Two objects have masses of #42 MG# and #25 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #21 m# to #15 m#?

Answer 1

The change in gravitational energy is #=133.4*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=42MG=42*10^6g=42*10^3kg#
The mass is #M_2=25MG=25*10^6g=25*10^3kg#
The distance between the centers is #=Rm#
The distance #R_1=21m#
The distance #R_2=15m#

Consequently,

#Phi_1=(-G*(42*10^3*25*10^3)/21)#
#Phi_2=(-G*(42*10^3*25*10^3)/15)#

Thus,

#Phi_1-Phi_2=(-G*(42*10^3*25*10^3)/21)-(-G*(42*10^3*25*10^3)/15)#
#=42*25*10^6*6.67*10^-11(1/15-1/21)#
#=133.4*10^-5J#
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Answer 2

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

ΔU = -G * ((m1 * m2) / r2_final - (m1 * m2) / r2_initial)

where: ΔU 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 objects r_initial is the initial distance between the objects r_final is the final distance between the objects

Plugging in the given values: m1 = 42 MG = 42 * 10^6 kg m2 = 25 MG = 25 * 10^6 kg r_initial = 21 m r_final = 15 m

ΔU = -6.674 × 10^-11 * ((42 * 10^6 * 25 * 10^6) / (15^2) - (42 * 10^6 * 25 * 10^6) / (21^2))

Calculating this expression will give you the change in gravitational potential energy.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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