Question

look at the graphs of gravitational potential energy, height, and mass. based on these graphs, write an argument on whether height or mass has a greater effect on gravitational potential energy.

Explanation:

The gravitational - potential - energy formula is $U = mgh$, where $U$ is gravitational potential energy, $m$ is mass, $g$ is the acceleration due to gravity, and $h$ is height. If we consider a change in height $\Delta h$ and a change in mass $\Delta m$, the change in potential energy due to height is $\Delta U_h=mg\Delta h$ and due to mass is $\Delta U_m = g h\Delta m$. The effect depends on the initial values of $m$ and $h$. If the initial mass is very small compared to the initial height, a change in height will have a greater effect. Conversely, if the initial height is small compared to the initial mass, a change in mass will have a greater effect. Analyze the graphs to see how changes in height and mass affect the gravitational potential - energy graph. If the slope of the gravitational - potential - energy vs height graph is steeper than the gravitational - potential - energy vs mass graph for the given ranges of values, height has a greater effect, and vice - versa.

Answer:

The effect of height or mass on gravitational potential energy depends on the initial values of mass and height and can be determined by analyzing the slopes of the relevant graphs.