Question

steel ball with a mass of 40.0g is dropped from a height of 2.00 m onto a horizontal steel slab. The ball rebounds to a height of 1.60m. A) Calculate the impulse delivered on the ball during the impact. B) If the ball is in contact with the slab for 2 ms find the average force on the ball during the impact?

Answer 1

Concepts and reason

The concepts used to solve this problem are impulse, and the average force using Newton’s law.

First, the initial velocity when the ball hits the slab can be calculated by using the relationship between velocity, gravitational acceleration, and the height from which the ball dropped. Later, the final velocity when the ball hits the slab can be calculated by using the relationship between velocity, gravitational acceleration, and the height from which the ball rebounds. After that, the impulse on the ball can be calculated by taking the difference between the final and initial momenta. Finally, the average force can be calculated by using the ratio of the momentum change to the time.

Fundamentals

The expression for the initial velocity when the ball hits the slab is as follows:

Here, is the initial velocity when the ball hits the slab, is the gravitational acceleration, and is the height from which the ball is dropped.

The expression for the final velocity when the ball rebounds is as follows:

Here, is the final velocity when the ball rebounds, is the gravitational acceleration, and is the height from which the ball rebounds.

The expression for the impulse on the ball is as follows:

$J=Ap $

Here, is the impulse on the ball, and is the change in the momentum of the ball.

The expression for the change in the momentum is as follows:

Here, is the mass of the ball.

The relationship between the average force and impulse is as follows:

Here, is the force on the ball, and is the time.

(A)

The expression for the initial velocity is as follows:

Substitute for and for .

The expression for the final velocity is as follows:

Substitute for and for .

The expression for the impulse is as follows:

$J=Ap $ …… (1)

The expression for the change in momentum is as follows:

…… (2)

Solve Equation (2) and Equation (1).

Substitute for , for , and for .

(B)

The relationship between the average force and impulse is as follows:

…… (3)

Rewrite the above expression in terms of F.

Replace for in the above equation.

Substitute for , for , for , and for.

Ans: Part A

The impulse on the ball is.