.
A. Here is an ordinary automobile tire - inflated. We agree that
the atmosphere is hot - the ground is hot - the tire is hot -
the air in the tire is hot. Now we depress the valve stem and out
comes some HOT air. But how does it feel? IT FEELS COLD!
IT IS COLD! That is - its temperature is lower the instant it
B. There is a simpler demonstration of this strange business: The air
in my lungs is HOT. I now blow out some of this air from my
mouth. With my mouth wide open the air coming out IS HOT.
With my lips pursed as if to blow a whistle the air comes out
COLD! So - I am a strange creature: I can blow both hot and
C. Consider a CO2 fire extinguisher. We release the gas. The temperature drops so low that we get "CO2 snow".
D. We have a device which might well be called a SPUTNIK! It is
like a Hero's engine. A CO2 cartridge is lodged in a chamber -
the cartridge is pricked - the gas emerges - the Laws of Newton
play their proper role and the arm rotates. The gas comes out this—
a-way — the chamber goes that-a-way! Our interest here is this:
it is so cold that the water vapor in the room has condensed on it
and there is "frost" on the cartridge.
E. A cast-iron "bomb" is filled with water. ... filled completely with
the occluded gases first gotten rid of. We place this vessel in a
tub - a pail - of ice water. The water IN the chamber freezes.
The forces of expansion are tremendous and the "bomb" is shattered.
Dangerous to do! And we encounter this strange property of water:
that it expands when it freezes.
The forces arising in the expansion of a gas can be nicely shown with an Earth-bound Rocket. A steel pipe is tightly closed at one end. The pipe is filled with solid CO2 - "dry ice". The open end of the chamber is stoppered up. The CO2 goes into gas. The pressure increases. Out pops the stopper.
G. The Galilean Thermometer is an enchanting historical piece. A glass vessel of spherical shape has a one-hole stopper fitted to it with a glass tube. The vessel is held in a clamp upside down with the open end of the glass tube in a beaker of colored water. The air in the spherical vessel is cooled - say with ice put on it. The liquid in the lower beaker "climbs" up into the spherical chamber. If now with the column of liquid high in the tube the spherical vessel is warmed - as by placing the hand on it - the liquid is driven down. Here is an example of a higher column - a longer column - meaning a LOWER temperature! Nor must we forget the role that pressure plays in this demonstration. Galileo's thermo-meter was really a pressure-meter!
|The Strange Thermal Behavior of Ice and Water
Of all the things of Nature WATER must rank as one of the strangest. It is indeed an incredible STUFF. Its behavior is uncommon and its properties serve man in extraordinary ways.
A. We first show the changes which occur when we consider ONE gram
of ice at 0°C to which heat energy is conveyed. We note that in
CHANGE OF STATE no change in temperature takes place. The
Heat energy therefore must go into "tearing" the bonds which hold
the stuff together. We discover from this sequence of operations
that the liquid state is more "energetic" than the solid state and
the vapour (vapor) state - or gaseous - more energetic than the
B. We observe the behavior of a thermometer in a beaker of ice. As
the ice melts we might - if we did not know better! - we might
expect the thermometer to show a rise. But it does not. As long
as any vestige of ice remains the thermometer will read 0°C -
if this is the temperature of the ice to begin with. Change of state - NO change in temperature.
C. Consider a glass of ice-and-water — so called ice-water - resting on the table. Let the vessel be FULL absolutely full.
That means that some ice is ABOVE the level of the water. Now as time goes some ice melts. Question: Will the water run over — will the glass - as we say - overflow? Answer: NO. Since 1. 1 cmJ of ice = 1.0 cm of water. Most of the ice of an iceberg is below the level of the sea. Question that comes to me suddenly: Is an iceberg salty?
D. We take a huge block of ice - support it on a platform - and
put around it a wire loaded on both ends. The wire in due course
'sinks" into the ice - cuts into the ice. .The pressure of the wire melts the ice - the water which arises again freezes. This process is called regelation. We encounter this when we make a snowball by squeezing the snow in hand. The snow melts under the pressure; the water refreezes and we have an "ice ball".
E. Here is a demonstration for engagement at the DINNER TABLE.
We have ice water served to each guest. Each guest is supplied
with a tiny length of string - three inches or so. The problem
is this: Get out a hunk of ice - a cube of ice - using the string as the agent for lifting out the ice. Some try to tie the string to a cube of ice! But it is too short for this! SOLUTION: Lay the string atop a hunk of ice. Gently pour on the string some fine salt from the salt shaker. Wait a few seconds. The salt melts some of the ice immediate to the string. This ice water at once refreezes. The string is thereby fixed to the ice. Now gently pull up on the free end of the string.
F. We show an array of photographs of men who gave us abundant
knowledge of these things. It is very important to have a mind to
MEN AND EVENTS and to the national origin of these people —
Maxwell — a Scot — Joule an Englishman — Bernoulli a Swiss —
and so on.
|Heat Energy Transfer by Conduction
How do we get heat energy or thermal energy from one place to another? ANSWER: ONE of the mechanisms is CONDUCTION. In this mechanism energy only gets from here to there. That is - there is no transfer of heated stuff. Heat is applied to one end of a conductor - say - and the resulting higher agitation of the elemental parts is felt by collision along the conductor.
A. We do a classic experiment first done by Ben Franklin. A copper
rod and an iron rod are tightly joined at one end. The common
junction is placed in some hot STUFF - boiling oil - say - and
the remote ends are held in the hands. After a time we FEEL some¬
thing. And we feel it sooner - quicker - faster on the copper
rod. Copper has roughly ten times the thermal conductivity of iron.
It is also a better electrical conductor.
B. A metal rod and a wooden rod are smoothly fitted end-to-end.
Over the common junction we wrap a sheet of paper - tight.
We now hoW the system over a flame at the junction. And what
do we see? The paper is scorched where the wood is but not
where the metal is. REASON: the metal being a good conductor
takes the heat energy away before the paper has a chance to heat
up high enough to kindle.
C. We put a flame under a paper cup. The paper cup burns - as we
might expect! Now we fill another cup with water - still paper
- and we can boil the water in the paper cup without any injury
to the paper! Indeed - we can boil the water all away! MORAL: why not do all our cooking in paper pots?
D. A thermometer reads room temperature. We quickly immerse the
bulb in a vessel of HOT water. What do we see FIRST? Answer:
A DROP in the reading. And after a time the mercury column
climbs. Any why is the thermometer bulb cylindrical? To expose
greater surface for quicker response to mercury. Remember the
beautiful properties of spheres. Which is why raindrops are spher¬
ical. The energy of a system tends toward least.
E. A burning cigarette on a glass ashtray is likely to go out when the
hot end gets to the glass. Why? The glass conducts the heat away.
F. A burning cigarette on the edge of a wooden block? IT scorches
the wood. See B again.
G. A dinner table TRICK? Wedge a spoon and a fork together with a
match properly lodged and balance the whole thing on the edge of
a glass. Add to the dilemma by having another match uniquely
placed giving the idea that this second match is NECESSARY for
stability! Now we propose to light all the matches. What will
happen? Take a wager!
H. And how to bake BIG potatoes QUICK? Trivial - Watson -says Holmes: just lodge some big nails in them. The metal is a good conductor!
I. And how about a roast in the oven - a BIG one? With a bone in it the heat conduction is very rapid. And bone is a wonderful thing - very wonderful! A blood factory!
J. Is it not better to put your feet out of bed on to a deep matted rug rather than on to a bare floor? And remember: They are both at the same temperature - remember this. But the matted rug is a poor thermal conductor — which is to say - it is a good thermal insulator.
