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Impulse
and Momentum
1. Introduction
The
impulse-momentum theorem relates impulse, the average force applied
to an object times the length of time the force is applied, and
the change in momentum of the object:
Here
we will only consider motion and forces along a single line. The
average force, is the net force on the object, but in the case
where one force dominates all others it is sufficient to use only
the large force in calculations and analysis.
For
this experiment, a dynamics cart will roll along a level track.
Its momentum will change as it reaches the end of an initially slack
elastic tether cord, much like a horizontal bungee jump. The tether
will stretch and apply an increasing force until the cart stops.
The cart then changes direction and the tether will soon go slack.
The force applied by the cord is measured by a force sensor. The
cart velocity throughout the motion is measured with a motion sensor.
Using "datalogger software" to find the average force
during a time interval, you can test the impulse-momentum theorem.
2. Objective
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Measure
a cart momentum change and compare it to the impulse it receives. |
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Compare
average and peak forces in impulses. |
3. Equipment
List
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Datalogger
interface |
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Motion
sensor |
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Force
sensor |
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Dynamics
cart and track |
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Elastic
cord |
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String |
Procedure
| 1.
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Measure
the mass of your dynamics cart and record the value in the data
table.
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| 2.
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Connect
the motion sensor and force sensor to the datalogger interface.
Reset the force sensor.
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| 3. |
Open
the datalogger software and the experiment worksheet.
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| 4. |
Place
the track on a level surface. Confirm that the track is level
by placing the low-friction cart on the track and releasing
it from rest. It should not roll. If necessary, adjust the track.
|
| 5. |
Attach
the elastic cord to the cart and then the cord to the string.
Tie the string to the force sensor a short distance away. Choose
a string length so that the cart can roll freely with the cord
slack for most of the track length, but can be stopped by the cord
before it reaches the end of the track. Clamp the force sensor
so that the string and cord, when taut, are horizontal and in
line with the cart motion.
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| 6. |
Place
the motion sensor beyond the other end of the track so that
the detector has a clear view of the cart motion along the entire
track length. When the cord is stretched to maximum extension,
the cart should not be closer than 0.4cm to the detector.
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| 7. |
Reset
the force sensor to zero.
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| 8. |
Practice
releasing the cart so it rolls toward the motion sensor, bounces
gently, and returns to your hand. The force sensor must not
shift and the cart must stay on the track. Arrange the cord
and string so that when they are slack they do not interfere
with the cart motion. You may need to guide the string by hand,
but be sure that you do not apply any force to the cart or force
sensor. Keep your hands away from between the cart and the motion
sensor.
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| 9. |
Start
the datalogger software to collect data; roll the cart and confirm
that the motion sensor detects the cart throughout its travel.
Inspect the force data. If the peak is flattened, then the applied
force is too large. Roll the cart with a lower initial speed.
If the velocity graph has a flat area when it crosses the x-axis,
the motion sensor was too close and the run should be repeated.
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| 10. |
Once
you have made a run with good distance, velocity, and force
graphs, analyse your data. To test the impulse-momentum theorem,
use the datalogger software to calculate the velocity before
and after the impluse and record the value in your data table.
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| 11. |
Now
record the time interval of the impulse.
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| 12. |
Perform
a second trial by repeating Steps 9 - 11, and record the information
in your data table.
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| 13. |
Change
the elastic material attached to the cart. Use a new material,
or attach two elastic bands side by side.
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| 14. |
Repeat
Steps 9 - 12, and record the information in your data table.
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DATA
TABLE
| Trial |
Final
Velocity
 |
Initial
Velocity
 |
Change
of Velocity
|
Average
Force
F |
Duration
of Impulse
|
Impulse |
| Elastic
1 |
(m/s) |
(m/s) |
(m/s) |
(N) |
(s) |
(N*s) |
| 1 |
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| 2 |
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| Elastic
2 |
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| 1 |
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| 2 |
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| Trial |
Impulse
|
Change
in Momentum |
%
Difference between Impulse and Change in Momentum |
| Elastic
1 |
(N*s) |
(kg*m
/s) or (N*s) |
(N*s) |
| 1 |
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| 2 |
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| Elastic
2 |
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| 1 |
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| 2 |
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Analysis
| 1.
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Calculate
the changes in velocities and record the results 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. |
| 2.
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Determine
the impulse for each trial from the average force and time interval
values. Record these values in your data table. |
| 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?
Does your data support the impulse-momentum theorem? |
| 4. |
Look
at the shape of the last force versus 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? |
| 5. |
When
you use different elastic materials, what changes occur in
the shapes of the graphs? Is there a correlation between the
type of material and the shape? |
| 6. |
When
you used a stiffer or tighter elastic material, what effect
did this have on the duration of the impulse? What effect did
this have on the maximum size of the force? Can you develop
a general rule from these observations? |
Extensions
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Use
other elastic materials and repeat the same experiment. |
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