A cardboard box rests on the floor of an elevator. The box a mass m = 2.5 kg and

Question

A cardboard box rests on the floor of an elevator. The box a mass m = 2.5 kg and the elevator has an upward acceleration of a. (a) Select the correct Free Body Diagram for the system. Write an expression for the sum of the forces acting on the box in the y-direction, sigma F_y, given that up is the positive y-direction. Your answer should be in terms of F_N, m, and g. Write an expression for the normal force, F_N, that the block experiences in terms of the elevator's acceleration, the block's mass, and the acceleration of gravity. If the elevator's acceleration has a magnitude of g in the downward direction, what would the normal force, F_N1 be in Newtons? If the elevator's acceleration had a magnitude of g in the upward direction, what would the normal force F_N2 be in Newtons? F_N2 =

Explanation / Answer

b) Sum of the forces acting on the box in the y-direction

FN - m g

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c) Expression for the normal force, FN

m a = FN - m g

FN = m a + m g

FN =  m (g + a)

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d) The elevator's acceleration had a magnitude of g in the downward direction a = -g [+ g because of downward direction]

normal force FN1 = 0 N

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e) The elevator's acceleration had a magnitude of g in the upward direction a = g [+ g because of upward direction]

FN = m (g + a)

FN2 = m( g + g) = 2 m g

= 2 * 2.5 kg * 9.81

normal force FN2 = 49.05 N

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