Serway & Jewett — Linear Momentum and Collisions: Problem 54

On a horizontal air track, a glider of mass \( m \) carries a G-shaped post. The post supports a small dense sphere, also of mass \( m \), hanging just above the top of the glider on a cord of length \( L \). The glider and sphere are initially at rest with the cord vertical. A constant horizontal force of magnitude \( F \) is applied to the glider, moving it through displacement \( x_1 \); then the force is removed. During the time interval when the force is applied, the sphere moves through a displacement with horizontal component \( x_2 \). (a) Find the horizontal component of the velocity of the center of mass of the glider–sphere system when the force is removed. (b) After the force is removed, the glider continues to move on the track and the sphere swings back and forth, both without friction. Find an expression for the largest angle the cord makes with the vertical.