a crane lifts a cargo box 10 m off the ground. if the crane lifts the cargo box twice as high, the potential…

Explanation:

Step1: Recall potential - energy formula

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

Step2: Calculate initial potential energy

Let the initial height be $h_1=10\ m$, so the initial potential energy $U_1 = mgh_1$.

Step3: Calculate final potential energy

The final height $h_2 = 2h_1=20\ m$, and the final potential energy $U_2=mgh_2 = mg(2h_1)=2mgh_1$.

Step4: Find the ratio of final to initial potential energy

$\frac{U_2}{U_1}=\frac{2mgh_1}{mgh_1}=2$.

Answer:

C. two times.