Two objects have masses of $32 M G$ $32 MG$ and $23 M G$ $23 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $7 m$ $7 m$ to $32 m$ $32 m$ ?

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Answer 1 · 2018-03-20T09:49:32

The change in gravitational potential energy is $= 547.9 \cdot 10^{- 5} J$ $=547.9*10^-5J$

Gravitational potential is the potential energy per kilogram at a point in a field.

So the units are $J, Joules$ $J, "Joules"$

$Phi=-G(M_1M_2)/R$

The gravitational universal constant is

$G=6.67*10^-11Nm^2kg^-2$

The masses causing the field is $=M_1 kg$ and $=M_2 kg$

The mass is $M_1=32MG=32*10^6g=32*10^3kg$

The mass is $M_2=23MG=23*10^6g=23*10^3kg$

The distance between the centers is $=Rm$

The distance $R_1=7m$

The distance $R_2=32m$

Therefore,

$Phi_1=(-G*(32*10^3*23*10^3)/7)$

$Phi_2=(-G*(32*10^3*23*10^3)/32)$

So,

$Phi_1-Phi_2=(-G*(32*10^3*23*10^3)/7)-(-G*(32*10^3*23*10^3)/32)$

$=32*23*10^6*6.67*10^-11(1/32-1/7)$

$=-547.9*10^-5J$

Two objects have masses of 32 MG32MG32 MG and 23 MG23MG23 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 7 m7m7 m to 32 m32m32 m?