Two objects have masses of $4 M G$ $4 MG$ and $7 M G$ $7 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $320 m$ $320 m$ to $450 m$ $450 m$ ?

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Two objects have masses of $4 M G$ $4 MG$ and $7 M G$ $7 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $320 m$ $320 m$ to $450 m$ $450 m$ ?

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Answer 1 · 2016-03-15T06:42:08

Change in gravitational potential energy
$= 1.69 \times 10^{- 6} J$ $=1.69xx10^-6J$ rounded to two decimal places

Explanation:

Gravitational potential energy $P E_{g}$ $PE_g$ between two objects of masses $m_{1} and m_{2}$ $m_1 and m_2$ is given by the relation

$P E_{g} = - \frac{G m_{1} m_{2}}{r}$ $PE_g = − (Gm_1m_2)/r$ ,
where $r$ $r$ is the separation between their centres and $G$ $G$ is the universal gravitational constant ( $6.67 \times 10^{- 11} m^{3} k g^{- 1} s^{- 1}$ $6.67 xx 10^(−11) m^3 kg^-1 s^-1$ )

As the distance between their centres changes from $r_{I} = 320 m$ $r_I=320m$ to $r_{F} = 450 m$ $r_F=450m$ , the change in gravitational potential energy can be found from
$Delta PE_g=− (Gm_1m_2)/r_F-(− (Gm_1m_2)/r_I)$
$=− (Gm_1m_2)[1/r_F-1/r_I]$
Inserting the given values, mass $1Mg=10^3kg$
$=-(6.67 xx 10^(−11)xx4xx10^3xx7xx10^3)[1/450-1/320]$
or $=-(186.76 xx 10^(−5))xx(-9.02 dot7xx10^-4)$
$=1.69xx10^-6J$ rounded to two decimal places

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Two objects have masses of $4 M G$ $4 MG$ and $7 M G$ $7 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $320 m$ $320 m$ to $450 m$ $450 m$ ?

1 Answer

Explanation:

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Two objects have masses of $4 M G$ $4 MG$ and $7 M G$ $7 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $320 m$ $320 m$ to $450 m$ $450 m$ ?