Halliday, Resnick & Walker — Gravitation: Problem Problem_94

Spheres blown apart. Figure 13.35 shows two identical spheres, each with mass \(m = 2.00 \text{ kg}\) and radius \(R = 0.0200 \text{ m}\), that initially touch somewhere in deep space. Suppose the spheres are blown apart such that they initially separate at the relative speed \(1.05 \times 10^{-4} \text{ m/s}\). They then slow due to the gravitational force between them. Center-of-mass frame: Assume that we are in an inertial reference frame that is stationary with respect to the center of mass of the two-sphere system. Use the principle of conservation of mechanical energy (\(K_f + U_f = K_i + U_i\)) to find the following when the center-to-center separation is \(10R\): (a) the kinetic energy of each sphere and (b) the speed of sphere B relative to A. Sphere frame: Next, assume that we are in a reference frame attached to sphere A (we ride on the body). Now we see sphere B move away from us. From this reference frame, again use \(K_f + U_f = K_i + U_i\) to find the following when the center-to-center separation is \(10R\): (c) the kinetic energy of sphere B and (d) the speed of sphere B relative to sphere A. (e) Why are the answers to (b) and (d) different? Which answer is correct?