Question

which equation correctly represents the gravitational potential energy of a system?
a. gpe = me - 1/2 mv²
b. gpe = 1/2 mv² - me
c. gpe = me + 1/2 mv²
d. gpe = me / (1/2 mv²)

Explanation:

Step1: Recall total - energy formula

The total mechanical energy (ME) of a system is the sum of its kinetic energy (KE) and gravitational potential energy (GPE). The formula for kinetic energy is $KE=\frac{1}{2}mv^{2}$. So, $ME = GPE+KE=GPE + \frac{1}{2}mv^{2}$.

Step2: Solve for GPE

Rearrange the formula $ME = GPE+\frac{1}{2}mv^{2}$ to isolate GPE. Subtract $\frac{1}{2}mv^{2}$ from both sides of the equation. We get $GPE=ME - \frac{1}{2}mv^{2}$.

Answer:

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