K. And when you touch the metal faucet it FEELS COLD. It is no colder than the table top!
L. A more formal demonstration can be done with a device having a metal hub - like the hub of a wheel - from which spokes emanate - and the spokes are different metals.
Thus we see in these various demonstrations how heat energy or thermal energy isCONducted from a place of higher temperature to a place of lower temperature - and there is no transfer of heated stuff.
|Heat Energy Transfer by Convection
In this mechanism of heat energy transfer there is an actual motion of heated stuff - a motion which results from differences in density and by the action of gravity. A look at the Latin origins of the words conduction and convection will make their meanings clearer. So - as I like to say - knowing Latin - and Greek - is good for knowing Physics!
A. We show two smoke stacks in a glass-walled box. Under one stack
is a lighted candle. By observing the behavior of smoke in the box
we see clearly the flow of heated stuff. Thus we see too why it is
that huge smoke stacks have such a good "draft:. And - strangely
enough - we learn that "wet" air is lighter than dry air. Which
is NOT what we might first think!
B. In a framework holding water which we color a bit with food dye
we see how great the convection forces due to change in density.
Thus in A and in B we encounter convection in FLUIDS - the
generic name for liquids and gases. We have an actual transfer
of STUFF. ~
C. A candle resides in a dish. We bring down over the burning candle a glass cylinder. In a short time the candle flame must certainly
"expire" - the flame is wanting air to breathe. Now we introduce a partition which provides TWO channels - one for the cold
air to fall down into - and another for the hot air to come up.
Remember: it is not good to say that HOT AIR RISES. Nothing
can RISE! It must be pushed up.
D. We show more of DEMONSTRATION L in LESSON 7 - with a
wheel equipped with hub and spokes. An interesting inquiry a-
rises: TWO bars are of the same stuff - iron - but one is twice the
diameter of the other. So some geometry Js necessary. Double
d - we make A four times. We make S - the surface twice as much. So although conductivity is made four times greater the heat loss due to radiation is doubled. Hence the net gain is only twice.
E. A "gag" can be done with a clean silver coin and a handkerchief.
But be careful. The fit must be tight and the coin clean or you'll
end up with a hole in the handkerchief.
F. Since the action of the mercury column in a mercury-in-glass thermometer is not too easily seen we can witness things better by fitting up a "whiskey" flask with a stopper and glass tube. And a bit of color in the water gives the matter some prettiness. Now immerse the flask in hot water. What do we see FIRST? The column FALLS!
The mechanisms of conduction and convection constitute TWO important actions for the transfer of thermal energy. For these we need some STUFF. The question arises: How can heat energy get from place to place with nothing in between?
|Heat Energy Transfer by Radiation
In conduction and in convection we need some STUFF. In this mechanism called RADIATION things go better with nothing in between! Which is a strange business.
A. We energize an incandescent lamp. Nearly INSTANTLY we FEEL
the heat energy on the arm a foot or so away — but the lamp bulb
still is unheated. The radiation passes through the glass envelope
- falls on the flesh - is absorbed - and this is commuted to
thermal energy IN THE FLESH. The mechanism is very complicated.
B. The classical RADIOMETER: Here is a device that nearly every¬
body has seen. Strangely enough - even physicists do not thoroughly understand it! Radiation falls upon the vanes. The black
faces retreat. A good inquiry to investigate is this: How would
this enchanting device work if placed between two big cakes of
ice? Try it.
C. THE CASE OF THE THREE CANS: One is shiny - one is black -
one is covered with a thin layer of asbestos. Thus we would say
that this one is insulated. We fill them equally with hot water.
They cool at different rates - obviously. And we can hardly believe it: the asbestos covered can — the insulated can - cools
off the fastest! HINT: The surface of this can is very very rough
thus exposing very much area for radiation losses!
D. THE CASE OF TWO THERMOMETERS: The bulb of one is black -
the bulb of the other is white. We place them in the Sun. What
do we see AT ONCE? Answer: The black one rises faster -
sooner — but in due course they both come to read the same. These
ideas are very important.
E. THE CASE OF THE TWO THERMOMETERS: The bulb of one is
wrapped with cotton batting LIGHTLY - LOOSELY — the bulb
of the other is wrapped with the same mass - the same weight -
the same amount - of batting - but tightly. How do they be-
have in the Sun? Answer: The tightly wrapped one climbs higher
sooner - faster - quicker — but in due course they come to the
same reading. The air lodged in the loose wrapping is a good ther¬
F. A Dewar flask - which is a thermos bottle — utilizes this mechanism. Quiet air is a good insulator — but better still - NO
air at all is a good insulator. So the thermos bottle has two glass
walls - an inner one and an outer one - and the space between
evacuated - mostly. Also: The outer wall and the inner wall are
both shiny - for good reflection.
G. An interesting problem:* THE CASE OF THE BLACK COFFEE AND
a. We pour a cup of hot coffee black.
b. We are on the verge of adding cream when the phone rings.
c. We wish to answer the phone and return to find the coffee
as hot as possible.
d. QUESTION: Do we add the cream before going to the phone
e. ANSWER: We add the cream BEFORE! See why? And do
not say that the cream holds the heat in or some such worth¬
H. We show a chart of ELECTROMAGNETIC RADIATIONS - the E-M SPECTRUM. Of the entire range we know the visible light is but a tiny part. Human vision, although a wonderful mechanism, utilizes only a small - very small - part of the whole thing. And what lies beyond we can not now say. There may be wavelengths yet undiscovered.
|Evaporation, Boiling, Freezing: A Dramatic Adventure
Some very strange things are here encountered. Indeed - some of it borders on witchcraft! But this is how NATURE behaves - in strange and wonderful ways!
A. We boil some water in a flask. We drive out all the occluded
gases and air. We stopper the flask. We take away the heat
source. The water STOPS boiling. Now we put our hands on
the flask. Mirabile dictu: the water begins to boil again —
with NO heat being added. Indeed - what we are doing is
TAKING HEAT ENERGY AWAY! The mechanism? The hands
are cold for the flask. Some of the water vapour condenses. The
pressure in the flask is reduced. The water can boil at lower pressure at a lower temperature. Strange indeed! And we can continue this operation for all of an hour. Try it - you will be enchanted.
B. If this is all true then we can do an astonishing thing. We can reduce the pressure above some water under a bell-jar. The water
can boil at lower and lower pressure and thus at lower and lower
temperature AND - mark this: it can boil at so low a temperature that it freezes! Hard to believe. This scheme of things
is known as THE TRIPPLE POINT since the water is in three phases:
liquid - solid - vapour. It is as dramatic an adventure as one
C. And here is an adventure for the dining table: Some ice resides
in a glass of ice water. We supply the guest with a short piece of
string. PROBLEM: get out some ice using the string. HOW? Lay
the string on the ice - gently - pour on some table salt. Wait
a bit. The salt melts some ice - the water which results freezes
again. The string is fixed to the ice. Strange business!
D. And all the while we are doing these wonderful things we can re¬
turn to the flask of water and BOIL IT AGAIN by laying on the
|Miscellaneous Adventures in Heat
The subject is filled with DRAMA. NATURE is wonderful to contemplate.
A. We do an old classic - boil water in a tin can - stopper it up -
and the atmosphere does its stuff! Incredible really. I suppose I
have done this very adventure ten thousand times and it never fails
to stir me. What do we do? We condense the water vapour in the
can - the pressure is reduced - the atmosphere pushes the can in.
