Verifying the Conservation of Linear Momentum

Transcription

1 Chabot College Physics Lab Scott Hildreth Verifying the Conservation of Linear Momentum Introduction In this experiment, you ll stage s using very-low friction rolling carts, and compare initial and final momenta to verify whether linear momentum is indeed conserved. This lab will challenge your skills in measurement, your understanding of, and especially your ability to analyze errors. Your goals for the exercise are: Observe s between two carts, testing for the conservation of momentum. Measure energy changes during different types of s. Classify s as elastic, inelastic, or completely inelastic. Demonstrate your understanding of the difference between precision - measuring carefully and accounting for in your measurement - and accuracy - measuring correctly and coming close to the right answer. Work together in a group setting, dividing up the work fairly and double-checking one another. You will need at least two people to take data, two people to analyze data, someone to keep the team on task, and someone to ensure that the write up is completed and turned in on-time. Write up Expectations Turn in one full write up for the team, on or Thursday 3 December /Friday 4 December (at the usual lab time for your team). Include: a) The names and lab duties of each of the participants, and a short abstract that summarizes your results, including the achieved percentage error between measured and expected values of initial and final momenta for the experiments in general. b) The organized data and analysis tables for all experiments, either on paper or preferred as a spreadsheet. c) The answers to the questions asked in the lab and at the conclusion. d) A thorough analysis of sources of in your work, and the errors you saw in comparing initial and final momentum for each experiment.

2 Chabot College Physics Scott Hildreth Verifying the Conservation of Momentum Experiment A: One Cart at Rest & Velcro Bumpers 1. You ll use two dynamics carts for this experiment, rigged with a sail to trigger the photogates, and enable you to calculate their average velocity. Measure the masses of your carts and record them in your data table, along with your measurement uncertainties. Label the carts as cart 1 and cart 2. Measure the length of the sail ( x) and its. 2. Set up the track so that it is horizontal. Test this by releasing a cart on the track from rest. The cart should not move. Push the cart along the track, and verify that two photogates within cm of each other register the same time interval t, implying the same velocity. If the photogates do not display exactly the same times, repeat the test and record their average difference. Question 1: How will a difference in the two photogates measurements of a cart supposedly at constant speed affect your in calculations of momenta? 3. Practice creating gentle s by placing cart 2 at rest in the middle of the track, and release cart 1 so it rolls toward the first cart, Velcro bumper toward Velcro bumper. The carts should stick together without knocking one another off the track. 4. Place a photogate at each end of the track, one to measure the initial velocity of cart 1, and one to measure the final velocity of the combined carts. 5. Create a with cart 2 at rest, measuring both the inbound cart 1 initial speed, and the outbound speed of cart 1 and cart 2 stuck together. Record the Run #1 t values for both photogates. Be sure to consider the uncertainties in your measurements, and include the appropriate significant figures. 6. Repeat Step 5 an additional two times, and record values for t for these Runs #2 & 3. Experiment B: One Cart at Rest & Magnetic Bumpers 7. Turn the carts so the magnetic bumpers face one another. The carts should bounce off one another smoothly. Practice making the new, again starting with cart 2 at rest. 8. In this experiment, you may need to use one photogate twice first to record the initial velocity of a cart, and then to record a final velocity (if any). Be sure to have one team member read off the initial velocity of the cart and then immediately zero out the photogate so that it can capture a second separate t. Create a with cart 2 at rest, measuring speeds of cart 1 ( and the ) as well as cart 2 ( the ). Measure and record the appropriate t values for three trials (Runs #4-6). Question 2: If the carts are approximately equal in mass, the should cart 1 be moving at all? If it does move, what does that imply about the accuracy of the experiment? Experiment C: One Cart at Rest & Velcro-Magnetic Bumpers 9. Face the Velcro bumper on one cart to the magnetic bumper on the other. The carts will not stick, but they will not smoothly bounce apart either. Practice this, again starting with cart 2 at rest. 10. Using the procedure in Step 8, record the t s in your data table for three trials (Runs #7-9).

3 Chabot College Physics Scott Hildreth Verifying the Conservation of Momentum Experiment D: Both carts in motion & Velcro Bumpers 11. Turn both carts so that their Velcro bumpers will engage, and practice creating a where the carts are moving, most likely at difference speeds, and then stick together without knocking one cart off the track. 12. Place a photogate at each end of the track, one to measure the initial velocity of cart 1, and one to measure the final velocity of the combined carts. As with step 8 above, you ll need to move quickly to read the t values for the photogates both coming and going. 13. Create s with both carts in motion, measuring both the inbound initial values for t for each cart, and the outbound valued of t for cart 1 and cart 2 stuck together. Record the t values for both photogates for 3 trials (Runs #10-12) Experiment E: Both carts in motion & Magnetic Bumpers 14. Change the by turning the carts so the magnetic bumpers face one another. The carts should bounce off one another smoothly. Practice making the new, again starting with cart 2 now in motion. 15. In this experiment, you will need to use BOTH photogates twice first to record the initial velocity of each cart, and then to record their final velocities. Be sure to have one team member read off the initial velocity of the cart and then immediately zero out the photogate so that it can capture a second separate value for t. Create s with both carts in motion, measuring the t s for both carts and the. Measure and record the appropriate t values for three trials (Runs #13-15). Experiment F: You design it! 16. So far you have used carts with approximately the same mass. Design an experiment that explores the conservation of momentum where one of the carts has more mass (at least g). You can opt for a simple, where one mass is at rest, or a more complex where both are in motion. Either way: a. Develop a scenario to explore, b. Create your hypotheses (what do you think will happen? Which cart will move, in which direction the?) c. Set up the experiment, measure the variables, consider your uncertainties, and record your results. d. Decide how many trials you need to run; the sample data table has a few spaces, but you are free to use more or less depending upon your preferences.

