PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
Two blocks, Block A of mass m and Block B of mass 2m, are connected by an ideal light spring of relaxed length L on a frictionless horizontal surface. At t=0 the spring is compressed to length 0.5L, Block A is at position x=0, and Block B is at position x=0.5L. Both blocks are released simultaneously with no external horizontal forces acting on the system.
(a) Derive an expression for the x-coordinate of the center of mass as a function of time, xcm(t), in terms of the initial center-of-mass position xcm(0) and the initial center-of-mass velocity vcm.
(b) Show explicitly that xcm(t) is independent of the changing length of the spring during the subsequent oscillations.
(c) The initial velocities of the blocks are both zero. Calculate the numerical value of xcm(0) using the given data.
(d) Suppose a constant external force F directed to the right begins acting on Block B at t=T (after several oscillations). Write an expression for the acceleration of the center of mass for t≥T and explain why internal forces no longer cancel in that interval.