Normal Force
As a consequence of Newton's Third Law, forces come in (interaction) pairs. The weight of a body is a force acting at the center of mass of the body towards the center of the earth, it is one of the gravitational-force pair. The partner is the force acting at the center of the earth towards the center of mass of the body. Of course, the force pair are equal in magnitude but opposite in direction. The fact that is usually overlooked is that the interaction pair must act at different bodies.
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Therefore, the weight of the body (w) is not the partner of normal force (N), because simply they act at the same body. While the partner of w acts at the center of the earth, the partner of N acts on the plane. It means that the plane suffers from a force N′, the magnitude of which is equal to N, but downward. |
So, what the scale reads when you weigh your body?
The answer is N′, not w.
Experiments to prove this answer
- Use your hand on a scale
When you put your hand on the scale, it reads the "weight" of your hand. Does the reading change if you push your hand against the scale? Yes, of course. Therefore, the scale does not measure the weight, but the force acting on it, that is, N′.
- Put the scale inside an elevator
While you stand on the scale, push the elevator button to move up/down. Does the reading change at the very moment the elevator moves up/down? Yes, it reads larger number when the elevator starts moving up and reads smaller number when the elevator starts moving down.
Why? Because our body has to be accelarated to start a motion up or down. To accelarate a body we need a net force acting at the body. There are two forces acting on the body: w and N. While the magnitude of w is relatively constant, the magnitude of N does change to accomodate a net force.
When the accelaration is upward, N > w, therefore the scale reads higher number.
When the accelaration is downward, N < w, therefore the scale reads smaller number.