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

Answer 1

It is increased by 72%

The gravitational potential energy is

#U = -G(m_1*m_2)/r #
where G #=6.67 xx 10^-11 (Nm)/(kg^2)#is the universal gravitational constant, #m_1 and m_2# are masses, and r is the separation between# 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(m_1*m_2)/r_1 = -G( 17MG*22MG)/(55m) #
#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 : #U_2/U_1= 55/32 #
Then #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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Answer 2

The change in gravitational potential energy between two objects can be calculated using the formula: ( \Delta U = -\frac{G \times m_1 \times m_2}{r_f} + \frac{G \times m_1 \times m_2}{r_i} ), where ( G ) is the gravitational constant (approximately (6.674 \times 10^{-11}) Nm²/kg²), ( m_1 ) and ( m_2 ) are the masses of the objects, ( r_i ) is the initial distance between the objects, and ( r_f ) is the final distance between the objects.

Plug in the given values and solve for the change in gravitational potential energy.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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