And - if we listen carefully we can hear the water boiling in the
can. Now try to pull out the stopper; it is fixed in very firmly.
B. We lodge a silver coin in a block of dry ice - solid CO2. And a
wonderful thing ensues. The coin oscillates and sings. Why? The
heat energy in the coin "melts" some of the dry ice. Gas arises.
This pushes the coin over to one side. Conduction is better on
closer contact and gas arises on this side. Silver is a good conductor. Moreover - the pitch of the note emitted gets higher as
the coin gets colder. Watch for this. We shall see more of this in
the demonstrations on sound as well as in the next adventures on
REALLY COLD STUFF.
C. For the housewife: To cook hamburgers fast cook 'em slowly! Why?
When cooked FAST they are likely to be burned on the outside. Carbon is a good thermal insulator. So the meat is burned on the outside but not cooked on the inside! Thus PHYSICS plays an important
role in the kitchen!
D. Does peeling onions make you cry? Solution: Chill them. The vapour pressure is lowered and they do not trouble you so much. Again
E. VISCOSITY: how easily - how readily - how swiftly - do things
FLOW? We have heard the phrase: As slow as cold molasses. So
the viscosity of liquids goes DOWN with rise in temperature. Just
what the oil in the crankcase of your car does. And so when you
pour cold molasses the "glubs" are slow and sluggish. When warm
they are faster.
F. A strange thing indeed! A very carefully designed copper sphere
- hollow - has a very special volume and a very special weight.
It has some lead or copper "shot" inside it to give it EXACTLY the
weight we wish. We put this sphere in a beaker of warm water.
IT SINKS. Add ice - cool the water - the sphere comes UP. OR - start again. Put this sphere in a beaker of COLD water. It floats. As time goes by the water warms up - as we say. And now the sphere sinks. WHY IS THIS? The density of water varies with its temperature.
G. We have discovered that the viscosity of liquids goes DOWN with
rise in temperature. How about the viscosity of gasses? Or gases?
Strangely enough the viscosity of gases goes UP with rise in temperature. And we show this with an un-symmetric T-tube. When the
matter is more fully explored and we know enough mathematics we
can prove all these things by Kinetic Theory arguments or by Quantum Mechanics.
As a closing adventure we play with the silver coin on the dry ice once again. This device has its historical origins in a mechanism called THE TREVELYAN ROCKER - which you might look up.
|The Drama in Real Cold Stuff: Liquid Nitrogen
How cold can STUFF get? Theory tells us that the very lowest we can EVER hope to get is -273 C - called Absolute Zero. But who really knows? It might be lower somewhere in this Universe! For ordinary ad¬ventures we can get the following:
Ice and salt -20°C or so.
Dry Ice and alcohol -78.5°C or so.
Liquid Nitrogen -195°C.
And this is pretty cold — as we shall see.
A. A teakettle filled with liquid nitrogen boils on a cake of ice!
B. And now we proceed with a number of things - all showing how
this VERY COLD STUFF changes the properties of ordinary things:
a. We freeze a "hot dog".
b. We freeze an onion.
c. A lead spring which is : lifeless" at room temperatures becomes
VERY SPRINGY AND ELASTIC.
d. A rubber ball which bounces at room temperature becomes
frightfully brittle when made so cold.
e. A lead plate which hardly "sings" at room temperature emits a
beautiful high note when very cold. It becomes elastic.
f. A lamp lights so bright - or dim - at room temperature.
We lower the temperature of the coil connected to it. The lamp now flares up. WHY? The electrical resistance of conductors goes down with drop in temperature. . .so the electrical conductivity is higher.
Thus we see that the properties which STUFF possesses changes with the temperature. An understanding of this is very important. The pistons in your automobile engine get very hot. Space vehicles get very cold. On the Moon - with no atmosphere - as we now believe - you could stand at the very edge of light and dark and freeze one side of you and boil the other.
|The Physics of Toys: Mechanical
Toys - they say - are for children! They are for child's play. But toys embrace a vast reservoir of PHYSICS. And since ENERGY may be characterized as mechanical or acoustic or thermal or electrostatic or magnetic and so on - I choose to distinguish toys in this same fashion -by the KIND OF ENERGY they incorporate. So it is my conviction that PHYSICS can be taught to children by looking circumspectly at how the thing works. As young Maxwell put it: "What's the go of it?"
A. Pluto on a String: A dog is pulled over the table top by a string
fixed to his nose and a weight over the edge of the table. The dog
"wobbles" on his legs toward the very edge of the table top. And
we expect him to fall over the edge. But he does not. WHY? Because a horizontal pull can produce a horizontal motion and a vertical pull has no component in the horizontal. Thus we encounter
B. The Bernoulli Car: A spring-wound car has a chimney and a fan
inside. We store elastic energy in the wound-up spring. A ball
atop the chimney stays with the car as the car rolls on the table
top. AND - the ball stays aloft even with the chimney tilted
off the vertical. WHY? The answer lies in Bernoulli's Principle
- which tells us why an airplane can fly - why a bird can soar
- why a ball can be thrown in a curve - and a thousand such like matters.
C. A wound-up spring puts a propeller aloft. The blades of the propeller "grip" the air. The air is thus pushed down which is why
the mechanism goes up. And when it lights on the table top it
spins like a top.
D. A plastic gun and a pingpong ball lodged in it: We press a pingpong ball into the muzzle of a "gun". The air in the gun is compressed. We now squeeze the walls of the gun. Out pops the ball.
And we can explore range - height - angle of projection and
do the classic problem of Galileo: A target can be hit by two
routes - one as much greater than 45 as the other is smaller. All
with a toy!
E. The Monocyclist: A one-wheeled rider - a Monocyclist - is
placed atop a stretched string. He is very jjnstable. Why? First:
his center of gravity is high above his point of support. Second:
his moment of inertia is very small. . .meaning that he can readily
tip over. So what must we do? We put some long/arms into his
sides - at his shoulders - these long arms bearing heavy masses
on their remote ends - and we see at once two things: His center
of gravity is lowered below his point of support AND his moment of
inertia is increased many-fold. He can now ride gracefully back
and forth on the tight string.
F. The Jumping Dog: A plastic dog has a spring in his neck. We put
the nose of the dog in some sticky stuff - which holds his head
down. The spring SLOWLY loosens the nose from the mooring and
the impulsive force delivered to the neck lifts the dog into the air
whereupon he rotates about his center of gravity and lands on his
So we close this brief conversation on MECHANICAL TOYS by saying once again - we find here enchantment abundant and PHYSICS no end.
|The Physics of Toys: Acoustic and Thermal
This video is incomplete. Other copies exist on the internet--search for them if necessary.
A. We explored in another LESSON - on MECHANICAL TOYS -
the behavior of the TOY GUN which projects a pingpong ball.
Another question arises in this toy: When the ball is "fired" we
hear a "pop". A "poop". Where does THIS arise? Where does
the sound come from? So we see that this toy is not merely mechanical but gives rise to a question in ACOUSTICS. And the pitch of the "poop" can be altered by squeezing tightly or less so. . .suggest¬ing that it is the expanding air that emerges which gives rise to the sound. Much more can be said about this.
B. A disc - like a small saucer - has holes m rt. Another like it
is fitted to the first at their faces. We spin these on a string. We
are storing elastic twist energy in the wound-up string. On unwinding the "musical" system emits a pleasant array of sounds. . . .
the result of air rushing into and out of the holes. AND - what
do we see on the string? We see some standing waves set up. If
we examine this standing-wave mechanism closely we can relate
the wavelength on the string to the pitch of the note emitted. Beautiful thing.
