Two objects have masses of $6 M G$ $6 MG$ and $9 M G$ $9 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $320 m$ $320 m$ to $100 m$ $100 m$ ?

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Two objects have masses of $6 M G$ $6 MG$ and $9 M G$ $9 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $320 m$ $320 m$ to $100 m$ $100 m$ ?

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Answer 1 · 2017-08-03T11:31:57

$E_{P} = 1.72 \times 10^{- 5} J$ $E_("P") = 1.72 times 10^(- 5) " J"$

Explanation:

We need to use the formula $E_{P} = - \frac{G M m}{r}$ $E_("P") = - frac(G M m)(r)$ ; where $E_{P}$ $E_("P")$ is the gravitational potential energy, $G$ $G$ is the gravitational constant, $M$ $M$ and $m$ $m$ are the masses of the two objects, and $r$ $r$ is the distance between their centres.

Let's calculate the gravitational potential energy for our case.

$r$ $r$ will be the difference between the two distances:

$\Rightarrow E_{P} = - \frac{6.67408 \times 10^{- 11} m^{3} {kg}^{- 1} s^{- 2} \times 6 MG \times 9 MG}{110 m - 320 m}$ $Rightarrow E_("P") = - frac(6.67408 times 10^(-11) " m"^(3) " kg"^(- 1) " s"^(- 2) times 6 " MG" times 9 " MG")(110 " m" - 320 " m")$

$\Rightarrow E_{P} = - \frac{6.67408 \times 10^{- 11} m^{3} {kg}^{- 1} s^{- 2} \times 6000 kg \times 9000 kg}{- 210 m}$ $Rightarrow E_("P") = - frac(6.67408 times 10^(-11) " m"^(3) " kg"^(- 1) " s"^(- 2) times 6000 " kg" times 9000 " kg")(- 210 " m")$

$\Rightarrow E_{P} = \frac{6.67408 \times 10^{- 11} m^{2} {kg}^{- 1} s^{- 2} \times 5.4 \times 10^{7} {kg}^{2}}{210}$ $Rightarrow E_("P") = frac(6.67408 times 10^(-11) " m"^(2) " kg"^(- 1) " s"^(- 2) times 5.4 times 10^(7) " kg"^(2))(210)$

$\Rightarrow E_{P} = \frac{0.0036040032 {kg m}^{2} s^{- 2}}{210}$ $Rightarrow E_("P") = frac(0.0036040032 " kg m"^(2) " s"^(- 2))(210)$

$\Rightarrow E_{P} = 0.00001716192 {kg m}^{2} s^{- 2}$ $Rightarrow E_("P") = 0.00001716192 " kg m"^(2) " s"^(- 2)$

$\Rightarrow E_{P} = 1.72 \times 10^{- 5} {kg m}^{2} s^{- 2}$ $Rightarrow E_("P") = 1.72 times 10^(- 5) " kg m"^(2) " s"^(- 2)$

$therefore E_("P") = 1.72 times 10^(- 5) " J"$

Therefore, the gravitational potential energy between the two objects is $1.72 times 10^(- 5) " J"$ .

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Two objects have masses of $6 M G$ $6 MG$ and $9 M G$ $9 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $320 m$ $320 m$ to $100 m$ $100 m$ ?

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Explanation:

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Explanation:

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Two objects have masses of $6 M G$ $6 MG$ and $9 M G$ $9 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $320 m$ $320 m$ to $100 m$ $100 m$ ?