Newton's Second Law of Motion: The Elevator Problem 
Newton's Second Law of Motion: The Elevator Problem
by Prof. Miller
Video Lecture 3 of 46
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Date Added: February 5, 2015

Lecture Description

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.

Course Index

  1. The Idea of the Center of Gravity
  2. Newton's First Law of Motion: Inertia
  3. Newton's Second Law of Motion: The Elevator Problem
  4. Newton's Third Law of Motion: Momentum
  5. Energy and Momentum
  6. Concerning Falling Bodies & Projectiles
  7. The Simple Pendulum and Other Oscillating Things
  8. Adventures with Bernoulli: Bernoulli's Principle
  9. Soap Bubbles and Soap Films
  10. Atmospheric Pressure
  11. Centrifugal Force and Other Strange Matters
  12. The Strange Behavior of Rolling Things
  13. Archimedes' Principle
  14. Pascal's Principle: The Properties of Liquids
  15. Levers, Inclines Planes, Geared-wheels and Other Machines
  16. The Ideas of Heat and Temperature
  17. Thermometric Properties and Processes
  18. How to Produce Heat Energy
  19. Thermal Expansion of Stuff: Solids
  20. Thermal Expansion of Stuff: Gases & Liquids
  21. The Strange Thermal Behavior of Ice and Water
  22. Heat Energy Transfer by Conduction
  23. Heat Energy Transfer by Convection
  24. Heat Energy Transfer by Radiation
  25. Evaporation, Boiling, Freezing: A Dramatic Adventure
  26. Miscellaneous Adventures in Heat
  27. The Drama in Real Cold Stuff: Liquid Nitrogen
  28. The Physics of Toys: Mechanical
  29. The Physics of Toys: Acoustic and Thermal
  30. Waves: Kinds of Properties
  31. Sound Waves: Sources of Sound & Pitch and Frequency
  32. Vibrating Bars and Strings: The Phenomenon of Beats
  33. Resonance: Forced Vibrations
  34. Sounding Pipes
  35. Vibrating Rods and Plates
  36. Miscellaneous Adventures in Sound
  37. Electrostatic Phenomena: Foundations of Electricity
  38. Electrostatic Toys, Part 1
  39. Electrostatic Toys, Part 2
  40. Adventures with Electric Charges
  41. Adventures in Magnetism
  42. Ways to "Produce" Electricity
  43. Properties and Effects of Electric Currents
  44. Adventures in Electromagnetism
  45. Further Adventures in Electromagnetism
  46. Miscellaneous and Wondrous Things in E&M

Course Description

Demonstrations in Physics was an educational science series produced in Australia by ABC Television in 1969. The series was hosted by American scientist Julius Sumner Miller, who demonstrated experiments involving various disciplines in the world of physics. The series was also released in the United States under the title Science Demonstrations.

This program was a series of 45 shows (approximately 15 minutes each) on various topics in physics, organized into 3 units: Mechanics; Heat and Temperature / Toys; and Waves and Sound / Electricity and Magnetism.


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