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Solved: An elevator is moving upward at a constant speed
Chapter 3, Problem 84P(choose chapter or problem)
Problem 84P
An elevator is moving upward at a constant speed of 2.50 m/s. A bolt in the elevator ceiling 3.00 m above the elevator floor works loose and falls. (a) How long does it take for the bolt to fall to the elevator floor? What is the speed of the bolt just as it hits the elevator floor (b) according to an observer in the elevator? (c) According to an observer standing on one of the floor landings of the building? (d) According to the observer in part (c), what distance did the bolt travel between the ceiling and the floor of the elevator?
Questions & Answers
QUESTION:
Problem 84P
An elevator is moving upward at a constant speed of 2.50 m/s. A bolt in the elevator ceiling 3.00 m above the elevator floor works loose and falls. (a) How long does it take for the bolt to fall to the elevator floor? What is the speed of the bolt just as it hits the elevator floor (b) according to an observer in the elevator? (c) According to an observer standing on one of the floor landings of the building? (d) According to the observer in part (c), what distance did the bolt travel between the ceiling and the floor of the elevator?
ANSWER:
Solution 84P
Step 1
(a) Just after the bolts falls, the bolt will start moving with the acceleration due to gravity. Now from the elevators frame of reference the initial speed of the bolt is zero and the acceleration is
If the bolt takes s to fall, we can write that
Here, is the height of the bolt at elevator when it started falling, which is given as
Now from the above equation we can write that
Hence the bolt will take 0.78 s to fall.