Studio Physics I
Impulse and Momentum Change
The impulse, J=FDt , is a quantity that
combines the applied force and the time interval over which the force acts.
J = Dp = pf - pi
An Egg Toss Contest
1. Suppose that an egg of mass m is heading toward you at speed v. What is the momentum of the egg in terms of m and v? Now suppose that you catch the egg, bringing it to rest. What is the momentum of the egg now? What is the magnitude of the change in the egg’s momentum during the catch? What is the magnitude of the impulse imparted to the egg during the catch?
2. Does the total momentum change differ if you catch the egg more slowly? Or, is the momentum change the same?
3. Suppose the time to bring the egg to a stop is Dt. Would you rather catch the egg in such a way that Dt is small (for example, in a baseball mitt held stiffly out in front of you like a baseball catcher) or in such a way that Dt is large (for example, by allowing the mitt to move as the egg comes into contact with it)?
4. What do you suspect might happen to the average force you exert on the egg while catching it when Dt is small?
5. Combine all of your answers to the questions above into two or three sentences discussing the physics of an egg toss. However, rephrase your discussion so that you specifically focus on and use the term impulse in your discussion.
Impulse and Momentum Change
A) Open LoggerPro. Then go to file, open, rtp (or RealTime Physics), mechanics, L8A2-2 DFS (Impulse & mom). BE CAREFUL, THERE ARE TWO FILES WITH NEARLY IDENTICAL NAMES. YOU NEED TO GET THE ONE WITH DFS ON IT.
B) Once you have opened the correct file, the next thing that you must do is to calibrate your force probe. This will require making two probe readings with two different and known forces applied to the force probe. The forces are applied to the probe through the hook ATTACHED TO THE FORCE PROBE. Follow the steps below to carry out the calibration:
u Click “Set-up” at the top of the computer screen
u Click “Sensors”
u Click on the F with the DIN1 below it.
u Click the “Calibrate” tab above the F
u Click on “Perform now” off to the right (If you don’t have “perform now” showing, you did not make a connection to the ULI when opening the file. You will have to completely close LoggerPro and reopen the file.)
u Remove the hanging mass from the force probe if it is attached. There is now zero force on the probe.
u Enter zero in the box (replacing the –5) for the force
u Click “keep”
u Hook the string for the hanging mass on the hook of the force probe
u While holding the cart still, run the string over the pulley and let the mass hang down, pulling on the force probe. The force applied to the probe is now the weight of the mass. That is, (0.052 kg)(9.8 m/s2) = 0.51 N.
u While still holding the cart with hanging mass attached as discussed in the step above, enter 0.51 in the second box that has appeared on the right (replacing the 5) for the force.
u Click “keep”
u The calibration process is complete. Click on OK to close the calibration box.
C) Check to make sure that the calibration process has been successful. Failing to do this may result is a complete waste of time doing everything that follows. To check the calibration, read the force displayed on the bottom of the screen while the hanging mass pulls on the stationary cart. The force should be about 0.5 N. Now remove the string attached to the hanging mass from the force probe. Again read the force displayed at the bottom of the screen. The force should now be close to 0 N. If both of these readings check out, all is well. If you are having trouble, ask for help.
D) The experiment file has been set up to record force and motion data at 50 data points per second. A pull on the force probe will be recorded as a positive force, and velocity away from the motion detector is a positive velocity.
E) Be sure your track is level. The cart should not roll either direction when placed at rest in the center of the track. If the track is not level, use the leveling screw attached to the end stop to level the track.
6. Remove the hanging mass from the force probe. You will not use it again unless you need to recalibrate your force probe for some reason. Consider the following situation: The cart is at rest ( no hanging mass attached!!) when you give it a short pull with your fingers on the hook of the force probe. You then let the cart move freely. Take a minute or two to sketch an individual prediction of what the graphs of velocity versus time and force versus time would look like for the cart. Show times just before, during and after the pull on the force probe. After you make your own predictions, discuss them within your group.
7. Place the cart at least 0.5 meters away from the motion detector. Click the collect button to begin taking data. When you hear the motion detector start clicking, give the cart a short pull on the hook of the force probe, and then let the cart move freely. While you are collecting data, be sure to holding the cord to the force probe up off of the table (that is, don’t let the cord drag or pull on the cart), and keep your hand farther away than the cart from the motion detector. Sketch the actual velocity versus time and force versus time graphs on your paper. Write down the approximate value of the maximum force, the time period over which the force was applied and the velocity of the cart after the pull.
8. Examine the graphs carefully. Discuss how the time interval over which the force is applied compares to the time interval over which the velocity changes. Does the velocity change in time periods during which there is no force applied to the cart?
9. Discuss your results and answer to the question above in terms of the impulse applied to the cart and the change in the cart’s momentum.
10. Use the analysis and statistics features in the software to measure the average velocity of the cart before and after the pull. Don’t forget to include a sign. ( To get the average velocity from the graph, use your mouse to mark the region of interest, then go to analyze, then statistics and say ok). What is the average velocity after the pull? What is the average velocity before the pull?
11. Calculate the change in momentum of the cart. Show your calculations. The mass of the cart is 500 grams and the mass of the force probe is about 165 grams.
12. Use the integration routine in the software to find the area under the
force—time graph. This is the impulse. (The area under a curve is the same as the
integral of force vs. time). ( To do this, use your mouse to mark the region of interest, Go to analyze, then integral and say ok). Did the calculated change in momentum of the cart (question above) equal the measured impulse applied to cart during the pull? What is the percent difference between them?
13. Suppose that the cart had twice the mass as in activity above and you gave it approximately the same magnitude of a pull for the same time period. How large do you think the impulse would be? The same as before? Larger? Smaller? Why? How large do you think the change in momentum would be? The same as before? Larger? Smaller? Why?
14. Test your predictions. Add masses to your cart to make the total mass twice about twice as large. (Each black bar is 495 grams). What is the new mass of your cart and force probe? Zero the force probe by clicking on the zero button at the top of the screen. Then click collect, wait for the motion detector to start clicking and then give the cart the same pull (to the best of your ability). Be sure to keep the force probe cord from dragging and keep your hand out of the way of the motion detector. Try several times or until you get about the same force and duration as for your initial try above. (You should have written it down in #7). Sketch your graphs on your activity sheet.
15. Find the average velocity, as you did before and calculate the change in momentum. Find the impulse as before. Is the impulse now about the same as before or is it different by a factor of 2 (the change in the mass)? Is the change in momentum about the same as before or is it different by a factor of 2 ? What is different by about a factor of 2?