Question

Two objects have masses of `39 MG` and `21 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `8 m` to `3 m`?

Answer 1

`~=.0114J`

Explanation:

Gravitational Potential Energy can be found with the equation:

`GPE=-(m_1m_2G)/r`

http://www.softschools.com/formulas/physics/potential_energy_twobody_gravitation_formula/36/

Therefore the change in GPE is:

`DeltaGPE=-(m_1m_2G)/r_2-(-(m_1m_2G)/r_1)`

We can see that it will change linearly. The percent it will change by will be:

`-1/3+1/8=-8/24+3/24=-5/24~=-20.83%`

The actual change is (I'll interpret the units MG as Millions of Grams - and since the formula uses kilograms as the unit of mass, I'll adjust the numbers to get the units right):

`=-((39xx10^3)(21xx10^3))/3(6.673xx10^-11)+((39xx10^3)(21xx10^3))/8(6.673xx10^-11)`

`~=-.0547/3-.0547/8~=.0114J`

How much energy is this?

One way to view it is to say that it's the energy required to move a paperclip 1 metre (3 feet).

~~~~~

The following is the original answer, which answered the question regarding gravitational force:

The force of gravity between two masses can be found with:

`F_g=(m_1m_2)/r^2G`

Since we're changing the distance between the two objects, one way we can express the change is to see that:

`(r_1)^2=8^2=64=(m_1m_2)/F_(g1)G`

`(r_2)^2=3^2=9=(m_1m_2)/F_(g2)G`

And so the change in the two forces is an `64/9=711.bar1%` increase.

The actual numerical change is (I'll interpret the units MG as Millions of Grams - and since the formula uses kilograms as the unit of mass, I'll adjust the numbers to get the units right):

`F_(g2)-F_(g1)=(m_1m_2)/(r_2)^2G-(m_1m_2)/(r_1)^2G`

`=((39xx10^3)(21xx10^3))/(3)^2(6.673xx10^-11)-((39xx10^3)(21xx10^3))/(8)^2(6.673xx10^-11)`

`~=.0547/9-.0547/64~=.005N`

This is a remarkably small amount of force. If you put two snickers bars in your hand (100g), the amount of force pushing down on your hand is roughly 1N. To achieve .005N, eat one of the snickers bars (you don't need it) and take the other one and cut it up into 250 equal pieces. Take one piece from that and put it in your hand. That is roughly .005N.