Elevator You\'re standing on a scale in an elevator. Your apparent weight refers

Question

Elevator You're standing on a scale in an elevator. Your apparent weight refers to the reading on the scale, which may change depending on how the elevator is moving. If the elevator is standing still, we call the reading on the scale you weight, so your weight and apparent weight when the elevator is standing still. a. If the elevator is moving at a constant velocity, is your apparent weight the same as your weight? If not, is it larger or smaller? Explain. b. If the elevator is accelerating upward, is your apparent weight the same as your weight? If not, is it larger or smaller? Explain. c. If the elevator is accelerating downward, is your apparent weight the same as your weight? If not, is it larger or smaller? Explain. d. Is it possible for your apparent weight to be zero? If so, explain how the elevator must be moving for this to happen. If not, explain why not. e. Let W_a be your apparent weight, and let W be your weight. Let A_y be the acceleration of the elevator relative to the Earth (we take it's motion to be along the y-direction. Determine an expression for W_a in terms of W, A_y, and g. f. Use your result from part e. to compute a rough estimate of the maximum apparent weight you feel when you ride on the PAB main elevators from the 1st floor to the 4th floor. Kudos if you try to test your estimate in the PAB elevators (there are phone apps, like "Physics Toolbox Suite" that have accelerometers that enable you to do this sort of thing quite easily!

Explanation / Answer

A). As the elevator is moving with constant velocity, it means acceleration is zero. Under this condition, apparent weight will be equal to the actual weight.

B). Now when elevator is accelerating upwards, In this case, normal force acting on us by the elevator is given by

F = mg + ma

We will feel little heavier while elevator is acceleratin in upward direction as normal force will be equal to apparent weight.

C). Now when elevator is accelerating downwards, In this case, normal force acting will be

F = mg - ma

we will feel lighter while elevator is accelerating downwards.

D). Yes, it is possible for apparent weight to become zero. However, our actual weight is always acted upon by gravity which is our true weight. Our apparent weight will be zero. This phenomena of weightlessness will occue during free fall of elevator. During free fall, we feel like as if we are flying. This happens due to absence of forces from support or elevator's floor.

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