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 #39 m#?
1 Answer
That is, the gravitational potential energy will decrease by about
Explanation:
The gravitational potential energy of two masses
#color(crimson)(U_g=-(Gm_1m_2)/r)# where
#G# is the gravitation constant,#m_1# and#m_2# are the masses of the objects, and#r# 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)_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=17xx10^3"kg"# #|->m_2=23xx10^3"kg"# #|->r_i=5"m"# #|->r_f=39"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)(17xx10^3"kg")(23xx10^3"kg")(1/(5"m")-1/(39"m"))#
#=4.547xx10^(-3)"N"#
#~~color(crimson)(4.6xx10^(-3)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