Question

when you lift twice the load twice as high, in half the time, the increase in potential energy is ______.
view available hint(s)
○ three times
○ four times
○ twice as much
○ the same
submit

Explanation:

Step1: Recall Potential Energy Formula

The formula for gravitational potential energy is $PE = mgh$, where $m$ is mass (related to load), $g$ is gravitational acceleration, and $h$ is height.

Step2: Analyze Initial and New Conditions

Let initial load be $m_1$, initial height be $h_1$. New load $m_2 = 2m_1$, new height $h_2 = 2h_1$. Time doesn't affect potential energy (PE depends on $m$, $g$, $h$).
Initial PE: $PE_1 = m_1gh_1$
New PE: $PE_2 = m_2gh_2 = (2m_1)g(2h_1) = 4m_1gh_1$

Step3: Find the Ratio

Ratio of new PE to initial PE: $\frac{PE_2}{PE_1} = \frac{4m_1gh_1}{m_1gh_1} = 4$
So the increase in potential energy is four times the initial.

Answer:

four times (corresponding to the option "four times")