Chapter 7

Momentum and Collisions

Practice Problems

Problem 7-24

A small block of mass m = 0.07 kg, initially at rest, is struck by an impulsive force F of duration 10 ms whose strength varies with time according to the following graph:

What is the resulting speed of the block?

Problem 7-25

Two balls roll toward each other. The red ball has a mass of 0.5 kg and a speed of 4 m/s just before impact. The green ball has a mass of 0.3 kg and a speed of 2 m/s. After the head on collision, the red ball continues forward with a speed of 2 m/s. Find the speed of the green ball after the collision. Was the collision elastic?

Problem 7-26

An object of mass m moves with velocity v toward a stationary object of mass 2m. After impact, the objects move off in the directions shown in the following diagram:

(a) Determine the magnitudes of the velocities after the collision in terms of v.

(b) Is the collision elastic? Explain your answer.

Problem 7-27

A steel ball of mass m is fastened to a light cord of length L and released when the cord is horizontal. At the bottom of its path, the ball strikes a hard plastic block of mass M = 4m, initially at rest on a frictionless surface. The collision is elastic.

(a) Find the tension in the cord when the ball's height above its lowest position is 0.5L. Write your answer in terms of m and g.

(b) Find the speed of the block immediately after the collision.

(c) To what height h will the ball rebound after the collision?

Problem 7-28

A ballistic pendulum is a device that may be used to measure the muzzle speed of a bullet. It is composed of a wooden block suspended from a horizontal support by cords attached at each end. A bullet is shot into the block, and as a result of the perfectly inelastic impact, the block swings upward. Consider a bullet (mass m) with velocity v as it enters the block (mass M). The length of the cords supporting the block each have length L. The maximum height to which the block swings upward after impact is denoted by y, and the maximum horizontal displacement is denoted by x.

(a) In terms of m, M, g, and y, determine the speed v of the bullet.

(b) What fraction of the bullet's original kinetic energy is lost as a result of the collision? What happens to the lost kinetic energy?

(c) If y is very small (so that can be neglected), determine the speed of the bullet in terms of m, M, g, x, and L.

(d) Once the block begins to swing, does the momentum of the block remain constant? Why or why not?

Problem 7-29

An object of mass m moves with velocity v toward a stationary object of the same mass. After their impact, the objects move off in the directions shown in the following diagram:

(a) If denotes the kinetic energy of Object 1 before collision, what is the kinetic energy of this object after collision? Write your answer in terms of and .

(b) What is the kinetic energy of Object 2 after the collision? Write your answer in terms of and .

(c) What is the relationship between and ?

The End