Two objects have masses of $4 M G$ $4 MG$ and $48 M G$ $48 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $7 m$ $7 m$ to $2 m$ $2 m$ ?

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Two objects have masses of $4 M G$ $4 MG$ and $48 M G$ $48 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $7 m$ $7 m$ to $2 m$ $2 m$ ?

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Answer 1 · 2017-07-18T09:33:45

We will use the formula for the graviattional potential enegry
$U = - G \frac{M m}{r}$ $U=-G(Mm)/r$

Explanation:

Let's start with the $7 m$ $7m$

$U_{1} = - G \frac{M m}{r} = - \frac{6.67 \cdot 10^{- 11} \cdot 4 \cdot 48 \cdot 10^{6}}{7} = - 0.002$ $U_1=-G(Mm)/r=-(6.67*10^(-11)*4*48*10^6)/7=-0.002$ Joules

and at $2 m$ $2m$

$U_{2} = - G \frac{M m}{r} = - \frac{6.67 \cdot 10^{- 11} \cdot 4 \cdot 48 \cdot 10^{6}}{2} = - 0.006$ $U_2=-G(Mm)/r=-(6.67*10^(-11)*4*48*10^6)/2=-0.006$ Joules

so the difference is $ΔU=U_2-U_1=-0.004$ Joules

The potential energy decreases because the masses come closer.

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Two objects have masses of $4 M G$ $4 MG$ and $48 M G$ $48 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $7 m$ $7 m$ to $2 m$ $2 m$ ?

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Two objects have masses of $4 M G$ $4 MG$ and $48 M G$ $48 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $7 m$ $7 m$ to $2 m$ $2 m$ ?