C. Another musical device like that in B is made up of two hemispheres
face to face - with holes in each. The pitch emitted is different
- the rotational speed different - the mechanical properties of a disk different from the mechanical properties of a sphere.
D. An airplane on a string is swung round and round - the other end
of the string fitted to the shaft of a stick held in the hand. And we
hear strange things! The string on the shaft is grabbed and let go -
grabbed and let go - like a violin bow grabbing the string on the
fiddle and letting go — relaxation oscillations - we call this.
Thus it is that the nose of the airplane is pulled out and relaxed -
pulled out and relaxed - and since it is flexible the air around
it has pulses delivered to it.
E. Another device of like nature: A winged insect. But here the
creature has a hollow chamber. And so what can we do? We first
listen to the note emitted with the chamber open then we close the
chamber with a cork stopper. And the note is changed because
open pipes and closed pipes emit different pitches.
F. The Bird Whistle: A chamber has a sliding piston. Its length can
thereby be changed. The pitch can thus be changed. Now too we
can heat the chamber whereupon the pitch changes. Thus we see
how length of pipe and temperature affect the pitch emitted. So
in orchestras: The temperature goes up - the stringed instruments
get lower - the winds get higher. Watch for this when next you
listen to an orchestra.
G. The Xylophone: An array of metal strips is fixed to "runners". The
metal strips are fastened at unique points - nodes. The strip is
struck with a tiny hammer. Each emits a note governed by its length
- its size - its thickness - its stuff.
H. Two Frogs: A metal frog has a highly elastic flexible metal strip fixed to his body underneath. We flex the metal strip. What we hear is governed by the geometry and mechanical properties of the strip. The heavier the strip the greater the inertia and - in general
- the lower the sound emitted.
I. A spinning wheel has a low-melting point metal fixed to it. The
mechanical energy delivered by the hand turns the wheel which scrapes the metal which heats it to incandescence which gives light. So we have the conversion of several kinds of ENERGY. . . mechanical - thermal - optical.
J. A Pop Gun: A long cylindrical chamber has a stopper closing one end. We drive a piston into the cylinder. Out pops the stopper and we hear a "poop". The longer the chamber the lower the pitch.
K. We show several other ACOUSTIC TOYS thus revealing the beauty and drama in things which are essentially for child's play but in which reside really rough and troublesome PHYSICS PRINCIPLES.
|IV. Waves and Sound
|Waves: Kinds of Properties
A wave is a strange thing. Try to answer this question: What is a wave? It is not so easy to say. The best we can do for the moment is to say this: A wave is a disturbance which transmits energy. A better attack is this: let us show some waves and seeing what a wave does will tell us better what a wave is. This we call in Physics the operational point of view.
A - We have two rubber tubes - one called "empty" - the other filled with sand. I say "called empty" because it is really NOT empty. It has air in it! One end of the tube is fixed I hold the other end. Now by a slight blow with the hand I depress a bit of the tube and we see a pulse travel along the tube to the remote fixed end. This wave is a transverse wave - where the particle disturbance is at right angles to the direction of the energy propagation. If enough energy gets to the fixed and we might have a reflection. And we see the wave travel at a certain velocity. It I pull up on the tube and increase the tension the waves travels faster. With the sand-filled tube we see the wave velocity slower. It can be shown either experimentally or mathematically the velocity of a transverse wave is given by the expression V= T/m where T is the tension and m the linear density
B- We now show a different kind of wave with a spring called a SLINKY. Here we give rise to a pulse traveling along the spring in the same direction as the energy propagation. This kind of wave we call a compressional or longitudinal wave. Sound - we shall see - is a compressional wave mechanism.
C - With a piece of blackboard chalk we show a torsional wave by twisting the cylinder of chalk. Torsional waves are important - as in of a steamship shaft which delivers energy from the driving mechanism to the propeller - or in the drive-shaft of your car - where a torque is needed.
D - A dramatic showing of the propagation of a compressional wave arises in the collision of steel spheres on a track. One sphere strikes an array at rest. The compression travels with the speed of sound in steel - about 15,000 feet per second. Pretty fast !
E - Now transverse waves possess a special character: They can be polarized -just like light can be polarized. Compressional waves cannot be polarized.
F - Water waves are especially "tricky" business. They are made up of wave motions of several types but we understand these pretty well. The expression for the velocity of a water waves comes out
w _ ug x lambda 7 2 pi T
2 pi lambda x d
Which LOOKS awfully rough but really is not!
G - Conduction of sound energy requires a medium. And the more elastic the medium the greater the conduction. Thus it is that a metal rod conducts a compressional wave better than a rubber tube. And this is why a stethoscope works as it does. Look at one closely.
H - If sound is a compressional wave it needs something to compress if it is to be transmitted. Accordingly a bell in a bottle can be heard if there is stuff in the bottle - air - say — but if the air is pumped out no sound can be heard. So on the Moon - with no atmosphere - how will we hear each other?
|Sound Waves: Sources of Sound & Pitch and Frequency
To have a SOUND we must have a vibrating system. There must be a thing moving. For the energy to be felt elsewhere there must be an intermediate stuff - a medium for travel. The vibrating body has a certain mechanical frequency. The note emitted we call the pitch.
A - We have two metal bars fixed to a resonating chamber. We strike one. It emits a sound. It has a certain vibrational frequency. The note we Hear is A. The bar is vibrating at 440 vibrations per second. Thus it is that the frequency governs the pitch.
B - We strike a tuning fork. It vibrates at 256 vps. The note it emits we call Middle
C - We take in hand different metal plates. When they are flexed they vibrate at different rates. The sound they emit is governed by this.
D - I talk hard and firm against my arm. I feel the pressure changes. Thus the evidence that a sound is the advance of a compressional wave. The sound that comes forth from my mouth is governed by many things: The -frequency of my vocal cords - the amplitude of their vibration - how I hold my tongue - how I hold my lips -whether I have teeth or not!
E - We have a shaft to which is fixed an array of slotted disks. The slots number 4 - 8 - 16 - 32. If this shaft is rotated in a motor and we hold a flexible card or metal strip against the disks we get an array of musical sounds of frequencies f - 2f - 4f - 8f.
F - A disk with holes in it is rotated on a motor. A stream of air is directed through the holes. The more holes the higher the pitch. AND - where the holes are symmetrically spaced we get MUSIC -where they are unsymmetric we get NOISE. We distinguish these by saying that musical notes can be represented by simple mathematics. Noises can not be so simply described. The question is: Is boogie-woogie music? And what is Bach or Mozart? And how about Rock and Roll?
G - An ordinary stick like a yard-stick or a meter stick is held by the hand on the table top with some hanging over. We flex that part hanging over. It vibrates. We hear a sound. Thus in a very simple way we can demonstrate vibrational rates and the pitch which emerges.
H - We do a classic experiment first explored by Galileo. The finger nail is moved over the milled edge of a silver coin. A sound comes forth. We tear some cloth: some sound emerges. We file a board: some sound comes forth. We flex a deck of cards. A sound comes out. We flex some metal plates. They SOUND. But how about the lead plate? No sound! Yes there is. But the frequency is too low - the pitch too low - for the human ear to detect it. Human hearing has a range roughly from 16 vps to 16000 vps - more or less.
I - A tuning fork is a metal bar which is bent. The region near the stem is a node.
