Two objects have masses of #9 MG# and #5 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #36 m# to #48 m#?

Question

Two objects have masses of #9 MG# and #5  MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #36    m# to #48   m#?

Olivia Askew · Accepted Answer

#GM_1M_2(\frac{1}{D_1}-1/D_2)# Hint: In general, the gravitational potential energy #U# of two point masses #M_1# & #M_2# at a distance #D# between them is given as #U=-\frac{GM_1M_2}{D}# Hence, if the distance between the masses changes from #D_1# to #D_2# such that #D_2>D_1# then the change in gravitational potential energy #\Delta U# is given as follows #\Delta U=U_2-U_1# #=-\frac{GM_1M_2}{D_2}-(-\frac{GM_1M_2}{D_1}_# #=GM_1M_2(\frac{1}{D_1}-1/D_2)#

Axel Acevedo · Answer

undefined To calculate the change in gravitational potential energy, you can use the formula:

ΔU = - G * (m1 * m2) * (1/r2 - 1/r1)

Where:
ΔU = change in gravitational potential energy
G = gravitational constant (6.674 × 10^-11 N*m^2/kg^2)
m1, m2 = masses of the objects (in kilograms)
r1, r2 = initial and final distances between the objects (in meters)

Plugging in the values:
m1 = 9 MG = 9 × 10^6 kg
m2 = 5 MG = 5 × 10^6 kg
r1 = 36 m
r2 = 48 m

Calculate:
ΔU = - (6.674 × 10^-11 N*m^2/kg^2) * (9 × 10^6 kg * 5 × 10^6 kg) * (1/48 - 1/36)

ΔU ≈ - (6.674 × 10^-11) * (9 * 5 * 10^12) * (1/48 - 1/36)

ΔU ≈ - (6.674 × 10^-11) * (45 * 10^12) * (0.02083 - 0.02778)

ΔU ≈ - (6.674 × 10^-11) * (45 * 10^12) * (-0.00695)

ΔU ≈ 2.515 × 10^8 joules

So, the change in gravitational potential energy between the objects is approximately 2.515 × 10^8 joules.