Question

two students lift identical boxes. student a lifts the box 1 meter off the ground. student b lifts the box 3 meters. which box has greater potential energy, and why?
a. student a’s box, because it requires less force.
b. student b’s box, because potential energy increases with height
c. student a’s box, because potential energy depends on mass only.
d. both boxes have equal potential energy because they are identical.

Explanation:

Step1: Recall potential - energy formula

The gravitational potential energy formula is $U = mgh$, where $m$ is mass, $g$ is the acceleration due to gravity, and $h$ is height.

Step2: Analyze the situation

The boxes are identical, so $m$ is the same for both, and $g$ is a constant near the Earth's surface. Student A lifts the box to $h_A=1$ m and Student B lifts the box to $h_B = 3$ m. Since $U = mgh$ and $m$ and $g$ are constant, and $h_B>h_A$, the potential energy of Student B's box is greater.

Answer:

B. Student B’s box, because potential energy increases with height