4 Chabot College Physics Scott Hildreth Verifying the Conservation of Momentum Analysis 1. Assume the motion of cart 1 is along the positive x direction. Determine the momentum (mv) of each cart the, the, and the total momentum and the. Be sure you include the correct sign of the momentum. Calculate the ratio of the total momentum the to the total momentum the. You can enter the values into the Data Analysis Table #1, but preferably you should do the analysis in a spreadsheet. 2. Determine the kinetic energy (½ mv 2 ) for each cart and the. Calculate the ratio of the total kinetic energy the to the total kinetic energy the. Enter the values in your Data Analysis Table #2 (or your spreadsheet). 3. If the total momentum for a system is the same and the, momentum is conserved. If momentum were conserved, what would be the ratio of the total momentum the to the total momentum the, p total(final) / p total(initial)? 4. If the total kinetic energy for a system is the same and the, we say that kinetic energy is conserved. If kinetic were conserved, what would be the ratio of the total kinetic energy the to the total kinetic energy the? 5. For your trials, inspect the momentum ratios. Even if momentum is conserved for a given, the measured values may not be exactly the same and due to measurement. The ratio should be close to one, however. Is momentum conserved in your s? Which experiment produced the most accurate results? Which produced the least accurate results? Why? 6. Repeat the preceding question for the case of kinetic energy. Is kinetic energy conserved in the magnetic bumper s? How about the Velcro s? Is kinetic energy consumed in the third type of studies where the bumpers were mixed? Classify the three types as elastic, inelastic, or completely inelastic. 7. Analyze the experiment you designed, where the masses were different. Were your hypotheses confirmed? Did the difference in mass improve or negatively affect the accuracy of your results? 8. Now look at your uncertainties. The in velocity depends upon the in mass and the in velocity; the in velocity depends upon the uncertainties in time and the measurement of the size of the sail. Develop a general equation to estimate the overall percentage for each measurement of individual momentum (initial and final) for each cart. 9. How can you estimate the overall percentage in the total momenta (initial and final)? For example, if p total = p initial (1) + p initial (2), what is p total(initial) /p total(initial) x 100? Develop another general equation to calculate that value for each experiment s total initial and final momenta. 10. Now consider the final ratio p total(final) /p total(initial). Given the percentage uncertainties you found for each value of the total momenta, what is the in that ratio? Using a spreadsheet, calculate this value for each trial, and create an overall average for each experiment. A sample table is attached; adapt this as needed. Discuss how your overall measurement affects your conclusions about whether momentum was conserved or not for each experiment. 11. You do not have to repeat the analysis for your kinetic energy calculations, but you should consider and answer this final question: How do your uncertainties affect the assessment of whether energy was conserved or not for each experiment? Explain.

5 SAMPLE DATA TABLES Mass of Cart 1 kg +/- Mass of Cart 2 kg +/- Sail Length m +/- t +/- Experiment Run number sec t of cart 1 t of cart 2 t of cart 1 t of cart 2 (m/s) (m/s) (m/s) (m/s) A: Velcro bumpers 1 0 Same 2 0 Same 3 0 Same B: Mag. bumpers C: Mixed bumpers D: Both moving, velcro 10 Same 11 Same 12 Same E: Both moving, mag F: Different mass

6 Analysis Table 1: Momentum Run number Momentum of cart 1 Momentum of cart 2 Momentum of cart 1 Momentum of cart 2 Total momentum Total momentum (kg m/s) (kg m/s) (kg m/s) (kg m/s) (kg m/s) (kg m/s) Ratio of total momentum / 1 0 Same 2 0 Same 3 0 Same Same 11 Same 12 Same

7 Analysis Table 2: Energy Run number KE of cart 1 KE of cart 2 KE of cart 1 KE of cart 2 Total KE (Joules) Total KE (Joules) Ratio of total KE /

8 Sample Uncertainty Table for Momentum Analysis Run number in p cart 1 in p cart 2 in p cart 1 in p cart 2 Total in p (initial) Total in p (final) Uncertainty p (final)/ p (initial)