University of Virginia
Physics Department

## The Energy of a Bouncing Ball

A Physical Science Activity

2003 Virginia SOLs

• PS.1
• PS.6

Objectives

Students will

• investigate the properties and motion of a bouncing ball, exploring the motion of the ball as it collides with a hard surface;
• determine the bounce/drop height ratio of certain balls;
• apply the law of conservation of energy to bouncing balls;
• use the following skills: observing, interpreting, and measuring and graphing data.

Motivation for Learning

Discrepant Event

Materials

• Raquetball
• Ping-Pong ball

Procedure

1. Drop a racquetball on the floor and then a Ping-Pong ball on the floor. Ask the students to decide which one bounces the best. It should be clear that the racquetball bounces higher than the Ping-Pong ball.
2. Now, ask them what would happen if you placed the Ping-Pong ball on top of the racquetball and drop them both at the same time. When you drop the balls in this manner, some of the kinetic energy of the racquetball, released on impact, will be transferred to the Ping-Pong ball and it will bounce quite high.
(Placing a racquetball on top of a basketball also works well. It can be difficult to keep the racquetball on top of the basketball; gluing a small (~0.7" diameter) rubber O-ring on top of the basketball that the raquetball can be placed in will help.)

As a second demonstration of energy transfer, you can line up four tennis balls on the table and ask students, "what will happen to the row of tennis balls if a fifth tennis ball is made to collide into the first one?" Again the energy on impact will be transferred through the ball to the last one and it will move. (This experiment is difficult to do, because it is difficult to hit the balls straight on.)

Background Information

It doesn't take much effort to lift a ball off the ground. However, work is being done to the ball as it is being lifted, giving it energy. We call this energy potential energy. When the ball is dropped, the ball begins to move. The potential energy begins to be converted into kinetic energy - the energy of motion. There is obviously a very close association between work and energy. Energy is defined as the ability to do work and both work and energy are measured in Joules. To help understand this concept, scientists have classified energy into two types or states. Potential energy is the energy acquired as work is being done to an object and kinetic energy is the energy released by the object as it is doing work. The amount of work put into an object, its potential energy, must always be equal to the amount of work the object can do, its kinetic energy. For example; the higher the ball is lifted off the ground, the higher it will bounce after hitting the ground. Experience tells us that the ball can never bounce back to its original height. The falling ball looses some of its energy to air friction, to internal forces within the ball, and to friction between the ball and the ground on impact. After impact, the ball and the spot directly under the ball are slightly warmer, as some of the energy is lost as heat.

The gravitational potential energy of an object, like a rubber ball, is related to its mass and the height to which the ball is lifted and can be expressed by the formula:

 G.P.E.= Weight X Height = mgh

You can see from the formula that the greater the weight and the higher the position of the ball, the greater the potential energy. The kinetic energy of the falling ball is related to the mass of ball (m) and its velocity (v). This mathematical relationship is expressed as:

 K.E. = 1/2 mv2

According to the equation, the heavier the ball and the faster it is moving, the greater the impact on the ground. Neglecting friction for the ball we're using, the potential energy before you drop the ball will be equal to the kinetic energy just before it hits the ground.

### Student Activity

Materials

• At least two types of bouncing balls: super ball, racquetball, Ping-Pong ball, and rubber ball will work.
• 2-meter sticks (i.e. two meters long)
• Graph paper
• Hard surface for bouncing
• Calculator

Procedure

1. Make a three-column data table on a separate piece of paper. Label the first column "drop height," the second column "bounce height" and the third column "bounce/drop ratio".
2. Release one of the two balls from a height of two meters. Another member of the group should measure the bounce height and a third can record both heights in the table and divide the drop height by the bounce height to get the bounce/drop ratio. Record all data.
3. Repeat the procedure by decreasing the drop height by 25 cm each time.
4. Graph your results by placing the drop height on the horizontal axis and the bounce height on the vertical axis.
5. Repeat the entire procedure for the other ball.
 Drop Height (cm) Bounce Height (cm) Bounce/Drop ratio

Extensions

Conduct and experiment with two balls of similar material, each suspended from a piece of string. Pull the balls apart at equal angles and let them collide with each other. How many bounces do they undergo before stopping? Repeat the experiment with two balls of different material, let them collide and record the bounces for each one.

Students with special needs

Assessment

1. Describe the shape of the lines plotted for both graphs.

2. As long as you were using the same type of ball, were the bounce ratios the same for all the heights?

3. Are the bounce/drop ratios the same or different for both balls?

4. Which ball retained the greatest percentage of its kinetic energy on each bounce?

5. Explain why the balls never bounce as high as the original bounce height.

6. Explain why the shape of the graphs was similar for each ball used.

7. Suppose you had carried out your investigations on a carpeted floor. How would your results have been affected?