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#?

Question

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#?

William Audy · Accepted Answer

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.

William Audy · Answer

undefined 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.