Two objects have masses of $17 M G$ $17 MG$ and $22 M G$ $22 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $55 m$ $55 m$ to $32 m$ $32 m$ ?

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Two objects have masses of $17 M G$ $17 MG$ and $22 M G$ $22 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $55 m$ $55 m$ to $32 m$ $32 m$ ?

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Answer 1 · 2017-12-29T22:12:48

It is increased by 72%

Explanation:

The gravitational potential energy is

$U = - G \frac{m_{1} \cdot m_{2}}{r}$ $U = -G(m_1*m_2)/r$

where G $= 6.67 \times 10^{- 11} \frac{N m}{k g^{2}}$ $=6.67 xx 10^-11 (Nm)/(kg^2)$ is the universal gravitational constant, $m_{1} and m_{2}$ $m_1 and m_2$ are masses, and r is the separation between $m_{1} and m_{2} .$ $m_1 and m_2.$ Any objects that attract each other have negative potential energy; otherwise, objects that repel each other has positive potential energy.

Hence, when the distance between shrinks, the gravitation energy becomes stronger (or more negative).

Let
$U_{1} = - G \frac{m_{1} \cdot m_{2}}{r_{1}} = - G \frac{17 M G \cdot 22 M G}{55 m}$ $U_1 = -G(m_1*m_2)/r_1 = -G( 17MG*22MG)/(55m)$

$U_{2} = - G \frac{m_{1} \cdot m_{2}}{r_{2}} = - G \frac{17 M G \cdot 22 M G}{32 m}$ $U_2 = -G(m_1*m_2)/r_2 = -G( 17MG*22MG)/(32m)$

You calculate the potential energies above explicitly if you wish by substituting G with the numerical value given above, and then find their difference.

Or you can compare the final to the initial potential energy to get
:
$\frac{U_{2}}{U_{1}} = \frac{55}{32}$ $U_2/U_1= 55/32$

Then
$U_{2} = \frac{55}{32} U_{1}$ $U_2 = 55/32U_1$

That is, the potential has become 1.72x stronger than before.

The change is:
$Delta U= U_2-U_1 = 55/32 U_1 - U_1 = 23/32U_1$

The percentage change is:

$(Delta U)/U_1 xx100% = 23/32 xx 100% =72%$

Thus the potential energy is 72% stronger then before.

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Two objects have masses of $17 M G$ $17 MG$ and $22 M G$ $22 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $55 m$ $55 m$ to $32 m$ $32 m$ ?

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Explanation:

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Two objects have masses of 17 MG17MG17 MG and 22 MG22MG22 MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 55 m55m55 m to 32 m32m32 m?

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Explanation:

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Two objects have masses of $17 M G$ $17 MG$ and $22 M G$ $22 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $55 m$ $55 m$ to $32 m$ $32 m$ ?