J - The Classical Knotched Stick: This is a toy of very great complexity. We impose a vibration on the edge of the prismatic rod. A propeller is driven in one direction. We impose the vibration on another edge. The propeller goes the other way. This is a demonstration of compounded harmonic motions.
And finally we ask again: what happens to the instruments in an orchestra when things get hot? Their frequencies change - their pitches must change. And a good conductor hears this and if he is of a serious mind - as most are - the musicians had better adjust for this!
|Vibrating Bars and Strings: The Phenomenon of Beats
A - We look again more circumspectly at the two bars mounted on a reson¬ating chambers. They are fixed at two very special points. When sounded each alone they sound ALIKE - IDENTICAL. But they are not! One is 440 and the other 441. Hence we hear ONE beat per second. The "beat frequency "is the difference in the natural frequencies.
B - We explore this matter with two mounted tuning forks. They ARE identical. But now we load one with a rubber band - thus in¬creasing its inertia and lowering its pitch.
We now hear beats.
C - A long steel bar is held at a certain place along its length.. .at a point quite like the point where the A-bar is fixed to its resonating chamber. We strike the bar transversely. It vibrates with two nodes.
We ask: How far along the length of the bar is a node? The answer might well appear to be 1/4 the length - that is 0.25 L. But this is not quite right. It is 0.224 L — and this is a very difficult exercise for students of Physics. Look into this some time.
E - Two tuning forks mounted on their resonating chambers are highly responsive to each other. If they are identical we can strike ONE -damp it - that is - stop it - and low and behold - the other is heard.
F - A set of tuned sticks cut to precise lengths - of hard wood - clear -grained - can give rise to the major diatonic scale if dropped in proper sequence on a hard floor.
G - We now look at vibrating strings: A magnetically-driven steel sliver has a string fixed to it. We hold the remote end of the string. With a certain length and a certain tension in the string we can show the fundamental of the string - the first overtone - the second - and so on — called by some the harmonics. What the string does is governed by its length - its tension - its linear density - that is -how fat it is.
And so we see and hear the beautiful things that sounding devices give us. Of all our human faculties and senses that of hearing is a truly remarkable one and it is a pitiful thing for those who cannot hear.
|Resonance: Forced Vibrations
If a sound of a certain frequency moves through a medium - say the air -and the pulses fall upon a member FREE to vibrate - and that member has the natural frequency of the wave coming upon it - that member will "pick up" the pulses and vibrate on its own. This is resonance.
A - Air columns have certain lengths. They therefore have certain special resonant responses. If now a sounding fork is addressed to such an air column the pipe will resonate. Clearly - closed pipes will have one responsive length - open pipes another - but these lengths can be readily calculated. We show such resonance response with card¬board tubes - one sliding within another to provide various lengths. Thus it is that organs have pipes of many lengths and different di¬ameters - and some are closed - some are open.
B - We have a monochord - ONE lone string mounted on a resonating box. We fix the string at a certain length - under a certain tension. The string is a wire so fat - so thick We now excite a tuning fork and present the stem of the fork to the bridge where the string passes over. On the string is a bit of paper so we can SEE what happens. The string is put into vibration by the fork and the amplitude is enough to bounce off the paper rider. A pretty thing to see. Now the important aspect of all this is this: That the string responds to ONE fork only.. .although it MAY respond to another of multiple frequency.
C - We excite a tuning fork. We put its stem on top of the table. The table vibrates. But what we hear sounds not like the fork. Why? Consider A played on a piano and A played on a fiddle. Do they not sound unlike? They are of the same frequency but they have different QUALITY.
D - The human vocal cavity called the mouth is a most remarkable thing. If explored for resonance with forks of different frequencies we find that - in general - female voice boxes have higher frequency response than male.
E - This business of RESONANCE has interesting historical aspects. In New England there are wooden bridges still standing from the pioneer days which have signs reading: "No trotting of horses on this bridge". And soldiers crossing a bridge break their step.
And in the Old Testament we read - Joshua 6:20 - "The priests blew their trumpets and walls fell down flat". Which is very good Physics! And so I ask: Why did the ancients not fell walls of the enemy cities by having their trumpeters blow on their trumpets?
F - Cables carrying electric current cross-country often are put into oscillation by stout winds. The cables are demonstrating resonant response to wind pulses. To minimize this action the cables are loaded at strategic points with "dampers" - which you can see if you look carefully at the high-voltage transmission lines.
And finally - the human ear responds just like this. The ear-drum takes up the oscillations which fall upon it. It goes into vibration - into oscillation. And imagine the acute response to every slight change in pitch. This energy is transmitted to the bopes of the inner ear and thence to the brain — so in the last analysis we hear with our brains.
A - We have a wind-chest - an air-tight box so equipped at the top that we can place pipes in holes so they can be blown simultaneously. We start with two identical pipes - identical length - identical diameter - and therefore identical pitch. We sound them together. They emit alike. Now the question: How can we change the pitch of a pipe? Answer: By various means. First we change its length with a sliding sleeve. Doing this gives rise to beats with the other pipe. The greater the difference in lengths the greater the beat frequency. If one pipe has a frequency f. and another a frequency f„ -the beat frequency will be f„ - f,. And now else can we change the pitch? By changing the medium with which the pipe sings. So we heat one pipe and beats again rise. The higher the temperature of the air in the pipe the higher the velocity of sound in the pipe and the higher the pitch.
B - We show the amazing performance of thermally-excited pipes. A metal pipe has a bit of metal screen lodged in it. We heat the screen. Re¬move the pipe from the heat source. And an enchanting thing is witnessed. The pipe sings! With the pipe held horizontally no convection can exist so no music can come out. As I like to say: The music cannot fall out when the pipe is horizontal! And further exploration of this sort-reveals what we expect: Longer pipes have lower pitch. AND - note well this detail: These metal pipes with wire screen sing AFTER they are removed from the heat source.
C - We now explore the enchanting behavior of CARDBOARD TUBES - the like of which rugs come rolled on. This I call intellectual fun! These pipes can sing while they are being energized! A whole array of these could provide a Bach choral! Are we not agreed that SINGING PIPES have enchantment abundant?
|Vibrating Rods and Plates
A - A metal rod is held in the finger and thumg near one end - the rod in a vertical line. With a hammer we strike one end of the rod. As the position of the holding changes the pitch emitted by the bar changes. We are exciting the bar compress!onaIly - longitudinally. What it emits is governed by many things: its stuff - its geometry -where it is held. For certain positions of "damping" the bar has enormous acoustic life and very very high Q. By the Q of a system we mean - in a general way - how much energy it returns for the energy we give it. At certain positions this bar gives rise to fantastically high-pitched emission.
B - We have an array of metal plates - of different stuff - of different shape. These are called CHLADNI PLATES. They are fixed at the center to a pin rigidly bound to the plate. We bow the plate with a violin bow. It sounds. It is vibrating. But HOW? It is too fast to see. So we sprinkle it with sand or with sugar and low and behold - a WONDROUS thing arises: The sand takes up beautiful patterns - governed by how we bow the plate - where we bow the plate and so on. The beautiful figures resulting are called CHLADNI FIGURES.
C - It is rather well known that glasses and goblets can be stroked -
excited - bu rubbin a wet finger along the edge. If now we arrange a set of these - say eight - tuned with different levels of water - a delightful music can be played. And here again we have relaxation oscillations - the finger grips the edge of the glass - I ets go - and this action is repeated.
D - So too a steel drum can be shaped with a hammer - giving different shaped segments - of different size - of different thickness. The music which these emit is indeed delightful.
