Impulse
Lab 7
In this experiment you will verify the
elationship between force and
momentum through impulse.
Using the short spring adapter, the
iOlab will measure force as a
function of time, as well as the
velocity before and after, a
collision.
(1)
(2)
(3)
Demonstration Video
https:
www.youtube.com/watch?v=ELLk7WrYuHg
1. Attach the hook to your iOlab. We will now measure the actual mass of the device. We
will do this by picking the mass up and holding it steady, then measuring the applied force
on the object as it balances out gravity.
m
Part 1 – Finding Mass of iOLab (skip if you have done this
in previous experiments)
2. As always, first Cali
ate both the
accelerometer and the force sensor.
3. Choose the Accelerometer Sensor
and select Ay.
4. Select the Force Sensor.
5. Click Record, then pick up the device,
hold it for a second or two, then set it
ack down and stop recording.
6. Zoom in on the constant non-zero
applied force after you have picked up
the mass and before you set it down.
7. After zooming in, highlight a section of
the graph. Your graphs should now look
like...
...this.
8. Write down the average acceleration As your object is at rest, your device is
directly measuring the acceleration due to
gravity and not the actual acceleration.
9. Write down the average force.
10. Now calculate the actual mass of the device by...
Include this value in your report.
Part 2 – Impulse
1. Attach the short spring to your iOlab.
2. As always, first Cali
ate both the accelerometer and
the force sensor.
3. Choose the Wheel Sensor and select Velocity only.
4. Select the Force Sensor.
5. Find a smooth surface and somewhat sturdy object
for your iOLab to collide with such as the iOLab box or
your phone.
6. Practice pushing (wheels down) your iOLab into the
ox and allowing it to recoil. You do not want to push
the device so hard that it may damage the device (or
your wall). You want to make sure that there is time
after your push before the collision to measure the
velocity.
7. Click Record. Push the object into the wall and allow it to recoil. Repeat this process a total
of three times. Stop recording. Your graphs should look like the graph below. Include a screen
grab of your results in your report.
8. Next, zoom into one of the peaks. Your Force versus time, and velocity versus time, graphs
should look as follows.
9. Create a table as below to collect the important date from the experiment. Include this table
in your report.
10. Calculate the area under the Force versus time graph (J1). Place it in the table below under
Trail 1. Include a screen grab of your graph in your report.
11. Make a note of your approximate initial and final time associated with the collision and
include them in your table.
12. Using your t values and area under the curve (J1), calculate the average force.
13. Indicate the initial and final velocity of the collision in your table. As impulse is the change in
momentum, which is a vector, direction matters (indicate positive/negative sign). Include a
screen grab of your graph in your report.
14. As momentum is defined as p = mv, calculate the change in momentum (J2).
15. As you have now calculated impulse two separate ways, calculate the percent difference
etween the measurements.
16. Zoom out and repeat steps #8-15 for the remaining two collisions. Include their data under
Trial 2 and 3 your table.
14. Discuss your results with your lab partners. Were your Impulse values close? What were
sources of uncertainty? What could you have done differently in your experiment/analysis to
improve your results.
Extended Questions
15.
16.
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Centripetal Motion
Lab 8
ω
ac = ω2
Consider an object rotating at angular
velocity ω. The centripetal acceleration at
distance r from the rotation axis (here the
center of the object) is given as ac = ω2 r.
ω
ac
ax
ay
ac2=ax2+ay2
Just like any vector, ac can be decomposed
into x and y components.
ω
ac = ω2
Accelerometer – measures the acceleration.
Gyroscope – measures the angular velocity.
ω
As the accelerometer is offset from the
gyroscope by a distance r...
ω
ac
ax
ay As the accelerometer is offset from the
gyroscope by a distance r, by measuring the
centripetal acceleration and angular speed,
you will verify this distance dynamically.
ac = ω2
Centripetal Acceleration
1. Say something nice to your lab partners.
2. As always, first Cali
ate both the accelerometer and the
force sensor.
3. Choose the Accelerometer, and select only Ax and Ay.
4. Select the Gyroscope, and select only ωz.
5. Find a smooth surface to spin your device on.
6. Practice spinning your iOLab (wheels up) on a surface.
7. Select Record, then spin your iOLab on the floor (wheels
up) and allow the iOLab to come to rest. Repeat this step four
more times. Stop collecting data.
***Here the object is rotated clockwise, hence ω is negative.
You may rotate your iOLab either direction.
8. Zoom into one of the spins, they should look like below***. The areas highlighted co
espond
to your rotation. While the relationship between centripetal acceleration and angular velocity,
is consistent throughout, we will
choose the time right after your
influence when the angular
velocity is at a maximum.
9. Note the maximum angular
velocity. Place your data in a table
like the one below.
10. Note the co
esponding x- and
y-components of the centripetal
acceleration. Place your data in a
table like the one below.
Table 1
Table 1
9. Note the maximum angular
velocity. Place your data in a table
like the one below.
10. Note the co
esponding x- and
y-components of the centripetal
acceleration. Place your data in a
table like the one below.
Table 2
ac = ω2
11. Repeat steps 9 and 10 for the remaining spins and dill
in Table 1.
12. As the relationship between centripetal acceleration
and angular velocity is
y graphing angular acceleration (y-axis) versus angular velocity squared (x-axis) you retrieve
the distance between the accelerometer and gyroscope r as the slope. Use a spreadsheet
program (Excel/Google Sheets/etc.) to create such a graph. Use XY-Scatter (i.e. no
connecting line between the points) for the data, and then use a linear fit. Include a copy of
this graph and Table 2 in your report.
13. Record the slope of your graph as the experimental distance rexp.
y = ms x +
ac2=ax2+ay2
14. Using a ruler, measure the actual distance between
the accelerometer and the gyroscope ract.
15. Calculate the percent e
or between the actual
distance and the experimental value.
16. Compare your experimental value of rexp and your
percent difference with your your lab partners.
16. What force (and co
esponding torque) causes your iOLab to come to rest after you
elease the object?
17. How could you use the data you took to calculate the co
esponding angular
acceleration (deceleration) to 16?
Bonus: What additional measurements/information would you need to calculate the
moment of inertia of the iOLab device from this experiment?
Extended Questions
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