Two objects have masses of $4 MG$ and $8 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $150 m$ to $450 m$ ?

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Answer 1 · 2017-03-05T21:05:31

$8.45xx10^-8N$

Gravitational potential energy between two object is given by

$U = G(m_1m_2)/r^2$

where $U$ is the gravitational potential energy, $G=6.67xx10^-11$ , $m$ is the mass, and $r$ is the distance between them.

Notice it is the same equation as for gravitational force.

Put the values in the question into the equation, so the initial G.P.E is

$U = 6.67xx10^-11 xx (4xx10^3 xx 8 xx 10^3)/150^2 = 9.5xx10^-8N$

The final G.P.E after the objects have moved apart will be

$U = 6.67xx10^-11 xx (4xx10^3 xx 8xx10^3)/450^2 = 1.05xx10^-8N$

Therefore, the total change in the G.P.E is

$9.5xx10^-8 - 1.05xx10^-8 = 8.45xx10^-8N$

Two objects have masses of 4 MG4 MG and 8 MG8 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 150 m150 m to 450 m450 m?