Two objects have masses of 27 MG27MG and 13 MG13MG. How much does the gravitational potential energy between the objects change if the distance between them changes from 48 m48m to 90 m90m?
1 Answer
The gravitational potential energy will decrease by about
Explanation:
This seems to be a popular question.
The gravitational potential energy of two masses
color(crimson)(U_g=-(Gm_1m_2)/r)Ug=−Gm1m2r where
GG is the gravitation constant,m_1m1 andm_2m2 are the masses of the objects, andrr is the distance between them
The change in gravitational potential energy will then be:
DeltaU_g=(-(Gm_1m_2)/r)_f-(-(Gm_1m_2)/r)_iΔUg=(−Gm1m2r)f−(−Gm1m2r)i
color(darkblue)(=>Gm_1m_2(1/r_i-1/r_f))
There are two ways I can see to interpret
The second is that
We have the following information:
|->m_1=27xx10^3"kg" |->m_2=13xx10^3"kg" |->r_i=48"m" |->r_f=90"m" |->"G"=6.67xx10^(-11)"Nm"//"kg"^2
Substituting in these values into the above equation:
Gm_1m_2(1/r_i-1/r_f)
=>(6.67xx10^(-11)"Nm"//"kg"^2)(27xx10^3"kg")(13xx10^3"kg")(1/(48"m")-1/(90"m"))
=2.276xx10^(-4)"N"
~~color(crimson)(2.3xx10^(-4)N)
That is, the gravitational potential energy will decrease by about
Note: It may seem odd that we would state a potential energy as being negative, but this is due to the way this particular form of potential energy it is defined—it was chosen that