Question

Which of the graphs below best shows the relationship between a freely falling object’s gravitational potential energy and the object’s height from the ground?

Answer 1

The relationship between a freely falling object's gravitational potential energy (GPE) and its height from the ground can be described using the formula:

\[
\text{GPE} = mgh
\]

where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \) near the Earth's surface), and
- \( h \) is the height of the object above the ground.

From this equation, we can see that Gravitational Potential Energy is directly proportional to the height \( h \). This means that as the height increases, the gravitational potential energy also increases linearly.

Therefore, the graph that best represents this relationship would be a straight line that starts at the origin (0,0) and rises upward as height increases. The slope of this line would correspond to the product of the mass \( m \) and the acceleration due to gravity \( g \).

If you have options for graphs, look for a linear graph with an upward slope when plotting gravitational potential energy on the y-axis and height on the x-axis.