Two identical 19.8-kg spheres of radius 12 cm are 29.2 cm apart (center-to-center distance).

Question

(a) If they are released from rest and allowed to fall toward one another, what is their speed when they first make contact?

(b) If the spheres are initially at rest and just touching, how much energy is required to separate them to 1.03 m apart? Assume that the only force acting on each mass is the gravitational force due to the other mass.

Answer 1

a. put a coordinate system where one is fixed. The potential energy of the other is GMM (1/.24-1/.29) that is PE of the starting position minus the final position (24cm cneter to center).

That PE turns to KE (1/2 M V2),but in reality, both are moving, so the KE is divided between the two, so 1/2 MV^2=1/2 PE
so you can find then the V each has when colliding.

Answer 2

Thanks...I figured out part b