Two objects have masses of $3 M G$ $3 MG$ and $10 M G$ $10 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $130 m$ $130 m$ to $24 m$ $24 m$ ?

Question

Two objects have masses of $3 M G$ $3 MG$ and $10 M G$ $10 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $130 m$ $130 m$ to $24 m$ $24 m$ ?

1 Answer

Impact of this question

1702 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-25T17:08:12

$= - 6.79 \cdot 10^{- 23} J$ $=-6.79*10^-23J$

Explanation:

$m_{1} = 3 M G = 3 \cdot 10^{- 6} k g$ $m_1=3MG=3*10^-6 kg$
$m_{2} = 10 M G = 10 \cdot 10^{- 6} k g$ $m_2=10 MG=10*10^-6 kg$
$Gravitational Potential Energy = - \frac{G m_{1} m_{2}}{r}$ $"Gravitational Potential Energy"=-(Gm_1m_2)/r$
when $r = 130 m$ $r=130m$
Potential Energy is $U_{1} = - \frac{G m_{1} m_{2}}{130}$ $U_1=-(Gm_1m_2)/130$
when $r = 24 m$ $r=24m$
Potential Energy is $U_{2} = - \frac{G m_{1} m_{2}}{24}$ $U_2=-(Gm_1m_2)/24$

Change in Gravitational Potential Energy $= U_{2} - U_{1}$ $=U_2-U_1$
$= - \frac{G m_{1} m_{2}}{24} - (- \frac{G m_{1} m_{2}}{130})$ $=-(Gm_1m_2)/24-(-(Gm_1m_2)/130)$
$= - \frac{G m_{1} m_{2}}{24} + \frac{G m_{1} m_{2}}{130}$ $=-(Gm_1m_2)/24+(Gm_1m_2)/130$
$= G m_{1} m_{2} (\frac{1}{130} - \frac{1}{24})$ $=Gm_1m_2(1/130-1/24)$
$= 6.67 \cdot 10^{- 11} (3 \cdot 10^{- 6}) (10 \cdot 10^{- 6}) (\frac{24 - 130}{24 \cdot 130})$ $=6.67*10^-11(3*10^-6)(10*10^-6)((24-130)/(24*130))$
$= 6.67 \cdot 3 \cdot 10 \cdot 10^{- 23} (\frac{- 106}{24 \cdot 130})$ $=6.67*3*10*10^-23((-106)/(24*130))$
$= - 6.79 \cdot 10^{- 23} J$ $=-6.79*10^-23J$

Science

Math

Humanities

... and beyond

Two objects have masses of $3 M G$ $3 MG$ and $10 M G$ $10 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $130 m$ $130 m$ to $24 m$ $24 m$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Two objects have masses of 3MG3 MG and 10MG10 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 130m130 m to 24m24 m?

1 Answer

Explanation:

Related questions

Impact of this question

Two objects have masses of $3 M G$ $3 MG$ and $10 M G$ $10 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $130 m$ $130 m$ to $24 m$ $24 m$ ?