Question

which equation correctly represents the gravitational potential energy of a system?

a. ( \text{gpe} = \frac{\text{me}}{\frac{1}{2}mv^2} )

b. ( \text{gpe} = \text{me} + \frac{1}{2}mv^2 )

c. ( \text{gpe} = \text{me} - \frac{1}{2}mv^2 )

d. ( \text{gpe} = \frac{1}{2}mv^2 - \text{me} )

Explanation:

Step1: Recall Mechanical Energy Formula

Mechanical energy (ME) is the sum of gravitational potential energy (GPE) and kinetic energy (KE). The formula for kinetic energy is $KE = \frac{1}{2}mv^2$, so $ME = GPE + \frac{1}{2}mv^2$.

Step2: Rearrange for GPE

To solve for GPE, subtract $KE$ (which is $\frac{1}{2}mv^2$) from both sides of the mechanical energy equation. So, $GPE = ME - \frac{1}{2}mv^2$.

Answer:

C. $\text{GPE} = \text{ME} - \frac{1}{2}mv^2$