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#?

1 Answer
Dec 29, 2017

It is increased by 72%

Explanation:

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.