To show the relationship between an object's gravitational potential energy (GPE) and its height above the ground, you would typically see a graph that plots gravitational potential energy on the y-axis and height on the x-axis. The relationship is linear, meaning that as the height increases, the gravitational potential energy also increases proportionally, assuming mass and gravitational acceleration remain constant.
The equation for gravitational potential energy is given by:
\[ PE = mgh \]
Where:
- \( PE \) = gravitational potential energy (in joules)
- \( m \) = mass of the object (in kilograms)
- \( g \) = acceleration due to gravity (approximately \( 9.81 , m/s^2 \) on Earth)
- \( h \) = height above the ground (in meters)
As a result, you would expect a straight line with a positive slope starting from the origin (0,0) if the mass is constant.
If you have specific graph options to evaluate, I can help you determine which one illustrates this relationship accurately.
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