E - A tuning fork - say 512 vps - one octave above middle C - is struck. You hear 512 vps. Now if this fork is moved toward a distant hearer and then away from the hearer a change in pitch is noted. This is called the Doppler Effect. It plays a role in both light and in sound since it is a consequence of more waves or less waves reaching the observer per unit time. You detect this when you hear a Police siren! I
|Miscellaneous Adventures in Sound
A - Since oscillating systems have intimate connection with the production of SOUND we show here a very pretty thing - THE BLACKBURN PENDULUM. A rigid support has two strings fixed to it which join a third to constitute a pendulum of interesting complexion. A funnel hangs as a pendulum bob. We put salt or sand or sugar in the funnel - draw the pendulum aside from its equilibrium position - and let it go. Sand pours out and the pendulum bob executes interesting gyrations. We have here compounded harmonic motions. The result is a figure of great beauty. These figures are called Lissajous Figures.
B - A glass tube has within it a metal rod. This metal rod is damped at its midpoint. In the glass tube we lay out some cork-dust. We now stroke the metal rod with a cloth bearing resin (or rosin) and an amazing thing ensues: The cork dust takes up very unique positions in the glass tube. What happens is this - briefly: The cloth with resin on it grabs the rod and lets go - grabs the rod and lets go — again our relaxation oscillation business. The compressional wave thus generated _m the rod "|umps off" the end of the rod - so to speak - travels to the far end of the glass tube -which is tightly closed with a stopper - and is reflected. This reflected wave or pulse joins hands with the incident wave to give rise to a standing wave - which we see in the configurations the cork dust takes up. And what can we do with all this? Answer: Determine the velocity of sound in the metal rod. This tube is known as Kundt's Tube.
C - An array of bar magnets hanging on strings permits the showing of a
compressional wave advancing. One magnet is pulled aside at the very end of the array and let go. It approaches its neighbor and drives it away - since the plarization is aligned this way. The pulse goes down this array - and suffers reflection from the ."open" end. It can be observed that a change in phase accompanies this reflection.
D - We explore once again the vibrations of high-voltage cables. Dampers are fixed to these cables to reduce the amplitude of oscillation. We show dampers made in the USA - in Germany - in Sweden.
E - The BULL ROARER: A slender strip of wood or masonite is fixed to a string at one end. We swing the strip in a vertical circle. A sound is produced. The strip catches up the air and pushes it to¬gether thus giving rise to a pressure pulse. The effect depends on Bernoulli's Principle - which see in an earlier Lesson in Mechanics.
We close this series on SOUND AND WAVES by showing the CHLADNI PLATES once again for here lies extraordinary beauty and drama. It is this point of view that I urge on all who study anything for then the subject becomes FUN and ENJOYABLE and the SPIRIT is lifted up.
|V. Electricity and Magnetism
|Electrostatic Phenomena: Foundations of Electricity
All stuff is electric in nature! Everything is electric! Stones - stars -all living things. For all stuff is made up of atoms - and atoms are made up of charged particles.
A - It was THALES in ancient Greece who first reported the strange behavior wherein amber when rubbed acquired the property of attracting unto itself light bits of straw and dust. THIS was the foundation of all electrical science. So we show these things with a rubber rod rubbed with fur. Cork dust is quickly ''attracted".. AND - quite as important - the dust is soon DRIVEN AWAY. It is very important to UNDERSTAND these actions. Coulomb forces are strong and ever-present.
B - We show similar effects with a pocket-comb We do work by rubbing the comb on something. Charges are separated. Electric energy is thus made available.
C - We define the charge on a rubber rod when it is rubbed with fur as NEGATIVE. The fur therefore has an equal measure of POSITIVE charge. Similarly - a glass rod rubbed with silk has on it - by definition - a POSITIVE charge. To determine the nature of an unknown charge we use an ELECTROSCOPE which we can charge by CONDUCTION or by INDUCTION. The sequence of operations in both is very important. When an electroscope is charged by CONduction the charge on the instrument is that of the charger. When an electroscope is charged by INduction the charge on it is opposite that of the inducer.
D - Pith balls hang on silk strings. They are first electrically or electrostatically NEUTRAL. We now approach them with a charged rod. They flee swiftly to the rod - touch it - hang on a moment - and soon swiftly swing away_ They first FEEL the effects of induction. Then on contact they are charged by conduction. Having now the same charge as the rod they flee from the rod and from each other.
E - And where will an electroscope be unaffected by an electric field?
Answer: in a closed metal conductor - as in a wire cage. And thus we learn what places are safe in a lightning storm.
F - To show how ENORMOUS these electrostatic forces CAN be: Place a long 2 by 4 or a heavy clean plank astride a watch-glass so it can turn freely. Stroke one end of the 2 by 4 swiftly with a cat's fur. Also charge a rubber rod with fur. Now approach the end of the log with the charged rod. It turns! The electrostatic forces are really massive. It is an interesting exercise to compare these electric forces with the gravitational forces.
Finally this must be said: Although the operations we have done in this Lesson seem trivial they are fundamental to the science of ELECTRICITY and indeed constitute the FOUNDATIONS of all electrical science.
|Electrostatic Toys, Part 1
Demonstrations in physics - physics of toys: electrostatic, magnetic, miscellaneous
|Electrostatic Toys, Part 2
Demonstrations in physics - physics of toys: electrostatic, magnetic, miscellaneous
|Adventures with Electric Charges
A - The ELECTROPHORUS: We have in this device a remarkable scheme of things. A lucite slab is rubbed or slapped with a cat's fur. This WORK separates charges. Now we put on the lucite slab a metal plate equipped with an insulating handle. We touch the upper surface of the metal plate. This grounds this face of the plate! Row we lift the metal plate away from the lucite slab. This is now quite hard to do since the Coulomb forces are very large. But doing it requires WORK again and this energy shows itself in the availability of an electric spark. With this energy we can light a fluorescent lamp! And - a wonder to say: We can continue to take energy from this system FOREVER - which is a very long time! It is not that we have a Perpetual Motion Machine - no - never that - but rather that work is required to separate the plate from the slab -and work and energy are synonymous.
B - The Smoke Precipitator: A glass tube is fitted up with electrodes. We put some smoke in the tube. We connect the electrodes to a van de Graaff generator - a device for producing a large electric spark. Instantly the smoke disappears. The reason: the smoke is made up of charged stuff in abundance. When the van de Graaff is turned on large electric field arises between the electrodes whereupon the charged stuff migrates to the charged terminals - moving under the action of the electric field.
C - A three-vaned device has pointed ends - sharply pointed. We place it atop the sphere of a van de Graaff. Charges move to the sharp points. This accumulation of charge - which becomes very dense at sharp points - gives rise to a charge migration from the sharp points to ions in the air. These ions are abundant at all times - due to cosmic radiation. In addition - some are brought about by the intense electric field in the region of the points. The reaction forces turn the spin-wheel.
D - The Mad Professor's Head: An array of slips of paper are fitted to a stand. The system is put atop a van de Graaff. The charges move to the paper strips and because all the strips now carry the SAME charge the mutual repulsive forces drive the paper slips from each other. This can be done with the hair on your head - but be careful!
E - A candle flame is placed between two electrodes - one sharp pointed-the other a sphere. With charge from a van de Graaff it can be shown that the greatest charge density arises at sharp points. It is further seen that a flame contains ions in abundance. This brings to mind the classical report of Ben Franklin to The Royal Society wherein he recommended sharp points as lightning arrestors to protect homes and barns from "that mischievous thing called lightning".
