A 2-0 z bullet is fired horizontally with a velocity v=1000 ft / sec into the slender bar of a 3

step 1 So here on this problem we are given that a bullet is fired horizontally into a vertical bar as

A 2-0 z bullet is fired horizontally with a velocity v=1000...

A $2-0 z$ bullet is fired horizontally with a velocity $v=1000 \mathrm{ft} / \mathrm{sec}$ into the slender bar of a $3-1 \mathrm{b}$ pen dulum initially at rest. If the bullet embeds itself in the bar, compute the resulting angular velocity of the pendulum immediately after the impact. Treat the sphere as a particle and neglect the mass of the bar. Why is the linear momentum of the system not conserved?

Key Concepts

Conservation of Angular Momentum

Angular momentum remains conserved in a system about a pivot point even when an inelastic collision occurs, provided that there is no net external torque acting about that point. In rotational dynamics, if the collision happens quickly and the pivot forces produce negligible torque, then the angular momentum before and after the collision can be equated, which allows one to determine the resulting angular velocity of the pendulum.

Conservation of Linear Momentum

Linear momentum is conserved only in the absence of unbalanced external forces. In the problem, the pendulum is attached to a fixed pivot which exerts an external reaction force during the collision. This external force supplies an impulse that changes the linear momentum of the system, meaning that the overall linear momentum is not conserved during the impact.

Impulsive Forces from Constraints

When a collision occurs in a constrained system, like a pendulum with a fixed pivot, the pivot can impart impulsive forces that alter the system's linear momentum. Despite the collision being very rapid, these impulsive forces produce significant effects on linear motion by providing the necessary momentum change, even though they may not influence the rotational motion about the pivot due to having no moment arm.

Transcript

Please give Ace some feedback