LAB Xi: DAMPING
MOTION
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?
Applications:
