Question

A bolt of mass $0.3$ kg falls from the ceilling of an elevator moving down with an uniform speed of $7m/s$. It hits the floor of the elevator ( length of the elevator = $3$ m) and does not rebound. What is the heat produced by impact?

• A. $8.82J$
• B. $7.72J$
• C. $6.62J$
• D. $5.52J$

Answer 1

Answer: (A)

$8.82J$

As the elevator was moving with $constant$ speed i.e. $no$ acceleration so this can be treated as an $inertial$ frame,

so on considering the event from the elevator frame will not need any $psuedo$ force to be considered.

The bolt will start from $rest$ in the elevator frame(for a person in the uniform moving elevator the incident will be like occuring at ground asif he is observing from ground. And for that person the elevator the elevator will be at rest.) so velocity gained in falling a height of $3m$ will be $v=\sqrt[2]{22\times 9.8\times 3}m/s$

so loss in kinetic energy due to coming to rest will be $\frac{m{v}^2}{2}=0.15\times 58.8=8.82Joule$

All this $loss$ will be converted to $heat$.