Search any question & find its solution
Question:
Answered & Verified by Expert
A bolt of mass $0.3 \mathrm{~kg}$ falls from the ceiling of an elevator moving down with an uniform speed of $7 \mathrm{~m} / \mathrm{s}$. It hits the floor of the elevator (length of the elevator $=3 \mathrm{~m}$ ) and does not rebound. What is the heat produced by the impact? Would your answer be different if the elevator were stationary?
Solution:
2659 Upvotes
Verified Answer
Given : $m=0.3 \mathrm{~kg}, v=7 \mathrm{~m} / \mathrm{s}, h=3 \mathrm{~m}$
$\because \quad$ The relative velocity of the bolt w.r.t. the elevator is zero.
$\therefore \quad$ Only PE of the ball is converted into heat energy by the impact. Amount of heat produced $=$ PE lost by the ball $=\mathrm{mgh}=0.3 \times 9.8 \times 3=8.82 \mathrm{~J}$
The answer will not change if the elevator was stationary as the relative velocity of the bolt w.r.t. the elevator would still be zero.
$\because \quad$ The relative velocity of the bolt w.r.t. the elevator is zero.
$\therefore \quad$ Only PE of the ball is converted into heat energy by the impact. Amount of heat produced $=$ PE lost by the ball $=\mathrm{mgh}=0.3 \times 9.8 \times 3=8.82 \mathrm{~J}$
The answer will not change if the elevator was stationary as the relative velocity of the bolt w.r.t. the elevator would still be zero.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.