(a) [tex]-3.48\cdot 10^{-7} J[/tex]
The gravitational potential energy of the two-sphere system is given by
[tex]U=-\frac{Gm_A m_B}{r}[/tex] (1)
where
G is the gravitational constant
[tex]m_A = 94 kg[/tex] is the mass of sphere A
[tex]m_B = 100 kg[/tex] is the mass of sphere B
r = 1.8 m is the distance between the two spheres
Substitutign data in the formula, we find
[tex]U=-\frac{(6.67\cdot 10^{-11})(94 kg)(100 kg)}{1.8 m}=-3.48\cdot 10^{-7} J[/tex]
and the sign is negative since gravity is an attractive force.
(b) [tex]1.74\cdot 10^{-7}J[/tex]
According to the law of conservation of energy, the kinetic energy gained by sphere B will be equal to the change in gravitational potential energy of the system:
[tex]K_f = U_i - U_f[/tex] (2)
where
[tex]U_i=-3.48\cdot 10^{-7} J[/tex] is the initial potential energy
The final potential energy can be found by substituting
r = 1.80 m -0.60 m=1.20 m
inside the equation (1):
U=-\frac{(6.67\cdot 10^{-11})(94 kg)(100 kg)}{1.2 m}=-5.22\cdot 10^{-7} J
So now we can use eq.(2) to find the kinetic energy of sphere B:
[tex]K_f = -3.48\cdot 10^{-7}J-(-5.22\cdot 10^{-7} J)=1.74\cdot 10^{-7}J[/tex]
