Two objects have masses of #32 MG# and #23 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #7 m# to #32 m#?

Question

Two objects have masses of #32   MG# and #23    MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #7 m# to #32  m#?

Julia Aguilar · Accepted Answer

The change in gravitational potential energy is #=547.9*10^-5J#

The potential energy per kilogram at a point in a field is known as the gravitational potential.

So the units are #J, "Joules"#

#Phi=-G(M_1M_2)/R#

The universal constant of gravitation is

G is 6.67 * 10^-11 Nm^2 kg^-2.

The masses causing the field is #=M_1 kg# and #=M_2 kg#

The mass is #M_1=32MG=32*10^6g=32*10^3kg#

The mass is #M_2=23MG=23*10^6g=23*10^3kg#

The distance between the centers is #=Rm#

The distance #R_1=7m#

The distance #R_2=32m#

Consequently,

#Phi_1=(-G*(32*10^3*23*10^3)/7)#

#Phi_2=(-G*(32*10^3*23*10^3)/32)#

Thus,

#Phi_1-Phi_2=(-G*(32*10^3*23*10^3)/7)-(-G*(32*10^3*23*10^3)/32)#

#=32*23*10^6*6.67*10^-11(1/32-1/7)#

#=-547.9*10^-5J#

Charles Aeschliman · Answer

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

ΔPE = -G * ((m1 * m2) / r_final - (m1 * m2) / r_initial)

Where:
ΔPE is the change in gravitational potential energy,
G is the gravitational constant (approximately 6.674 × 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the objects,
r_final is the final distance between the objects, and
r_initial is the initial distance between the objects.

Using the given masses (32 MG and 23 MG), the initial distance (7 m), and the final distance (32 m), you can plug these values into the formula to find the change in gravitational potential energy.