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 $36 m$ $36 m$ to $45 m$ $45 m$ ?

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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 $36 m$ $36 m$ to $45 m$ $45 m$ ?

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Answer 1 · 2017-09-19T19:25:16

$1.03 \cdot 10^{- 23} J$ $1.03*10^-23J$

Explanation:

$m_{1} = 4 M G = 4 \cdot 10^{- 6} k g$ $m_1=4MG=4*10^-6 kg$
$m_{2} = 7 M G = 7 \cdot 10^{- 6} k g$ $m_2=7 MG=7*10^-6 kg$
$Potential Energy = - \frac{G m_{1} m_{2}}{r}$ $"Potential Energy"=-(Gm_1m_2)/r$
when $r = 36 m$ $r=36m$
Potential Energy is $U_{1} = - \frac{G m_{1} m_{2}}{36}$ $U_1=-(Gm_1m_2)/36$
when $r = 45 m$ $r=45m$
Potential Energy is $U_{2} = - \frac{G m_{1} m_{2}}{45}$ $U_2=-(Gm_1m_2)/45$

Change in Gravitational Potential Energy $= U_{2} - U_{1}$ $=U_2-U_1$
$= - \frac{G m_{1} m_{2}}{45} - (- \frac{G m_{1} m_{2}}{36})$ $=-(Gm_1m_2)/45-(-(Gm_1m_2)/36)$
$= - \frac{G m_{1} m_{2}}{45} + \frac{G m_{1} m_{2}}{36}$ $=-(Gm_1m_2)/45+(Gm_1m_2)/36$
$= G m_{1} m_{2} (\frac{1}{36} - \frac{1}{45})$ $=Gm_1m_2(1/36-1/45)$
$= 6.67 \cdot 10^{- 11} (4 \cdot 10^{- 6}) (7 \cdot 10^{- 6}) (\frac{45 - 36}{45 \cdot 36})$ $=6.67*10^-11(4*10^-6)(7*10^-6)((45-36)/(45*36))$
$= 6.67 \cdot 28 \cdot 10^{- 23} (\frac{9}{45 \cdot 36})$ $=6.67*28*10^-23((9)/(45*36))$
$= 186.76 \cdot 10^{- 23} (\frac{1}{180})$ $=186.76*10^-23((1)/(180))$
$= 1.03 \cdot 10^{- 23} J$ $=1.03*10^-23 J$

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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 $36 m$ $36 m$ to $45 m$ $45 m$ ?

1 Answer

Explanation:

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Math

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Two objects have masses of 4MG4 MG and 7MG7 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 36m36 m to 45m45 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 $36 m$ $36 m$ to $45 m$ $45 m$ ?