Newton's Second Law of Motion: The Elevator Problem
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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 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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