Suppose the elevator starts from rest and maintains a constant upward accelerati

Question

Suppose the elevator starts from rest and maintains a constant upward acceleration of 2.90m/s2 . A bolt in the elevator ceiling 3.10m above the elevator floor works loose and falls. It falls out the instant the elevator begins to move.

A) How long does it take for the bolt to reach the floor of the elevator?

B) Just as it reaches the floor, how fast is the bolt moving according to an observer in the elevator?

C) Just as it reaches the floor, how fast is the bolt moving according to an observer standing on the floor landings of the building?

D) According to an observer in the elevator, how far has the bolt traveled between the ceiling and floor of the elevator?

E) According to an observer standing on the floor landings of the building, how far has the bolt traveled between the ceiling and floor of the elevator?

Explanation / Answer

A. drel = 3.20 m

a_rel = 2.90 + 9.81 =12.71 m/s2

so d = ut + at^2/2

3.10 = 0 + 12.71t^2/2

t =0.698 sec

b) at time t = 0.698

v_rel = arel x t = 12.71 x 0.698 = 8.88 m/s

c) v = gt = 6.85 m/s

d) drel = 3.10 m

e) d = gt^2/2 = 2.39 m

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