Two objects have masses of $24 M G$ $24 MG$ and $42 M G$ $42 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $54 m$ $54 m$ to $32 m$ $32 m$ ?

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Answer 1 · 2018-08-14T18:07:42

40 yN

$F_{1} = - G \frac{m_{1} m_{2}}{r_{1}^{2}} and F_{2} = - G \frac{m_{1} m_{2}}{r_{2}^{2}}$ $F_1 = -G(m_1m_2)/(r_1^2) and F_2 = -G(m_1m_2)/(r_2^2)$

Therefore,
$Delta F = F_1 - F_2 = -Gm_1m_2 * (1/r_1^2 - 1/r_2^2)$

Using the values supplied, we get
$Delta F = -(6.67 * 10^-11 Nm^2/kg^2) * (24 mg) * (42 mg) * (1/(54 m )^2 - 1/(32 m)^2) = 4 * 10^-23 N$

So the force increases by 40 yoctonewtons.

Two objects have masses of 24 MG24MG24 MG and 42 MG42MG42 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 54 m54m54 m to 32 m32m32 m?