Two objects have masses of #17 MG# and #22 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #5 m# to #32 m#?
1 Answer
...I was in the middle of writing up an explanation of how gravitational force changes as the distance changed, and then I realized that wasn't what the question was.
The equation for calculating gravitational potential energy (U) is given as:
where g is the universal gravitational constant, m the mass of the smaller object, M the mass of the larger, and r the distance.
...the only variable that changes between the 2 cases is the distance, r.
You are not asked to calculate the magnitude of the potential energy, only how it changes. So, for the two cases, your numerator is the same number, but note that the minus sign makes this quantity Q negative.
So, we go from
...you want a factor to multiply
...call this factor z. So you want to solve for z:
...multiply both sides by
so, the magnitude of the second quantity will be 15.6% of the first.
But remember from our eq. 1 that this quantity is negative. So the value of the quantity becomes LESS negative by that 15.6% factor.
...or, alternately, it increases by a factor of 84.4%.
