Ball A of mass mA and ball B of mass mB are connected with a string of length l. Initially, the string is loose and the distance between the two balls is b. At time t0, ball B is given a velocity of v0 perpendicular to the line connecting A and B. At time t1, the distance between A and B becomes l and the string becomes taut. We want to find the velocities of each ball right after the string becomes taut.
(a) Choose an inertial frame and a set of coordinates to describe the motion of the balls. Write the position, velocity, and acceleration (kinematics) of both
the balls.
(b) Is the linear momentum of the two-ball system conserved? Why?
(c) Is the angular momentum of ball B conserved right before and right
after the string becomes taut around any point or points? Explain (one to two sentences).
(d) What are the linear momenta of A, B and the two-ball system right
before and right after the string becomes taut?
(e) Find the position and velocity of the center of mass of the system right
before and right after the string becomes taut?
(f) What is the linear impulse applied by the string on A as the string becomes taut?
