Two objects have masses of $16 M G$ $16 MG$ and $27 M G$ $27 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $25 m$ $25 m$ to $32 m$ $32 m$ ?

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Answer 1 · 2016-06-05T20:16:33

It changes of $3.78$ $3.78$ J.

The gravitational potential energy between two masses $M_{1}$ $M_1$ and $M_{2}$ $M_2$ at distance $r$ $r$ is

$U = - \frac{G M_{1} M_{2}}{r}$ $U=-(GM_1M_2)/r$ .

The difference in energy is

$\Delta U=-(GM_1M_2)/r_f+(GM_1M_2)/r_i$

$=GM_1M_2(1/r_i-1/r_f)$

Substituting the numbers and observing that the mass is expressed in units of $G$ , we have

$=16*27(1/25-1/32)=16*27*7/800$

$=189/50\approx3.78$ J

Two objects have masses of 16 MG16MG16 MG and 27 MG27MG27 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 25 m25m25 m to 32 m32m32 m?