Question

A pendulum consists of two 8 kg concentrated masses positioned as shown on a light but rigid bar. The pendulum is swinging clockwise through the vertical position with a angular velocity of 6 rad/s (0=-6 rad/s) when a 0.08 kg bullet traveling with velocity v = 320 m/s in the direction shown strikes the lower mass and becomes embedded in it. Determine the angular velocity ' of the pendulum has immediately after the impact and the maximum angular deflection of the pendulum after the impact.

Answer 1

To determine the angular velocity ' of the pendulum immediately after the impact, use the principle of conservation of angular momentum. To find the maximum angular deflection of the pendulum, analyze the system's kinetic and potential energy at different points in its motion.

Step-by-step explanation:

To determine the angular velocity ' of the pendulum immediately after the impact, we can use the principle of conservation of angular momentum. Before the impact, the total initial angular momentum of the system is given by the product of the moment of inertia of the pendulum and its initial angular velocity. After the impact, the bullet becomes embedded in the lower mass, changing the moment of inertia of the system. To find the maximum angular deflection of the pendulum, we can analyze the system's kinetic and potential energy at different points in its motion. At the lowest point of the swing, all the potential energy is converted into kinetic energy, so we can equate the initial potential energy to the final kinetic energy to find the maximum angular deflection.