F - We show a Dissectible Leyden Jar. This is a device made up of three parts - two conductors and an insulator. We can "store" electric charge in this thing with extraordinary results. With the inner conductor in contact with the charged sphere of a van de Graaff and the outer one grounded by hand we CHARGE the Leyden Jar - which we can call a condenser or a capacitor. Now if we connect the innermost conductor with the outermost a fat sharp spark is gotten - representing enormous energy. It is usual to say that the energy resides in the insulator which we call the dielectric.
|Adventures in Magnetism
We find in Nature certain stuffs which are magnetic. Fe - Ni - Co are naturally magnetic. And magnetite - an iron ore - is magnetic. In fact -everything is magnetic to some degree - some things more - some less. The reason for this is clear: The primordial origin of magnetic forces lies in the motion of electrons. In some stuffs the magnetic domains are more abundant than in others.
A - How can we make a magnet: Answer: Hold a magnetizable bar - like an iron bar -in the Earth's magnetic meridian. Give it a proper "dip". Now strike it sharply with a hammer... at one end. The bar is - presto! magnetized! A wonderful thing really. We can check this by approaching a compass needle with one end of the bar just magnetized. If the needle is repel led the bar IS magnetized. Only repulsion proves this. Attraction does not! The reason is clear: A bar of magnetic stuff unmagnetized will attract a compass needle. See why?
B - How else can we make a magnet? Answer: Wrap a coil of wire around a magnetic stuff - like an iron rod say. Energize the coil with an electric current. The bar becomes polarized. It is a magnet. This results from the fact that a current-bearing conductor gives rise to a magnetic field. . .discovered by Oersted in 1820.
C - How else can we make a magnet? Stroke a bar of iron - say - with a chunk of magnetite or with another magnet. The polarity of the sample magnetized is governed by the pole last leaving the sample.
D - Problem: We magnetize a sample of stuff - say an iron rod. It has a certain "pole strength". That is to say: it is so strong. Now we break this bar just magnetized. The pieces each become a complete magnet with their own poles. Question: What is the pole strength of each piece? A very good question. HINT: We do work to break the original magnet. THIS energy must play some role somewhere.
E - Problem: We have two identical bars - absolutely identical - or so they look. One however is magnetized - the other is not. How can we determine which is the magnet without any accessories whatsoever? No strings to hang them on - no needles to try - nothing at hand. We are free however to handle both bars with utter freedom. HINT: The influence of a bar magnet is largely concentrated at the ends. Need we say more?
F - Question: Is stainless steel magnetic? Answer: No. And so we ask further: Why?
G - How can we protect a region or a thing from magnetic influence? That is - how can we insulate against magnetism? We explore this with numerous stuffs - Al - Zn - Cu - wood - lucite - and so on. And we find that magnetic insulation is best accomplished by surrounding the thing we wish to protect with a proper thickness of soft iron.
H - We explore the region around an arrangement of bar magnets by
sprinkling iron filings. The forms which come to light are enchanting to see.
|Ways to "Produce" Electricity
It is to be noted that the word "PRODUCE" is in quotation marks. The reason is this: We do not really produce electricity. Electric charges already exist. They are in everything. All we do is separate them. This separation requires WORK and this work produces a difference of potential.
A - We show some commonplace events: A sliver of zinc and a sliver of
copper are lodged in a lemon. Here we have TWO DIFFERENT METALS in an electrolyte. These constitute a VOLTAIC CELL.. .after Alessandro Volta.
B - Two different metals in my mouth constitute a Voltaic Cell. And some important matters here arise: If the fillings in my teeth are different metals we have a very bad electrolytic cell and the chemical action can be destructive!
C - The plates in a storage battery - as the one in your car - are ALL
LEAD (Pb). How then can we get a current out of this? A difference of potential? An emf ? A voltaic cell requires TWO different metals. ANSWER: The plates are indeed all lead but when the battery is charged the charging mechanism makes the plates different! Thus the requirement of a voltaic cell is met.
D - Two different wires - two different metals - joined at their ends - constitute a thermocouple. If now one junction is kept at one temperature and the other junction at another temperature an electric current arises. This is called a thermal EMF.
E - The so-called DRY CELL is NOT dry! The center pole is a carbon rod -and this is the positive terminal. The can containing all the stuff is zinc. This satisfies the requirements for a voltaic cell. The sticky pasty stuff inside is WET.
F - In 1831 Michael Faraday discovered that a magnetic field can produce an electric current. This followed Oersted's discovery in 1820 that a current bearing conductor gives rise to a magnetic field. So - if a magnet is moved in and out of a coil an EMF arises. MOTION of the magnet or of the coil is required. Thus we have the magneto-electric generator where a coil of wire is turned in a magnetic field and enough current is generated to light a lamp.
G - On the matter of a voltaic cell: We have two different metals in an electrolyte. The emf is governed by the nature of the metals and by the nature of the electrolyte. The SIZE of the plates or the amount of the electrolyte change nothing as far as EMF goes. A huge vat with slabs as big as barn doors and a droplet of the electrolyte with tiny metal slivers give the same EMF. However - the bigger the system the longer the life of the system - that is - the longer the energy producing life. AND the larger the current available. This is all tied up with Ohm's Law.
H - For the magneto-electric generator: it must be observed that the current produced is an alternating current - a current which surges first this way than that. This is made evident by the flicker of the lamp energized this way.
|Properties and Effects of Electric Currents
A - The Oersted Frame: In 1820 Hans Christian Oersted - a Dane -
made an observation that stirred an avalanche in physical thought. He discovered that a current-bearing conductor gives rise to a magnetic field. We show this classic experiment. Faraday - an Englishman - heard of this great adventure and made a note in his notebook: "Make magnetism produce electricity". In 1831 Faraday did just this with his famous discovery of electromagnetic induction.
B - Metals are good electrical conductors - this we know. But how about liquids and solutions? We show a solution of copper sulphate with two lead electrodes. We "drive" a current through this solution from a storage battery and soon we see a marvelous thing: One of the lead plates has some COPPER ON IT. We thus show the conductivity in an electrolyte and the deposition of copper by electrolysis. This is copper plating.
C - How about conductivity in a "hot dog"? Sure enough - we impale a "cold" dog on two spikes - connect the system to the house line -110 volts AC - and we cook the dog! The conductivity is possible because of the salt in the meat which makes it a good conductor.
D - We connect a Cu wire to a dry-cell in a circular loop and present the wire to some iron filings. The filings gather tightly at the wire. Is the wire magnetized? No. It is not magnetized but the current-bearing wire produces a magnetic field which is strongest nearby the wire.
E - If two adjacent conductors carry a current the conductors may be pushed apart or pushed together depending on the direction of the current in them. So we suggest a demonstration using a coil known as Roget's Spiral. We avoid doing this experiment because it leads to the vaporization of mercury - which is very bad to breathe!
F - The Electromagnetic Gun: A coil of wire of HEAVY wire and few turns — this makes its Ohmic resistance low - is wound on an aluminum tube. In the tube resides an iron bar. We make connection for an instant to a 6-volt battery. The coil - now carrying a current -magnetizes the bar - draws the bar IN - AND - if we now open the circuit at the right instant the bar keeps going as a projectile. As can be seen - if the circuit is not closed and opened at critical times the weapon will not work!
G - We "short" a 6-volt storage battery by putting a Cu wire across its terminals. The current drawn momentarily may be as high as several hundred amperes.The heat developed burns the wire. What really happens is this: The wire is evaporated!
