Two objects have masses of $42 M G$ $42 MG$ and $26 M G$ $26 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $8 m$ $8 m$ to $9 m$ $9 m$ ?

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Answer 1 · 2017-07-17T22:14:39

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

We will first calculate the potential energy at 8m

$U_{1} = - \frac{6.67 \cdot 10^{- 11} \cdot 42 \cdot 26 \cdot 10^{6}}{8} = - 0.009$ $U_1=-(6.67*10^(-11)*42*26*10^6)/8=-0.009$ Joules

$U_{2} = - \frac{6.67 \cdot 10^{- 11} \cdot 42 \cdot 26 \cdot 10^{6}}{9} = - 0.008$ $U_2=-(6.67*10^(-11)*42*26*10^6)/9=-0.008$ Joules

so $ΔU=U_2-U_1=0.001$ Joules

the change is positive because the distance gets bigger

(I assumed MG is megagrams.)

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