Physics 211 Experiment #9 Impulse – Momentum Experiment
Discussion
Impulse, momentum, and the impulse-momentum relationship
are defined and discussed in the text. The

v
momentum of an object with mass m and velocity is
p  mv .
The impulse of a resultant force from time t1 to time t2 is When the force is plotted versus time, the
impulse is the area under the curve between t1 and t2.
t2
F
res
dt
t1
The impulse-momentum relationship states that if an object with mass m is acted on by a force over the
time interval from t1 to t2, the impulse is equal to the change in momentum:
t2
F
res
dt  p  p2  p1 .
t1
This can easily be derived from Newton’s second law
Fres  ma  m
dv
.
dt
Multiplying both sides of the equation by dt we obtain,
Fres dt  mdv  d  mv   dp .
Integrating from time t1 to time t2,
t2
F
res
t1
dt 
p2
 dp  p
2
 p1  p .
p1
In this experiment, a moving cart collides with a stationary “force sensor.” The force sensor measures the
collision force as it varies with time throughout the collision. A motion sensor detects the position of the
cart versus time, enabling its velocity to be calculated as a function of time. The computer graphs force
versus time, and also the cart’s velocity versus time.
A statistics package is used to integrate the force versus time curve to obtain the impulse. In addition, the
initial and final (maximum and minimum) velocities can be obtained, making it easy to calculate initial
and final momentum, and test the impulse-momentum relation.
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Pre-Lab Assignment
Complete the following problem, using the impulse-momentum relationship. A 4kg mass is initially
moving in the x direction at 5 m/s. A force in the positive x direction acts on the mass for 7 seconds as
follows:
a. The force grows linearly from 0 to 8 Newtons in 2 seconds.
b. The force stays constant at 8 Newtons for 3 seconds.
c. The force decreases linearly to 0 in 2 seconds.
1. Calculate the initial momentum.
2. Calculate the total impulse.
3. Calculate the final momentum.
4. Calculate the final velocity.
(Hint: For parts 1 to 4 above, graph the force vs. time.)
5. Answer the following question. A 4 kg ball moving at 3 m/s bounces off a wall and is observed to be
moving at 3 m/s in the opposite direction. What was the total impulse on the ball?
Apparatus
Pasco 750 Interface
1.2 meter dynamics track
Force sensor attached to the Force sensor bracket with attachments (hook, rigid spring, less rigid
spring, rubber bumper, magnetic bumper)
Dynamic cart (without plunger) and mass block
Motion sensor (set on "narrow beam')
Pulley and clamp
Large table clamp
Mass holder and 500 grams of masses
Thread
Mass block to elevate track
Detailed Procedure and Analysis for the Impulse – Momentum Experiment
I. Program Selection and Preparation
Turn on the Pasco Science Workshop Interface, then the computer, and login.
Launch the Data Studio program, choose Create Experiment, select Force Sensor, and Motion Sensor.
Connect the Force Sensor lead to Channel A on the Science Workshop Interface box. Double click on
the Force Sensor. In the Sensor Properties window, choose General, then select Fast Force Changes,
and increase the sample rate to 1000 Hz. Under Measurement, de-select all choices and select Force
(only Force should be checked). Click OK.
Connect the yellow motion sensor plug into digital channel 1, and the other plug into channel 2.
Double click on the Motion Sensor. In the Sensor Properties window, choose Measurement, then deselect Position and Acceleration, so only Velocity is selected. Choose Motion Sensor,and set the
trigger rate to 100. Click OK.
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To set up the graphs, drag the Force Sensor from the Data window to the Graph in the Displays
window.
Click and drag the Motion Sensor from the Data Window to the graph set up in the previous step.
Two graphs should appear in the same window.
To align the time origins of the graphs, click on the button at the top of the graph window with the
Lock on it.
II.
Set-up of Track, Force Sensor, and Motion Sensor
Figure 1a. Arrangement of apparatus to calibrate the force sensor. A string is
tied to a hook attached to the force sensor
Figure 1c. The apparatus arranged to study a collision. The dynamics cart is
rolling to the left. It will collide with a spring attached to the force sensor. (The
spring is not visible in the picture.)
Fig 1b. A close up of the clamp
and pulley arrangement used to
calibrate the force sensor.
Figure 1d. Close up
photograph showing how the
motion sensor clips to the end
of the track.
1. Set up the 1.2 meter track as shown in Figure 1a. Note that the left end of the track in Figure 1a is
near the computer. The end of the track closest to the interface should be raised about 2 centimeters
by using the black rectangular mass block, and should be at one edge of the table. The adjustable foot
on the opposite end needs to be raised until it doesn’t touch the table. The track needs to be braced, so
that it won’t move during a collision. Brace the far end of the track against the large table clamp.
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2. Attach the force sensor bracket with the force sensor attached to the low end of the track. Connect
the force sensor DIN plug into analog channel A of the interface.
