Question

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 \(U = mgh\), where \(m\) is the mass of the object, \(g\) is the acceleration due to gravity, and \(h\) is the height.

Step2: Analyze the effect of doubling the height

Let the initial height be \(h_1\) and the final height be \(h_2 = 2h_1\).
The initial potential energy \(U_1=mgh_1\).
The final potential energy \(U_2 = mgh_2\).
Substitute \(h_2 = 2h_1\) into the formula for \(U_2\), we get \(U_2=mg(2h_1)=2mgh_1\).
Since \(U_1 = mgh_1\), we can see that \(U_2 = 2U_1\).

Answer:

two times.