Free Fall - Determining the acceleration of gravity
Prior to Lab: Complete and hand in the Pre-Lab Excel Problem.
Object: The object of this experiment is to determine the value of the acceleration of
gravity by measuring the rate of acceleration of a freely falling object. In addition, you
will be able to compare kinematic theory with experiment for constantly accelerated
motion.
Apparatus:
Vernier Caliper
Large ring stand base and rod, right angle clamp, small rod
Pasco Drop Box, Timer Switch, AC Adaptor and Control Box
Pasco Time of Flight Accessory
1 large plastic ball, 1 plastic golf ball, 1 small plastic ball, and 1 small steel ball
Meter stick with caliper jaw
Discussion: An object dropped near the earth’s surface will accelerate uniformly with
the acceleration due to gravity (g) toward the earth. The magnitude of g at the Berks
Campus is 9.80 m/s2. Thus according to the equation describing motion for a uniformly
accelerated object, its position y as a function of time t is
y  yo  vot 
1 2
gt
2
If we assume that y0 is 0 m and v0 is 0 m when we start measuring the fall of the object,
then
y
1 2
gt
2
(1)
where down is assumed to be the positive direction and the object’s initial position is at
the origin of the coordinate system used. If we graph distance fallen vs. time squared
the data should yield a linear graph similar to the one shown below.
Experimental Overview
The Pasco 750 interface and associated free fall timing equipment allows us to
accurately time the fall of an object (ball). We will position the drop box at several
different heights and record the time of fall. We can then incorporate that data in a
spreadsheet, graph it, and determine a linear fit (linear trendline) from which the slope
is equal to ½ the acceleration of gravity. We can then compare our results with the
expected value of the acceleration of gravity.
Procedure:
I.
Equipment Set-up
1. Connect the AC Adapter to
the POWER jack on the
control box.
2. Connect one plug of the timer
switch to the PHOTOGATE
port on the control box.
Connect the other plug to
Channel 1 on the Science
Workshop 750 Interface Box.
3. Use the included cable to
connect the SIGNAL TO
DROP BOX jack on the
control box to the TO
CONTROL BOX jack on the
drop box.
4. Mount the drop box on the
ring stand post as shown in
the picture.
5. Place the time-of-flight
accessory pad directly below
the drop box and connect its plug to Channel 2 on the Science Workshop 750
Interface Box.
6. Hang the object from the drop box magnet. For the nonmagnetic objects, a steel
washer is under a paper cover and is used to hold the object to the magnet.
7. Set the ACTIVE/INACTIVE switch on the control box to ACTIVE.
II. Set-up of computer and interface
1. Verify that the indicator light on the PASCO 750 interface is on, then log onto
the computer.
2. Start DataStudio, then choose Create Experiment.
3. Click on the left most input (Channel 1) and choose photogate.
4. In the Measurements, window be sure velocity, Ch 1 (m/s) is unchecked
(deselected).
5. Click on the next input (Channel 2) and choose time-of-flight accessory.
6. In the summary bar on the left side of the screen in the Displays (bottom)
section find and double click on Table. A Table showing a column with elapsed
time should appear.
III. Running the Experiment
1.
2.
3.
4.
5.
6.
7.
Measure the distance between the time-of-flight accessory and the magnet on
the drop box. Record this distance.
Place a ball on the magnet.
In Data Studio, click the Start button. Result: Data Studio’s experiment clock
starts running, indicating that it is ready to collect data.
Press the timer switch button. Result: The ball is released from the drop box.
When the ball hits the time-of-flight accessory, the table in Data Studio displays
the elapsed (fall) time.
In Data Studio click the Stop button.
To measure another time: hang the ball from the drop box, wait until the green
LED on the drop box stops blinking, and repeat steps 1,2 and 3.
Repeat steps 2 through 6 above two more times for a total of 3 elapsed time
measurements.
IV. Collecting Additional Data
1. Change the height of the drop box and repeat the above procedure (III) until you
have collected elapsed time measurements for at least 5 different distances
between 0.20 m and 0.85 m.
2. Repeat the entire experimental procedure above for a second ball.
3. Measure the diameter of each ball you used in your experiment with the vernier
caliper. For the plastic balls, include the washer that is used to hold the ball to
the magnet.
V. Analysis:
1. Transfer your raw data for distance and elapsed time to a spreadsheet.
2. Correct the distance for actual distance fallen by subtracting the diameter of the
ball.
3. Calculate the average time fallen for each distance and square the result.
4. Plot a graph of distance fallen vs. time squared (see sample graph in these
instructions).
5. Add a linear trendline to your graph and display the equation of that trendline.
Determine the experimental value of g from the slope of your trendline.
6. Compare your results with the known value of 9.80 m/s2 for the acceleration of
gravity by determining the per cent difference.
7. In your lab report be sure to include any reasons why your results differ from
the known value for g.
Questions:
1. Does any of your data deviate significantly from your trendline?
2. Is equation (1) for constantly accelerated motion consistent with your data?
3. Is there any evidence that air resistance has affected your results? What is that
evidence?