Name____________________________________
PHYSICS 124 LAB 6:
IMPULSE-MOMENTUM THEOREM AND THE
CONSERVATION OF MOMENTUM PRINCIPLE
GOAL:
In this lab exercise, your mission is to use the laboratory apparatus, with which you are already
familiar (force sensor and motion detector), to study the Impulse-Momentum Theorem and the
Principle of Conservation of Momentum. In the following procedure it is assumed that you
remember how to use the apparatus to make the measurements required. Your group may at
times have to refer back to the descriptions of previous lab exercises for a quick review.
You will be asked to answer in detail many questions regarding how the quantities you have
measured relate to the physical ideas. Make sure that you discuss the questions with your group,
with other groups, and with your lab instructor or lab assistant as is necessary to achieve a full
understanding of each one. Write a thorough answer to each question before moving on.
Part I
Measuring Impulse
1. Plug a force sensor into the CH1 input and connect a Motion Detector into the DIG/SONIC1
input of the LabPro interface, and start the LoggerPro 3.4.1 program on your computer. Zero the
force sensor (which should be placed horizontal on the table) using “Experiment” – “Zero…”
and then uncheck the DIG1: Motion Detector box because we only want to zero the Force
Sensor, and then click “OK”.
2. Set the sampling rate for the force transducer to 1000 samples/second (use “Experiment” ”Data Collection” and enter 1000 in the sampling rate box). Put the force transducer on the
PASCO track and use a thumb and finger with a squeezing force to keep it from moving during
the following collision. You will roll one of the carts toward the force probe and cause a
collision with the movable arm of the sensor, which can be observed on a force vs. time plot.
Make sure that the time axis is set for a sufficient amount of time to observe the collision event.
You may have to play with different cart speeds to observe a reasonably well behaved force vs.
time curve. You should use the end of the cart with the spring-loaded plunger to produce a
"longer" collision. At the same time you should have the Motion Detector behind the cart in
order to measure its speed before and after the collision.
3. Rescale the time axis so that the collision takes up most of the plot. You should include a
region of the motion both before and after the collision, so that you can fit a line to the position
curve before the collision to get the initial velocity before the collision, and, similarly, fit another
line to an interval on the position curve to get the final velocity after the collision.
29
4. So far you have measured a time-dependent force. In other words, the force vs. time plot is
not a straight, horizontal line. In class, we have concentrated only on calculating an impulse by
using an average value of the force for the time interval over which it acts. To analyze your
force vs. time data, highlight the force curve by dragging the mouse from the initial time of the
impulse to the final time of the impulse, and select “Statistics” from the Analyze menu (or click
on the STAT button on the main menu). The computer will provide you with the average (mean)
value of force. Record the value of Fave below.
5. Write down from your force vs. time plot the values of ti and tf , the times when the force was
first applied and when the force ceased to be applied, respectively.
6. From the measurements made in the previous two steps, calculate in the space below the
impulse delivered to the cart during the collision. (You could also try the “Analyze” …
“Integral” sequence to see how the computer shades the area in red and calculates the impulse.)
7. Describe in detail below the effect of this impulse on the cart. The cart has a mass of about
500 g (weigh it to be sure) and you can calculate the initial momentum and the final momentum
from this mass and your measurements of initial and final velocities. Are your measurements
consistent with the impulse-momentum theorem?
30
Part II
Collisions and Conservation of Momentum
Now that you have observed the relationship between impulse and momentum, let's look at
elastic collisions between two carts. Place on the track two carts with magnets embedded in the
ends so that the magnets will repel each other when the carts approach each other at close
distances. This configuration of the carts will result in an essentially elastic collision if the carts
don't actually touch when they collide. For the following, refer to the elastic 1D collision
equations from your text (where we will use v2o = 0). You should exit the LoggerPro program,
disconnect the force sensor, and then plug in the motion detector to the DIG/SONIC1 port. Then
start the LoggerPro program again before making the velocity measurements below. You should
position the motion detector so that it observes the motion of the first cart which is initially
moving.
When cart 1 of mass m1 moving with a velocity V10 collides elastically with cart 2 of
mass m2 (stationary) (V2o = 0), the resulting final velocities of each cart in terms of the initial
velocity V10 of the moving cart are
 m1 - m2 
V10
m
+m
 1
2 
V1 = 

2m1
 m1 +m2
V2 = 

V10

or
V1  m1 - m2 
=

V10  m1 +m2 
V2  2m1 
=

V10  m1 +m2 
Now consider two carts with equal mass. Push the first cart into the second cart which is
at rest (stationary cart) in the middle of the track, and observe what happens and measure the
final velocity V1 of the first cart that was initially moving with velocity V10. Record the
velocities V10 and V1 in the data sheet. Compare with the predicted value. Now take one of the
black metal 500g blocks and place it in the stationary cart. This should approximately double the
mass, but you may want to weigh the cart to be sure. Again push the cart 1 at a reasonable speed
into the second cart, and measure the initial velocity V10 and final velocity V1 of the cart that was
initially moving. Does the ratio of the final velocity over the initial velocity (V1/V1o) agree with
the prediction? Continue the process of adding 500 gram masses on cart 2 and record your
results in the data table on the next page. Compare the measured V1 / V1o with the predicted
value for each case until 4 black metal blocks have been added to the initially stationary cart.
What do you observe? Is there a trend in the resulting final velocities?
31
Mass
(measured)
(measured)
(measured)
(Predicted)
V10
V1
V1
(Expt)
V10
V1  m1 - m2 
=

V10  m1 +m2 
m2 = m1
m2 = 2m1
m2 = 3m1
m2 = 4m1
What should happen as the stationary mass m2 becomes infinitely massive? Why?
Now redo the variable mass experiment by placing additional mass on the cart 1 which is
initially moving and by keeping the initially stationary cart 2 empty. Add mass to the moving
cart 1 in 500 gram increments. For each case, make the same measurements and observations as
you did in the steps above. How does adding mass to the moving cart affect the final velocities?
Is there a trend? What is it? What is the major difference in the motion of the carts after a
collision when adding the mass to the moving cart as opposed to the stationary cart?
(measured)
Mass
V10
(measured)
V1
m1 = m2
m1 = 2m2
m1 = 3m2
m1 = 4m2
32
(measured)
V1
(Expt)
V10
(predicted)
V1  m1 - m2 
=

V10  m1 +m2 