Julius Sumner Miller Lesson 3: 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.