# Two objects have masses of 9 MG and 7 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 36 m to 45 m?

May 12, 2017

Answer: $2.3345 \ast {10}^{-} 11$$\text{J}$

#### Explanation:

The formula for the gravitational potential energy between two objects is: $U = - \frac{G M m}{r}$, where $U$ is the gravitational potential energy in $\text{J}$, $G$ is the gravitational constant 6.67*10^-11"m"^3/("s"^2"kg"), $M$ is the mass of the first object in $\text{kg}$, $m$ is the mass of the second object $\text{kg}$, and $r$ is the distance between the two objects in $\text{m}$.

Note: $G \approx 6.67 \ast {10}^{-} 11$ "m"^3/("s"^2"kg")

Let ${r}_{1}$ be the initial distance between the two objects and ${r}_{2}$ be the final distance between the two objects:
Therefore, the change in gravitational potential energy can be written as:
$\Delta U = - \frac{G M m}{r} _ 2 - \left(- \frac{G M m}{r} _ 1\right) = - G M m \left(\frac{1}{r} _ 2 - \frac{1}{r} _ 1\right)$

We can substitute the given values into the equation:
$\Delta U = - \left(6.67 \ast {10}^{-} 11 \cdot 9 \cdot 7\right) \left(\frac{1}{45} - \frac{1}{36}\right)$
$= 2.3345 \ast {10}^{-} 11$$\text{J}$