SOLUTION

Conceptualize Compare the two different situations for which we have developed expressions for gravitational potential energy: $(1)$ a planet and an object that are far apart, for which the energy expression is $U(r)=-\frac{G{M}_{E}m}{r}$ and $(2)$ a small object at the surface of a planet, for which the energy expression is $U_g=mgy.$ We wish to show that the changes in potential energy calculated from these two expressions are equivalent for small displacements.

Categorize This example is problem.