Problem: What is the relationship between the height that a ball bounces and the number of times it bounces?

Background: To oscillate means to pass from one state to another and back again. A swinging pendulum is one example of an oscillating body. Another example would be a vibrating string on a musical instrument. Can you think of other examples? Many oscillating systems are said to undergo harmonic motion. Many things in nature exhibit harmonic motion. Can you think where this type of motion occurs in your body?

If we set a pendulum in motion it stops after a period of time. A vibrating string on an instrument also slowly stops. This decline of motion is referred to as damped harmonic motion. Today you will study one simple example of damped harmonic motion. That of a bouncing ball.

Try to determine what type of relationship you expect to observe today.

State your hypothesis. Justify your statement!

Materials: ping pong ball, rubber ball, meter stick

Procedure: Hold a ball at a distance of one meter from the surface of the table (diagram I). Drop the ball. Catch it after one bounce. Measure its height. Drop it again, and let it bounce twice. Measure the height after two bounces. Repeat this procedure at least five more times. Be sure to repeat the complete procedure at least three times, averaging your results (see class notes). Record all data in results.

Repeat if time permits using the rubber ball.

Results:

Table I: Ping pong ball

Number of bounces height (cm.)

0

1

2

3

4

5

6

7

Table II. Rubber ball

Number of bounces height (cm.)

0

1

2

3

4

5

6

7

Graphs: On the same graph make two plots. Plot I: plot number of bounces on the x axis and height on the y axis for the ping pong ball. Plot II: plot number of bounces on the x axis and height on the y axis for the rubber ball.

Discussion extra: Design an experiment to study the effects different materials would have on determining the height a ball bounces. Can a ball ever return to its starting point on the first bounce? Why? Try to determine a relationship that fits your data points.

1) What are the independent and dependent variables?

2) How are the variables changing with relationship to each other?

3) What happens to the dependent variable when the independent variable increases? decreases?

4) How does the relationship shown in this experiment compare with other relationships you have so far seen?

5) How does the equation for this relationship compare with those of other equations you have studied?

What is a mathematical relationship and what are the different types of mathematical relationships that apply to the laboratory exercises in the following activities.

**Lab 1:
The Spring Constant ** -- __Problem:__ What is the relationship between how much a spring stretches and the force pulling on the spring?

**Lab 2:
The Pendulum** -__-Problem:__ What is the relationship between the period of a pendulum and the length of the string of the pendulum?

**Lab 3: Mass, Volume and Density**-- __ Problem: __What is the relationship between the mass of a ball and its volume assuming a constant density?

**Lab 4: Light Intensity**--__ ____ Problem: __What is the relationship between the intensity of a beam of light and the distance from a light source?

**Lab 5: Acceleration--** __Problem: __What is a the relationship between how the distance travels and the time in travel for an accelerating object?

**Lab 6: Polarization **-- __Problem:__ What is the relationship between how much light passes through a Polaroid filter and the angle the filter is rotated?

**Lab 7: Ohms Law**-- __Problem:__ What is the relationship between current, voltage when there is a constant resistance in an electric circuit.

**Lab 8: Radioactive Decay-**- __Problem:__ What is the relationship between the decay of radioactive material and the time allowed for the decay?

**Lab 9: Water Pressure**--__ Problem:__ What is the relationship between water pressure and depth of water?

**Lab 10: Attractive and Repulsive Forces**-- __ Problem:__ What is the relationship between the distance between two magnets and the force between them?

**Lab 11: Damping Motion**-- __Problem:__ What is the relationship between the height a ball bounces and the number of times it has bounced?

**Lab 12: Buoyancy **- Problem: What is the relationship between the volume of a boat and the weight it can hold?