Problem 2 - Real vs Apparent Weight. By definition, the weight W of a body on Ea

Question

Problem 2 - Real vs Apparent Weight. By definition, the weight W of a body on Earth is the magnitude of the gravitational force the Earth exerts upon it. Thus, for an object of mass m we have W = mg, where g is the local acceleration due to gravity. If the object is at rest on the ground, then the weight must be cancelled by the normal reaction N of the ground on the object. Our bodies cannot sense gravity, but we can sense this normal force. We refer to this normal force as the apparent weight.
Consider a block of mass m placed on the floor of an elevator.

-Block accelerating upwards in an elevator. the elevator is accelerating upwards with acceleration a.

I - What is the normal force acting on the block?

?II - What acceleration would be required for your apparent weight to be one and a half times your actual weight?

III - What would be the apparent weight if the cable is cut? show all work please step by step

Explanation / Answer

I) The normal force is not only counteracting the gravitational force, but also providing an acceleration upwards, so it must be equal to mg + ma = m(g + a) II) Your current weight: W = mg If you want 1.5W = 1.5mg, the gravitational acceleration must increase by a factor of 2.5 1.5g = g + 0.5g ---> you would need an upwards acceleration of 0.5g III) Since you and the elevator are now both free falling, the floor of the elevator no longer provides a normal force reaction on your feet, so your apparent weight would be 0

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