So - in these adventures - we see that an electric current can produce mechanical effects - magnetic effects - heating effects - chemical effects - optical effects - and so on. And we must not lose sight of Oersted and Faraday and scores of others whose genius made it all possible.
|Adventures in Electromagnetism
A - Faraday's Toroid: An iron ring - like a donut - Faraday used the
ring of an anchor chain - has two coils of wire wound on it on opposite sides. The coils may have different turn-counts. These coils have no physical connection with each other - that is - they are not connected to each other. Now if we connect one coil to a seat of emf - a battery -say - and the other coil to a galvanometer - the second coil detects the magnetic field produced by the first one. Accordingly - in the second one we get an EMF of Induction. This is the principle of the transformer. The coil we energize we call the primary - the other is referred to as the secondary.
B - Two coils are free of each other - one sliding in the other - and we energize the one with current from a battery. The other "feels" the magnetic influence and has induced in it an emf. This emf is enhanced by closer coupling which is accomplished by having the coils closer upon each other or by providing an iron core.
C - An array of coils of different turn-count can be connected in series. The insertion of a bar magnet into a coil - one alone - or two in tandem - produces an emf. We can with this device discover that the emf is governed by the turn-count - by the polarity of the magnet -by the speed of the magnet into and out of the coil. The windings are such that some emfs add and others subtract. It is an interesting exercise to SEE what happens when certain coils are connected and then tell HOW they are wound and what their turn-count is.
D - This principle of electromagnetic induction has astonishing
consequences. If the primary coil is a few turns of heavy wire and the secondary many many turns of fine wire the induction can give rise to an emf across the secondary of many thousands of volts. A fat juicy heavy spark several inches long can be produced. And of the spark I like to ask: What is it that we SEE? What.is it that we HEAR? Why is the spark of some color - blue say or red or orange? All enchanting inquiries for enquiring minds.
|Further Adventures in Electromagnetism
A - A very "strong" horseshoe magnet - Alnico - rests upright on the table and a flexible electric lead (wire) lies innocently within the jaws of the magnet. We connect the ends of the wire to a 6-volt battery. Instantly the wire JUMPS out of the magnetic field! A very simple but pretty demonstration of the enormous forces arising in the interaction of magnetic fields. A "rule of thumb" can be given to show the relation of the F (Force) - the B (flux) -the I (current) leading to what I call the FBI RULE!
B - A dramatic array of things can be shown by a crude assortment of coils and stuff: A typewriter roller has many turns of wire wound on it. The hole in the roller is filled with soft iron wire. The coil is energized on 110 volts 60-cycle AC. The alternating current gives rise to a changing magnetic field in the region of the coil. Closed copper rings held over the coil experience enormous repelling forces. By induction they are quickly heated. Lamps can be lighted without ANY physical connections. Water can be instantly boiled in a closed copper loop. This device can be made literally out of junk but demonstrates abundantly the wondrous things arising in the study of electromagnetism.
C - We first show that an Al disk is NOT magnetic. .. at least for the magnetic forces ordinarily available to us. The disk is mounted on a central vertical pin. A strong Alnico horseshoe magnet is held by a cord over the disk - symmetrically. The cord is twisted up to store some "twist-energy" in it. As the cord untwists the disk takes up rotation! Strange business! Some say - ah ha - it is dragged along by the viscous friction of the air. No - it is not so. The moving magnet induces in the metal plate an emf. This emf gives rise to a current. This current produces its own magnetic influence. The interaction of the magnetic fields produces the rotation. This disk is known as Arago's Disk.
D - Another Al disk is mounted on a central vertical shaft. The
disk is given a spin and we note its spin-life...how long it spins. Now we bring up to the plate - the Al disk - a strong horseshoe magnet whose field envelopes the rotating plate. The rotation of the plate is nearly instantly arrested. Again we see the interaction of the field due to the permanent magnet with the field due to the current arising in the rotating plate. It is as if one hand washes the other!
E - In a playful mood we reproduce one of Faraday's delightful
experiments which he did for the children in his Royal Institution Lectures: We throw some nails at random onto a magnet resting on the lecture table. The nails are forcefully grabbed by the field and they all take up positions representing the lines of flux between the poles. Faraday used iron filings and the "tunnel" which grew in this playful action was "just right" - he said - "for a little mouse to pass through". Our beloved Faraday.
|Miscellaneous and Wondrous Things in E&M
The subject of ELECTRICITY & MAGNETISM possesses an endless abundance of enchanting things to explore and many things we do raise rather troublesome questions.
A - Here reside two 110-volt - incandescent - clear-glass - lamps.
They are identical in their physical properties. We energize them together. They look equally bright. But one of them - we say :— is energized on 110 volts AC and the other on 110 volts DC. How can we tell them apart? Answer: Approach one of them with a strong magnet. This we did. And what did we witness? The filament. oscillated in a pretty sweeping pattern. This lamp is clearly energized on 110 volts AC. The reason is obvious. Now we ask: what will the filament in the other do when that lamp is energized on 110 volts DC? Try it.
B - A solenoid is wound on a clear lucite plate. Iron filings are
sprinkled on the plate near the wire loops. They fall with abandon and no special way- We now energize the coil on a 6-volt battery and presto! The filings take up a beautiful pattern in and around the loops of the coil. The field of such a solenoid is quite like the field of a bar magnet. An interesting question arises: if we explore the field IN a solenoid mathematically we find the field strength on the axis of the coil in independent of the radius of the coil. That means that a small tiny coil and a big big coil have the same field strength along the axis - which is hard to believe. But it is true!
C - We have two lamps in series - one a 10-watt lamp - the other a 100-watt lamp. We energize the pair on 110 volts 60 cycle AC. Question: What do we see? Or - what happens? That is - do they both light up? Does only ONE light up? Or what? Maybe none lights up! We see that the small wattage lamp lights but the other does not. What must we say of this?
D - The Horn Gap or Jacob's Ladder: A pair of stiff metal conductors are fixed to a platform with their lower ends closer than their upper ends. We. connect the pair to a high voltage such as an induction coil. The spark bridges the gap at the lower end since the separation is only an inch or so. We see that the spark is making some effort to climb the ladder. It does - for a few inches. How can we have it climb all the way up to where the separation is some 10 inches or more? Answer: We need to provide for easier ionization across the greater gap. This we can accomplish by placing a candle between the conductors at the lower end. The heat of the candle creates ionization. Some say the heat of the candle "carries" the spark upward but this phrase is not correct. There is of course some thermal convection but the spark is not carried up by it.
E.- A CLASSICAL PROBLEM: A cubical frame - like the framework of a cubical box - has its edges made up of resistance wire. Let each edge of the box have a resistance R. We wish to know the total resistance between opposite vertices of the framework - that is -between the ends of the greatest diagonal. The answer is: 5/6 R. This is a classic student problem in the subject which every teacher and professor assigns some time in the subject. There are several methods of solution.
F - An aluminum slab is dropped from the hand. It falls - obviously - as a freely-falling body - with an acceleration g. We now drop it in the field of a strong Alnico magnet where the pole gap is very narrow and the field strength very high. And what do we see? It falls in a strange sluggish way as if falling in thick molasses or some such stuff. Why? As it falls it is a moving conductor in a magnetic field. So an emf is induced. This emf gives rise to a current. This current gives rise to a magnetic field. . .and so on.
So we conclude this series on Electricity and Magnetism. I hope that you have had some enchantment with the things we did and saw. All that we know comes from men and women of diverse talents and many national origins. It is appropriate that we honor them.