Two objects have masses of #33# #Mg# and #18# #Mg#. How much does the gravitational potential energy between the objects change if the distance between them changes from #81# # m# to #3# #m#?

Answer 1
Use Newtons gravitational law for celestial bodies: #F = G\(m_1 m_2) / r^2#.
G is the gravitational constant, equaling 6.67408 × #10^-11 N*m^2/(kg)^2#
The masses #m_1# and #m_2# are the masses you mentioned.
The #r^2# is 3 respectively 81 meters. (It is mentioned as #r_2# because it is meant to be a radius, which the same as the distance from the center of an object to the center of another)

Subtract the forces at each distance after calculating them.

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Answer 2

To calculate the change in gravitational potential energy between two objects, we can use the formula:

ΔPE = - G * (m1 * m2) * (1/r2 - 1/r1)

Where: ΔPE = change in gravitational potential energy G = gravitational constant (approximately 6.67 x 10^-11 N m^2/kg^2) m1, m2 = masses of the objects (33 Mg and 18 Mg, respectively) r1, r2 = initial and final distances between the objects (81 m and 3 m, respectively)

Plugging in the values:

ΔPE = - (6.67 x 10^-11) * (33 x 10^6 kg) * (18 x 10^6 kg) * (1/3 - 1/81) ≈ - (6.67 x 10^-11) * (33 x 10^6) * (18 x 10^6) * (0.3333 - 0.0123) ≈ - (6.67 x 10^-11) * (33 x 10^6) * (18 x 10^6) * 0.321

Therefore, the change in gravitational potential energy between the objects is approximately -191.84 x 10^6 joules.

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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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