Question

A box has a mass of 5.8kg. The box is lifted from the garage floor and placed on a shell. If the box gains 145J of energy, How high is the shell?
[Assume \[g = 10m/{s^2}\] ]
A) 2.5m
B) 1.5m
C) 3.5m
D) 14.5m

Answer 1

Hint: Here in the given question, we are asked to find the height of the shell, that means they are indirectly asking about the change in potential energy of the box. We are given the value of the gravitational constant of the earth and mass of the box.

Complete step by step answer:
As you have got the hint that we have to calculate the change in PE (Potential Energy) of the given box.
Formula for change in PE:
\[\Delta PE = mgh\]
Where:
\[m\] = mass of the body
\[g\] = gravitational constant of Earth
\[h\] = change in height of the body
Putting given values in the equation:
\[145 = 5.8 \times 10 \times h\]
\[h = \dfrac{{145}}{{5.8 \times 10}}\]
\[h = \dfrac{{145}}{{58}} = 2.5m\]
Hence, option A is correct.

Note: The gravitational potential energy of an object near Earth’s surface is due to its position in the mass-Earth system. In this question the person who lifts the box does work on the earth-box system and work done by all external forces is equal to change in mechanical energy(PE+KE) of the system, in this case change in potential energy $mgh$.