Two objects have masses of #4 MG# and #7 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #36 m# to #45 m#?

Question

Two objects have masses of #4 MG# and #7  MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #36    m# to #45 m#?

Lily Adams · Accepted Answer

#1.03*10^-23J# #m_1=4MG=4*10^-6 kg# #m_2=7 MG=7*10^-6 kg# #"Potential Energy"=-(Gm_1m_2)/r# when #r=36m# Potential Energy is #U_1=-(Gm_1m_2)/36# when #r=45m# Potential Energy is #U_2=-(Gm_1m_2)/45# Change in Gravitational Potential Energy #=U_2-U_1# #=-(Gm_1m_2)/45-(-(Gm_1m_2)/36)# #=-(Gm_1m_2)/45+(Gm_1m_2)/36# #=Gm_1m_2(1/36-1/45)# #=6.67*10^-11(4*10^-6)(7*10^-6)((45-36)/(45*36))# #=6.67*28*10^-23((9)/(45*36))# #=186.76*10^-23((1)/(180))# #=1.03*10^-23 J#

Adrian Ayala · Answer

undefined The change in gravitational potential energy between the two objects can be calculated using the formula:

ΔPE = G * (m1 * m2) * (1/r1 - 1/r2)

Where:
ΔPE is the change in gravitational potential energy,
G is the gravitational constant (6.674 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects (in this case, 4 MG and 7 MG),
r1 and r2 are the initial and final distances between the objects (36 m and 45 m).

Substituting the given values into the formula:

ΔPE = (6.674 × 10^-11) * (4 * 10^6) * (7 * 10^6) * (1/36 - 1/45)

Calculating the values:

ΔPE = (6.674 × 10^-11) * (4 * 10^6) * (7 * 10^6) * (0.02778 - 0.02222)

ΔPE = (6.674 × 10^-11) * (4 * 10^6) * (7 * 10^6) * 0.00556

ΔPE ≈ 0.09395 J

Therefore, the change in gravitational potential energy between the objects is approximately 0.09395 joules.