Answer
The work done by the gravitational force is $~~-2.9\times 10^{-11}~J$
Work Step by Step
In Problem 3, we found that the distance between the particles is $~~d = 19~m$
We can find the original gravitational potential energy of the two-particle system:
$U_i = -\frac{G~M_1~M_2}{d}$
$U_i = -\frac{(6.67\times 10^{-11}~N~m^2/kg^2)(5.2~kg)(2.4~kg)}{19~m}$
$U_i = -4.4\times 10^{-11}~J$
We can find the gravitational potential energy of the two-particle system if we triple the separation distance:
$U_f = -\frac{G~M_1~M_2}{3d}$
$U_f = -\frac{(6.67\times 10^{-11}~N~m^2/kg^2)(5.2~kg)(2.4~kg)}{(3)(19~m)}$
$U_f = -1.5\times 10^{-11}~J$
We can find the change in gravitational potential energy:
$\Delta U = U_f-U_i$
$\Delta U = (-1.5\times 10^{-11}~J)-(-4.4\times 10^{-11}~J)$
$\Delta U = 2.9\times 10^{-11}~J$
We can find the work done by the gravitational force:
$W_g = -\Delta U$
$W_g = -2.9\times 10^{-11}~J$
The work done by the gravitational force is $~~-2.9\times 10^{-11}~J$
