CONSERVATION OF ENERGY
CONSTANT ACCELERATION MOTION
Data Studio
Objective:
To study objects moving with constant acceleration.
Apparatus:
Aluminum track, cart, plastic beam blocker, photogate, motion sensor, support stand with clamps
and rod, meter stick, protractor, one bar mass (500g), Pasco Interface, laptop.
Introduction:
When a glider moves on an almost friction free inclined track, it should accelerate with
acceleration a = g sin (), where sin () = h/L (see fig. 1). In this experiment you are to observe
graphs of position versus time and velocity versus time, and using the second graph determine
the experimental acceleration from the slope of the velocity graph.
Figure 1.
Procedure Part A:
Plug in the power cord to the computer and to the interface. Start the laptop, and wait for it to
each the desktop. Start the Science Workshop interface, and plug it into the laptop. Connect
the photogate’s stereo phone plug to Digital Channel 1 on the interface. Setup the track as shown
in figure 1 with h at 10 cm as measured from the table top to the bottom of the track at its end.
Position the photogate beam to read the top grid (the 5mm grid) on the plastic beam blocker on
the cart. On the desktop of the laptop double click on the CLC Physics Experiment folder to open
it. Double click on the Constant Acceleration Experiment 01.ds file. After a short time Data Studio
will open. Click the START button, place the cart just above the photogate and release it,
catching it after it passes through the photogate before it hits the end bumper. Click the STOP
utton to stop taking data. The laptop will record the data as Run #1. The graph screen will show
velocity versus time for the glider as it passes through the gate.
Note the value of ‘m’, which represents the slope of velocity graph. This is the experimental value
of the acceleration of the cart. Measure h and L as shown in figure 1, h is the distance from the
table top to the bottom of the track at the elevated end and L is the total track length, 1.22 m.
Increase h to 20 cm and repeat the experiment by placing the cart just above the photogate and
eleasing it. The data will be stored as Run #2. Go to the data control at the top of the graph
window and turn off Run #1. Click the ‘Scale to Fit’ button on the upper left corner of the graph.
Use the “Fit” Control at the top of the graph window and select a linear fit for Run #2. Click and
drag with the mouse to select the useful part of the data run and take note of the slope.
Using the same new h value, repeat the experiment with the cart starting 20 cm above the
photogate. This is Run #3. Comment on the effect on the v versus t graph.
Again using the same new h value, repeat the experiment with the cart starting 20 cm above the
photogate, but this time add a 500 g bar to the cart. The data will be stored as Run #4. On the top
of the graph menu click the DATA button, pull down the menu and display the data for each run.
Click the ‘Scale to Fit’ button so that all the data is visible. Comment on the v versus t graphs in
your conclusion.
Save the file on the USB drive. Now you can close the file Constant Acceleration Experiment
01.ds. Make sure you do not save over the file on the laptop.
Data Part A:
L = 1.22m
Run h (m) aexp (m/s2) ath (m/s2) % E
o
Calculations Part A:
Determine the experimental value of the acceleration from the slope of the v versus t graph and
compare it with the theoretical value a = g sin () = g h/L for each trial.
Part B (Motion Sensor):
In this experiment you will investigate the acceleration of a cart as it moves up and then down an
inclined plane and determine whether the acceleration of the cart is constant and if so, what the
value of the acceleration is.
Procedure:
For this activity, a Motion Sensor will measure the motion of a cart that is pushed up an inclined
plane and allowed to return to the bottom of the incline. The Data Studio program calculates the
velocity and acceleration of the cart as it moves up and down the track.
Disconnect the photogate from the interface and then connect the stereo phone plugs of the
Motion Sensor to Digital Channels 1 and 2 on the interface. Plug the yellow-banded (pulse) plug
into Digital Channel 1 and the second plug (echo) into Digital Channel 2. Double click on
Constant Acceleration Experiment 02.ds and the program will open with three graph displays:
position versus time, velocity versus time, and acceleration versus time.
Measure the angle of the inclined track and record it in the Data section. Position the Motion
Sensor at the high end of the track in order to make sure the sensor is aligned and can “see” the
cart as it moves. Repeat with the cart at the low end of the track. The cart will start at the low end
and be pushed up toward the Motion Sensor.
Click the START button to begin recording data. Give the cart a firm push up the track, so the cart
will move up the inclined plane toward and then away from the Motion Sensor. BE CAREFUL!
Don’t push the cart so firmly that it gets closer than 40 cm to the sensor. Catch the cart by hand
when it reaches the low end of the track. Click the STOP button to end recording your sample
data after the cart returns to the bottom of the track. Run #1 will appear in the Data list.
Click the ‘Fit’ tool on the upper edge of the velocity graph window to open the statistics display.
Click the ‘Scale to Fit’ button to rescale the graphs. Select the region of the plot that shows the
cart’s motion after the push and before it stopped at the bottom of the track. The slope of the best
fit line (m) is the average acceleration. Record the value in the Data section.
In the plot of acceleration, select the region of the plot that shows the cart’s motion after the push
and before it stopped at the bottom of the track. Click the ‘Show Selected Statistics’ tool (marked
with a sigma: ). It is on the upper edge of the acceleration window. If it is not already selected,
select ‘Mean’. Record the mean value in the Data section. Save your data on the USB drive.
Data Part B:
Angle of track XXXXXXXXXX___________degrees
Acceleration (slope XXXXXXXXXX___________m/s2
Acceleration (mean XXXXXXXXXX___________m/s2
Acceleration (theoretical) ___________m/s2
Questions:
1. Describe the position versus time plot of the graph display. Why does the
distance begin at a maximum and decrease as the cart moves up the inclined
plane?
2. Describe the velocity versus time plot on the graph display.
3. Describe the acceleration versus time plot on the graph display.
4. How does the acceleration determined in the velocity graph compare to the mean
value from the acceleration graph?
5. What is the percent difference between the acceleration determined in the
velocity graph and the theoretical value for acceleration?
Part C (Vertical Free Fall):
Close ‘Constant Acceleration Experiment 02.ds’ and do not save any changes on the laptop.
Remove the Motion Sensor and connect a photogate. Open ‘Constant Acceleration Experiment
03.ds’. Mount the photogate off the table edge as shown. Click the START button, hold the
plastic grid just above the photogate and release it, allowing it to fall on a coat or other soft object.
Click STOP to quit recording data. The graph will show velocity versus time for the glider as it
passed through the gate.
Note the value of ‘m’, which represents the slope of velocity graph. This is the experimental value
of the acceleration of the plastic in free fall, which should be the acceleration due to gravity, since
air resistance is small under these conditions.
Repeat the experiment dropping the fence from a different height above the photogate. Compare
your average experimental value of g with the actual value of 9.81m/s2.
Save the file on the USB drive. Now you can quit Data Studio, making sure that you do not save
over the file on the laptop. Turn off the computer. Close the computer and disconnect the cords.
Data Part C:
gexp (m/s2) gave (m/s2) gthe (m/s2) %e
or