3. Attach a universal clamp and pulley to the opposite end of the track. This pulley assembly will be
used with 500 g of mass to calibrate the force sensor.
4. Measure the vertical height of the track at the rectangular block (measure the distance from the table
top to the bottom of the track) and also measure the distance along the track from the block to where
it touches the table. Use an appropriate trig function to calculate the angle of the track.
5. Weigh the dynamics cart and record its mass in kilograms.
III. Calibration of Force Sensor
The force sensor must be calibrated at the beginning of this experiment. If these instructions are not
followed EXACTLY, you might get a negative force instead of a positive one when the apparatus is
used to measure the force.
1.
2.
3.
4.
5.
6.
7.
Click twice on the Force Sensor icon. In the Sensor Properties window, choose Calibration.
With no force pulling on the force sensor, push the Tare button on the side of the force sensor. Find
the High Point Window on the computer screen. Change the 50 Newton value to zero, and click on
Take Reading.
Set up a pulley at the high end of the track so that a string from the force sensor hook can pass over
the pulley to a hanging 500 gram mass. Do not press the Tare Button again at this point!
Attach a total of mass of 500 grams to the string so that the force applied to the force sensor is (.5kg)
(9.8 m/s2) = 4.9 Newtons.
Find the Low Point Window, and change the 50 Newton value to –4.9, and click on Take Reading.
To check the calibration, look at the Current Reading Window. When the string exerts no force, the
Current Reading Window should display 0.00 Newton ( + about .03N.) When the 500 gram load is
applied, the Current Reading Window should display –4.9N. ( + about .03N.) Check to insure that
these readings are accurate.
Click on OK.
IV. Set Up the Motion Sensor and Record Data from a Collision
1. Replace the pulley and clamp with the motion sensor. Clip the motion sensor onto the track at the
high end of the track.
2. Set the switch on the motion sensor to Narrow Beam.
3. Remove the hook from the force sensor and replace it with the bumper holding the more flexible
spring.
4. Place the dynamics cart (including the mass block) on the track at least 40 centimeters from the
motion sensor.
5. Push on the tare button on the force sensor to zero it.
6. Click on Start.
7. Release the cart.
8. After the cart bounces off the force sensor and rolls uphill, click on Stop.
9. If the velocity data has large spikes in it, call the instructor over to check your results.
V. Obtaining Results from the Graphs
From the graph of force versus time, you will need to determine the impulse, and, from the graph of
velocity versus time, you will need to determine the change in momentum (see page 1 of this writeup).
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In addition, as described below, there is a small correction to the measured impulse due to the force of
gravity on the cart during the collision; to make this correction, you will need to know the collision
time interval.
1. Click on the Zoom Select button.
2. Drag a zoom rectangle enclosing the collision region of the force versus time graph and include only
a small amount of data before and after the collision.
3. The impulse is given by the area under the curve on the Force versus time graph. To obtain this, click
on the Legend Box within the Force versus time graph so it becomes yellow. Select the down arrow
next to  (which represents statistics). De-select everything that is checked, and select Area. The
area under the curve will appear on the graph. Record this value.
4. To obtain the maximum and minimum velocity, select the Legend Box within the velocity versus
time graph so it becomes yellow. Select the down arrow next to  (statistics). De-select everything
that is checked, and re-select maximum and minimum. The maximum and minimum values of the
velocity will appear on the graph. Record these values.
5. From the graph, record the time of the beginning and end of the collision.
VI. Obtain Additional Data
Make a second run by repeating the steps outline above. In addition, make two runs using each of the
other three bumpers: the more rigid spring, the rubber bumper, and the magnetic bumper. Remember
to push the tare button before each run. Print out one graph for each bumper.
For the magnetic bumper, the collision is more extended in time. The zoom rectangle must include all
data points from the full duration of the collision.
VII.
Calculations
For each run, calculate the initial and final momentum of the cart using the initial and final
(maximum and minimum) velocities of the cart, and calculate the change of the momentum of the
cart.
Compare the change in momentum with the impulse of the resultant force and calculate the percent
difference. (See the following note for the correct method to calculate the impulse.
Note: Follow the instructions below unless instructed otherwise.
Theoretically, the change of the cart’s momentum should equal the impulse of the resultant force on
the cart. The resultant force equals the bumper force minus the downplane component of the cart’s
weight. But the force sensor can only measure the impulse of the bumper force. So a correction must
be made to find the impulse of the resultant force. (Since the correction is small, your instructor may
tell you not to make this correction.) To make the correction, calculate Fx , g  mg sin  , the down
plane component of the cart’s weight. Calculate the total collision time t  t f  ti  t = tf - ti.
Calculate Fx , g t . Subtract Fx , g t from the recorded impulse of the bumper force to obtain the
impulse of the resultant force.
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