Force vs time. IMPULSE AND MOMENTUM Pre Lab Exercise: Turn in with your lab report

Transcription

1 IMPULSE AND MOMENTUM Pre Lab Exercise: Turn in with your lab report Newton s second law may be written r r F dt = p where F is the force and p is the change in momentum. The area under the force vs. time curve is called the impulse. Here is a typical force vs. time curve for a collision 1.2 Force vs time 1 Force (kn) Time (ms) In part one of this lab you will launch a glider from two chosen displacements of the rubber band and measure the resulting change in momentum of the glider when it collides with the force probe. In part two of this lab you will again launch the glider from the two chosen displacements and measure the resulting impulse on the force probe.

2 Now answer the following questions 1. Each little box in the above graph corresponds to an area (Impuse) of J = N s Estimate the area under the curve by estimating the number of rectangles under the curve and multiplying by the impulse in each rectangle Enter your estimate here 2. If a glider that has a mass 250 grams collides at an initial speed of 0.5 m/s with the impulse from #1, what would the final speed of the glider be? Show your work here: Enter your answer here 3. If a glider of mass 250 grams collides elastically (final speed equals initial speed) with the impulse given in #1 what must have been the initial and final speeds of the glider Show your work here: Enter your answer here

3 PURPOSE: The primary purpose of this experiment is to compare the impulse during a collision to the change in momentum caused by that impulse. APPARATUS: Air track & glider Force Probe Sonic Ranger Balance Mass holder Mass assortment Computer with ULI interface Sonic Ranger Force Probe Glider Airtrack Macintosh ULI Switch METHOD: In this experiment we want to examine a one-dimensional collision on a level air track by computing the impulse imparted to the glider and comparing this to the calculated momentum change. The sonic ranger is a sonar device that sends out and receives high frequency sound waves. When the reflected waves reach the sensor, the time of flight is used in conjunction with the speed of sound in air to determine the position of the object responsible for the reflections. A sonic ranger is used to monitor the speed of the glider as it collides with the force probe. This is done two times for a single starting position. Using this same starting position the computer now monitors the Force Probe. The Force Probe utilizes a flexible copper strip connected to a magnet. When the strip is flexed, the magnet moves closer to a sensor. This flex is proportional to the applied force. Using the DataLogger software, the graph of the force applied to the probe is integrated to find the impulse applied to the probe. The same impulse is applied by the

4 probe to the glider by Newton's third principle. For each of the three starting positions, the impulse is compared to the momentum change. PROCEDURE: 1. Make sure that the air track is level. 2. Measure the mass of the glider as precisely as possible using a balance in the lab. Momentum data 3. Click on Momentum. 4. You will launch the glider from the right side of the track by pushing the rubber band back about 4 cm then releasing the glider. Record the launch position so that it can be repeated. Click on Collect, release the glider within a couple of seconds and stop the glider shortly after the collision. 5. You should now see a graph of distance vs. time. 6. To compute the momentum change during the collision it is necessary to know the speed immediately before and immediately after the collision. Since the speed is nearly constant before and then again after all we need is the average speed during the times preceding the collision, then after it. Starting at your left, click and drag to highlight a portion of the graph for which the slope is nearly constant before the collision. With this area highlighted select Linear Fit from the Analyze menu. Do the same for a region after the collision. Your graph should now look something like this:

5 7. Save this first collision data on your disk, then make a second run from a different launching position. Save this second run also. Save your data as NAME.cmbl 8. Select Quit from the file menu. Impulse data 9. Select Impulse 10. Remove the Force Probe from the track by taking off the wing nuts that hold it. Select Sensors... from the Setup menu click on the Calibrate tab then click on Perform Now. Hang the probe from the hanger provided. With NO mass attached enter zero in the VALUE box then click on Keep. Then suspend a 50 g mass holder with an additional 450 g mass attached. (this 500 g has a weight of 4.9 N) Enter -4.9 as the calibration force in the VALUE box and click on Keep. Finally click on OK to return to the program. Remove the mass holder and masses and reinstall the Force Probe on the air track when the calibration is complete. Be sure the Force Probe is properly installed. Click on Zero at the upper right of the graph.

6 11. When you again have control of the cursor click on Collect, move the glider to your original starting position and release it as before when it says please wait on the screen and stop the glider after the collision. The resulting graph should look something like: Collision Integral = 0.18 Force (N) Time (seconds) 12. Select the region to integrate by dragging the mouse over the region with the button held down. From the Analyze menu select Integral. The integral value (area under the graph) is shown at the upper right of the graph. Click and drag again to change the limits of your integration if necessary. 13. When you are satisfied that your data is reasonable save it as NAME.cmbl, redo the experiment from procedure 11 to get a second set of force data. 14. Save this experiment on your disc under a different name as in step 12. Select Quit from the File menu. Eject your disc from the Special menu. ANALYSIS: 1. Take your disc to a computer with a printer. Make sure the computer is on and insert your disc. Open your first momentum file. 2. Referring to steps 10 and 11, print the graph appropriate for determining your best value of the velocity before and after impact. 3. From the File menu open the set of Force data. Print appropriate graphs for both trials. 4. Find the average impulse from your Force data. Compare the average impulse to the average momentum change by finding the percent difference.