Course and Section_______ Names ___________________________
Date___________ _________________________________
Free
Fall Lab
In this experiment you will use the motion sensor to
analyze the motion of a bouncing ball.
From your graphs, you will study the relationships between the position,
velocity, and acceleration of the ball, and you will measure the acceleration
due to gravity.
1. Before
doing the experiment, let us predict what will happen. First we’ll use words. Release your golf ball from a height of
about 1 meter above the table, and observe it as it bounces several times. Then describe in words, as completely as you
can, the motion of the ball.
2. A graph
is a good way to communicate information about motion. Sketch a graph of the position of the ball
versus time for the motion you described in part 1.
3. Now we’ll compare your prediction to experiment.
Mount the motion sensor on a stand a meter or so above the table. Orient the sensor so that the ultrasonic
beam will be projected downward. Open
Data Studio, select Create Experiment, and select Motion Sensor under the list
of sensors. Double click on Motion
Sensor and make sure the motion sensor is plugged into the Pasco
interface. Double click on the motion
sensor icon that is shown connected to the interface, select the Motion Sensor
tab, and set the trigger rate to 50.
4. Now
record the motion of the ball as it is dropped from about 20 cm below the
motion sensor onto the table. Try to
record the motion of the ball as it bounces at least three times. You may need to attempt this a few
times. If the ball drifts out of the
ultrasonic beam as it bounces, the sensor will not detect its motion. What
differences and similarities do you observe between the measured position and
your predicted graph? Can you explain
the differences?
5. Now we want
to think about the velocity of this ball.
(a) Sketch
what you think the velocity versus time graph will look like. Compare your description with your
neighbors’, and try to reach a consensus.
(b) What is the relationship between the position
and velocity graphs?
6. Double
click on “Graph” under “Displays” and drag velocity (under Data) onto the
position graph so that you have simultaneous plots of position and
velocity. Click the button on the menu
bar to align and match the horizontal axes of the graphs. Does your velocity graph look the way you
expected? Explain any differences you
see.
7. Now
predict, and sketch below, what you
think the acceleration graph will look like.
As usual, be as complete as you can.
Compare with your neighbors, and try to reach a consensus.
8. Drag
acceleration over to the graph as you did with velocity in part 6, and see if
your prediction was correct. Discuss
any differences you observe.
9. Finally,
let us describe these graphs mathematically.
Look first at the standard equations for a body in freefall, to see how
you might determine the acceleration of the ball from these equations. Select a time interval between bounces; highlight those data points. Fit the position data to a quadratic equation
and determine the acceleration of gravity from your fit parameters. Do this by clicking on the small “Fit”
button and choosing quadratic.
Likewise, fit the velocity data between bounces to a linear equation and
determine the acceleration of gravity. Now find the average acceleration of the ball during this time
interval from the acceleration graph. [To find the average of a set of data
points, click on the “S” button and choose “mean.”] Record your three results
(values for “g”) below.
Position graph:
Velocity graph:
Acceleration graph:
10. Turn in (1)
these pages with your predictions and your responses to the questions, and (2)
a printout of the measured curves.