How could you increase the GPE of a ball without raising it higher?

change the shape of the ball
change the volume of the ball
change the mass of the ball
insult the ball by calling it a triangle

1 answer

To increase the gravitational potential energy (GPE) of a ball without raising it higher, you would need to change the mass of the ball. The GPE is calculated using the formula:

\[ \text{GPE} = mgh \]

where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( h \) is the height above a reference point. Since you're not altering the height (\( h \)), increasing the mass (\( m \)) will directly increase the GPE.

Changing the shape or volume of the ball (while keeping mass constant) would not change the GPE, and insulting the ball does not have any impact on its physical properties.