Problems 56 and 70. (a) A metal ball moves toward the...

Problems 56 and 70. (a) A metal ball moves toward the pendulum. (b) The ball is captured by the pendulum. (c) The ball–pendulum combination swings up through a height h before coming to rest. A 1.25-kg wooden block rests on a table over a large hole as in Figure $P 9.57$ on page $274 .$ A 5.00 -g bullet with an initial velocity $v_{i}$ is fired upward into the bottom of the block and remains in the block after the collision. The block and bullet rise to a maximum height of 22.0 cm. (a) Describe how you would find the initial velocity of the bullet using ideas you have learned in this chapter. (b) Calculate the initial velocity of the bullet from the information provided.

Problems 56 and 70. (a) A metal ball moves toward the pendulum. (b) The ball is captured by the pendulum. (c) The ball–pendulum combination swings up through a height h before coming to rest.
A 1.25-kg wooden block rests on a table over a large hole as in Figure $P 9.57$ on page $274 .$ A 5.00 -g bullet with an initial velocity $v_{i}$ is fired upward into the bottom of the
block and remains in the block after the collision. The block and bullet rise to a maximum height of 22.0 cm. (a) Describe how you would find the initial velocity of the bullet using ideas you have learned in this chapter. (b) Calculate the initial velocity of the bullet from the information provided.

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Key Concepts

Conservation of Energy

In physics problems involving motion under gravity, energy conservation relates the kinetic energy of an object immediately after an event to the gravitational potential energy at its highest point. This concept is used to analyze how the velocity after a collision is converted into the vertical displacement or height reached.

Conservation of Momentum

This concept involves the idea that in the absence of external forces, the total momentum of a system remains constant during an interaction, such as a collision. In problems where an object embeds in another (inelastic collision), the initial momentum of the moving object is shared between the combined masses after the collision, helping determine the post-collision velocity.

Ballistic Pendulum

A ballistic pendulum is a classic experimental setup that combines a collision with a pendulum swing to measure an object's initial velocity. The collision part uses momentum conservation to find the speed of the system right after impact, while the subsequent swing uses energy conservation to relate that speed to the height achieved, providing a method to back-calculate the original projectile's velocity.

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