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Old Oct 11th 2011, 03:21 AM   #1
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Elevator problem

Hi,

I need help in solving the following elevator problem.

An elevator moves downward in a tall building at a constant speed of 5.00 m/s. Exactly 5.00 s after the top of the elevator passes a bolt loosely attached to the wall of the elevator shaft, the bolt falls from rest. (a) At what time does the bolt hit the top of the still-descending elevator? (b) Estimate the highest floor from which the bolt can fall if the elevator reaches the ground floor before the bolt hits the top of the elevator.

Thanks and regards,
AN
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Old Oct 11th 2011, 02:22 PM   #2
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For part (a) set up two equations of motion - one for the elevator and one for the bolt - and set them equal to each other. If the initial height of bolt off the grounbd is h, and measuring time from when the bolt stars to fall:

Bolt position: y_b = h - 1/2 g t^2

Elevator position: y_e = y0 - vt, where y0 = the elevator's position when the bolt started its fall. Since that is 5 seconds after it passes the bolt, and it's moving at 5 m/s, you know that y0 = h- vt = h-25 m. So:

y_e = h - 25 m - 5m/s x t

Set y_b = y_e and solve for t (notice that the h terms cancel out).

For part (b) you need to calculate how far the bolt falls in the time you calculated in part (a).
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Old Oct 14th 2011, 06:12 AM   #3
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Hi,

Thanks for the solution. I understood now.

Thanks and regards,
AN
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