Question

determining change in potential energy a crane lifts a cargo box 10 m off the ground. if the crane lifts the cargo box twice as high, the potential energy will increase by ○ half. ○ the same amount. ○ two times. ○ four times.

Explanation:

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy is \( PE = mgh \), where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( h \) is the height above the reference point (ground, in this case).

Step2: Analyze the initial and final heights

Let the initial height be \( h_1 = 10 \, \text{m} \). The final height \( h_2 = 2 \times h_1 = 20 \, \text{m} \) (since it is lifted twice as high).

Step3: Calculate the initial and final potential energies

Initial potential energy: \( PE_1 = mgh_1 \)
Final potential energy: \( PE_2 = mgh_2 = mg(2h_1) = 2mgh_1 \)

Step4: Find the ratio of final to initial potential energy

\( \frac{PE_2}{PE_1} = \frac{2mgh_1}{mgh_1} = 2 \)
This means the potential energy increases by two times when the height is doubled (mass and gravity remain constant).

Answer:

two times.