Chapter 9.1, Problem 14SSC

To determine

Whether the impulse on and the change in momentum of the basketball is zero when the basketball hits the floor. The direction in which the momentum change takes place. And to draw the basketball’s momentum vectors before and after it hits the floor.

Explanation of Solution

Introduction:

Momentum gives the quantity of a motion of a moving body. It is the product of mass and velocity of a moving body. Momentum is a vector quantity that means it has both magnitude and direction.

The impulse can be represented as a quantity which gives the overall effect of a force acting on an object over a time. It is equal to the force times the time. Impulse can cause change in momentum of an object. So, the change in momentum of an object caused by a large force applied for a short period of time is equal to that caused by a small force applied for a long period of time. Therefore, Impulse on an object = change in momentum of that object. This equivalence is known as impulse momentum theorem.

The change in momentum of the basketball is not zero when it hits the floor. Instead, it is in upward direction.

Momentum vector is in downward direction before the ball hits the floor as shown in the figure $1\left(a\right)$ .

Momentum vector is in the upward direction after the ball hits the floor as shown in the figure $1\left(b\right)$ .

  

In the figure $1\left(a\right)$ and $(b)$ , $p$ represents the momentum of the basketball, $v_i$ and $v_f$ are the velocity of the ball before and after hits the floor respectively.