Assume that a scale is in an elevator on Earth. What force would the scale exert

Question

Assume that a scale is in an elevator on Earth. What force would the scale exert on a 53 kg person standing onit during the following situations?
a) the elevator moves up at a constant speed. b)it slows at 2.0 m/s2 while moving upward. c)It speeds up at 2.0m /s2 while moving downward. d)It moves downward at a constant speed. e)It slows to a stop while moving downward with a constantacceleration. What force would the scale exert on a 53 kg person standing onit during the following situations?
a) the elevator moves up at a constant speed. b)it slows at 2.0 m/s2 while moving upward. c)It speeds up at 2.0m /s2 while moving downward. d)It moves downward at a constant speed. e)It slows to a stop while moving downward with a constantacceleration.

Explanation / Answer

Derive a general expression for the force exerted by the scale on aperson of mass m when the elevator is moving up with anacceleration a. Draw the free-body diagram of the man ; mg acts downwards Normal reaction R acts upwards If the net acceleration of the man is 'a' upwards (with theelevator). R - mg = ma or R = m(g + a) .....................(1) If the net acceleration of the man is 'a' downwards (with theelevator). mg - R = ma or R = m(g - a) .....................(2) Now, in the problem, m = 53 and g = 9.8 A. Constant speed means zero acceleration. Substitute in anyequation to get R = mg B. Acceleration is 2.9 m/s^2 downwards. Use equation (2) C. a = 2 m/s^2 downwards. Use equation 2 D. a = 0. Same as A. R = mg E. a is upwards. Use equation 1. R = m(g + a) > mg

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