Two carts of masses and are connected by a light spring of force constant on a horizontal
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Two carts of masses m1=1.0kg and m2=2.0kg are connected by a light spring of force constant k=120Nm−1 on a horizontal, frictionless track. The carts are held so the spring is compressed 0.10 m from its relaxed length and then released from rest at t=0. Neglect any resistive forces.
(a) Derive an expression for the position xcm(t) of the system’s center of mass measured from an origin fixed to the track. Express your result in terms of any needed parameters and initial conditions.
(b) Show explicitly that the net external horizontal force on the two-cart system is zero, and explain how this fact is reflected in your expression from part (a).
(c) At the instant the spring passes through its relaxed length for the first time, calculate the speed of each cart and the speed of the center of mass.