Two identical 21.4-kg spheres of radius 14 cm are 27.6 cm apart (center-to-center distance).
(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 1.08 m apart? Assume that the only force acting on each mass is the gravitational force due to the other mass.