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```							               Sample Lab Reports: Excellent Lab Report

Impulse and Momentum
George Celona
Lab Partners: Dan Folmar, Mark Myktiuch, and Mike Caban
Date: 4/17/06

Purpose: The purpose of this lab is to analyze the forces and changes in velocity of a
cart attached to a string. A cart will be pushed along a track in one dimension, while a
motion detector will plot the cart’s distance and velocity vs. time. Simultaneously, a
string is attached to the opposite end of the cart, and when it becomes taut, a force sensor
will measure the force acting on the cart and plot a graph of force vs. time. By
comparing the force exerted over some time interval to the change in momentum of the
cart, one can test the impulse-momentum theorem.

Background: The law of conservation of momentum states that in the absence of an
external net force, the momentum of a system will remain unchanged. Therefore, in
order to change an object’s momentum, an external net force must act on the system for
some finite period of time. The impulse-momentum theorem states that the product of
the average force acting on a system and the time over which it acts is equal to the change
in momentum of the object. In equation form, this is:
 f (t )dt  Ft  p  mv f  mvi (for constant mass)
Essentially, this is the same as Newton’s 2nd law, which states that an external net force
will cause an acceleration directly proportional to and in the same direction as the net
force. Using the LoggerPro prggram, one can find the change in momentum of a
dynamics cart by analyzing the velocity vs. time graphs produced by a motion detector.
Also, the impulse can be determined by measuring the area under the force vs. time curve
created by the force sensor.

Materials:
Dynamics Cart and Track        LabPro Interface                PC w/ Loggerpro software
Motion Detector                Dual-Range Force Sensor         Clamp
String                         Rubber Band                     Mass Set

Preliminary Questions:
1. In a car collision, the driver’s body must change speed from a high value to zero. This
is true whether or not an airbag is used, so why use an airbag? How does it reduce
injuries?
An air bag reduces injuries because it increases the time over which the change in
momentum occurs. Regardless of whether the airbag is used, the impulse will be
the same. Since Impulse = Force x Time, this could be a large force over a short
time (like hitting the steering wheel) or a small force over a long period of time
(like the airbag).
2. You want to close an open door by throwing either a 400-g lump of clay or a 400-g
rubber ball toward it. You can throw either object with the same speed, but they are
different in that the rubber ball bounces off the door while the clay just sticks to the
door. Which projectile will apply the larger impulse to the door and be more likely to
close it?
The rubber ball is more likely to close the door because it bounces. Since it bounces
off the door, its change in momentum is greater because in addition to losing its
initial momentum toward the door, it now has momentum in the opposite direction,
hence a greater change. Since the change in momentum is greater, so is the impulse,
and thus the force will be as well.

Procedure:
A dynamics cart with low-friction wheels was attached to a string or rubber band which
was then attached to a force sensor. The cart was placed on a track. A motion sensor
was set up to record the cart’s motion data, while the force sensor was set to record any
tension in the rubber band or string. The cart was given a push toward the motion
detector and away from the force sensor. Eventually, the string or rubber band became
taut and slowed down the cart. The change in momentum of the car was then compared
to the impulse using the data from the motion sensor and the force sensor. This procedure
was repeated using different strings and different masses on the cart.

Data:
mass of cart      Final Velocity   Initial Velocity    Δv      Avg Force    Duration of Impulse    Impulse
Trial         (g)               (m/s)              (m/s)        (m/s)       (N)               (s)              (N.s)
string 1     250.00             0.3571           -0.6403         0.9974     2.500              0.10           0.2454
string 2     750.00             0.3743           -0.6159         0.9902     9.000              0.08           0.7155
r.band
1        250.00             0.2057           -0.2338         0.4395     0.129              1.20           0.1552
r. band
2        750.00             0.3914           -0.4608         0.8522     0.780              0.86           0.6692

Calculations:

Δ v = vf – v0

Favg = Impulse/Duration of impulse

Change in Momentum = (mass of cart) * Δ v
% difference = {| impulse - Δp| /[(impulse +Δp)/2]}*100
Change In Momentum          % difference in
Trial      Impulse (N.s)         (kgm/s)                   values
string 1      0.2454              0.2494                   1.597
string 2      0.7155              0.7427                   3.724
r.band 1       0.1552              0.1099                   34.20
r. band
2         0.6692              0.6392                   4.594

Graphs:

Cart w. string and 500 g mass
Cart w/string and no mass
Cart w/ rubber band and 500g mass
Cart w/ rubber band and no mass

Analysis:
1. Calculate the change in velocities and record in the data table. From the mass of the
cart and change in velocity, determine the change in momentum as a result of the
impulse. Make this calculation for each trial and enter the values in the second data
table.

See Data Tables

2. If you used the average force (non-calculus) method, determine the impulse for each
trial from the average force and time interval values. Record these values in your data
table.

See Data Tables

3. If the impulse-momentum theorem is correct, the change in momentum will equal the
impulse for each trial. Experimental measurement errors, along with friction and
shifting of the track or Force Sensor, will keep the two from being exactly the same.
One way to compare the two is to find their percentage difference. Divide the
difference between the two values by the average of the two, then multiply by 100%.
How close are your values, percentage-wise? Do your data support the impulse-
momentum theorem?
The data does support the impulse-momentum theorem, with the exception of trial
3. The other trials had a very low % difference which is to be expected. In trial
3, the graph of force vs. time looks like a slightly different shape, suggesting that
perhaps another trial should have been performed.

4. Look at the shape of the last force vs. time graph. Is the peak value of the force
significantly different from the average force? Is there a way you could deliver the
same impulse with a much smaller force?

Yes, it looks as though the peak force is much larger than the average force. The
same impulse could be delivered with a smaller force if the time that the force
acts is increased.

impulse-momentum theorem.

The answers to the preliminary questions stand correct.
6. When you use different elastic materials, what changes occurred in the shapes of the
graphs? Is there a correlation between the type of material and the shape?

When the string was used, the force vs. time graphs came to a very sharp peak,
whereas the rubber band had a more rounded shape. Yes, there is a correlation
between the material used and the graph shape because the string only exerted
force for a short time when it became taut, while the rubber band exerted force
the entire time that it was being stretched.

7. When you used a stiffer or tighter elastic material, what effect did this have on the
duration of the impulse? What affect did this have on the maximum size of the
force? Can you develop a general rule from these observations?

The stiffer the material, the shorter the duration of the impulse, which made the
maximum force larger. Therefore, the shorter the time, the larger the force to
get the same impulse. This is obvious since impulse = Force x Time.

Conclusion:

The group successfully completed the purpose of this lab. This was done by showing that
the impulse exerted on the cart as measured by the force sensor was nearly equal to
the change in momentum of the cart measured by the motion detector, with an
average difference of about 11%. However, this value is skewed because only one of
the data points was above 5 % error, and this was probably an error in the force vs.
time graph, since its shape was different from the other 3. For the other trials,
discrepancies in values could be a result of friction in the track, an unlevel experiment
surface, or incorrect highlighting of the graphs. Friction was not accounted for in any
of the trials, so this could be a cause of error which would cause the final velocity to
be lower than predicted by the impulse momentum theorem. However, it should be
slight provided that the graphs were highlighted just before and just after the impulse
was exerted. An unlevel surface would cause the force sensor to be incorrect since it
only measures horizontal force. Clearly, in the majority of the trials, these problems
were minor, and so the data shows that the impulse-momentum theorem is correct.

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