Unit2_VirtualLabImpulse_Momentum (1)

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Experiment 20 Virtual Lab: Impulse and Momentum *Please Note* If you will be submitting your assignment electronically please use a different color of text for your answers. Thank you. 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, F , 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 connected to an elastic tether will roll along a level track. Momentum is conserved if there is not net external force acting on the system. If we consider the system frictionless momentum is conserved until the elastic tether becomes taunt. 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 time starts when the force is first felt and continues until the tether goes slack again. The cart velocity throughout the motion is measured with a Motion Detector. Using Logger Pro to find the average force during a time interval, you can test the impulse-momentum theorem. Physics with Computers 20 - 1

Experiment 20 Objectives ● Measure a cart’s momentum change and compare to the impulse it receives. ● Compare average and peak forces in impulses. Materials Computer dynamics cart and track Vernier computer interface clamp Logger Pro elastic cord Vernier Motion Detector Vernier Force Sensor string 500 g mass bubble level Preliminary questions and discussion Please take some time to answer the questions below. 1. In a car collision, the driver’s body must change speed from a high value to zero. This is true whether or not an airbag is used, so why use an airbag? How does it reduce injuries? When a car crash happens the people inside are moving at a fast speed and suddenly they need to stop. This sudden stop could cause serious injuries because their bodies feel a big force. Airbags are a cushion for you to hit which makes the stop happen more slowly spreading the force and helps prevent injuries, especially to your head. even though you still stop suddenly the airbag helps reduce injuries. 2. You want to close an open door by throwing either a 400 g lump of clay or a 400 g rubber ball toward it. You can throw either object with the same speed, but they are different in that the rubber ball bounces off the door while the clay just sticks to the door. Which projectile will apply the larger impulse to the door and be more likely to close it? When you throw both a rubber ball and a lump of clay with the same force the rubber ball hits the door and bounces back, pushing the door harder, but the clay just sticks to the door so it doesn’t push as much. Because the rubber ball gives a stronger push or impulse to the door the bouncing back, is like hitting it twice and is more likely to close the door compared to the lump of clay. 20 - 2 Physics with Computers

Impulse and Momentum 3. View the following video discussing these questions and the lab experiment: Impulse & Momentum Pre-Lab Video https://youtu.be/yVJyIZ65vzE Procedure The following procedure will be conducted by an instructor in lab as your “virtual lab partner” please be sure to record the data that is obtained during the experiment in the video in the following data table because you will be conducting the data analysis on your own. Please follow along with the experiment in this video: Impulse & Momentum Lab Experiment https://youtu.be/DBi2gc9BmNI 1. Measure the mass of your dynamics cart plus any weights placed on the cart and record the value in the data table. 2. Connect the Motion Detector to DIG/SONIC 1 of the interface. Connect the Force Sensor to Channel 1 of the interface. If your Force Sensor has a range switch, set it to 10 N. 3. Open the file “20 Impulse and Momentum” in the Physics with Vernier folder. Logger Pro will plot the cart’s position and velocity vs . time, as well as the force applied by the Force Sensor vs . time. 4. Calibrate the Force Sensor. a. Choose Calibrate ± CH1: Dual Range Force from the Experiment menu. (Click on the Calibrate Tab if it is not already the open tab.) Click . b. Remove all force from the Force Sensor. Enter a 0 (zero) in the Reading 1 field. Hold the sensor vertically with the hook downward and wait for the reading shown for CH1 to stabilize. Click . This defines the zero force condition. c. Hang the 500 g mass from the sensor. This applies a force of 4.905 N. Enter 4.905 in the Reading 2 field, and after the reading shown for CH1 is stable (If the weight is swinging it will take longer to stabilize, also the number may continue to change between 2 digits in the last decimal place.), click . Click to close the calibration dialog. 5. Place the track on a level surface. Confirm that the track is level by placing the bubble level on it. Also check by placing the low-friction cart on the track and releasing it from rest since the track can be warped in one spot.. It should not roll. If necessary, adjust the track. 6. 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 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’s motion. Physics with Computers 20 - 3

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Experiment 20 7. Place the Motion Detector (on the cart reading) beyond the other end of the track so that the detector has a clear view of the cart’s motion along the entire track length. When the cord is stretched to maximum extension the cart should not be closer than 0.2 m to the detector. 8. Click , select Force Sensor from the list, and click to zero the Force Sensor. 9. Practice releasing the cart so it rolls toward the Motion Detector, 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 Detector. 10. Click to take data; roll the cart and confirm that the Motion Detector detects the cart throughout its travel. Inspect the force data. If the peak exceeds 10 N, 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 time-axis, the Motion Detector was too close and the run should be repeated. 11. Once you have made a run with good position, velocity, and force graphs, analyze your data. To test the impulse-momentum theorem, you need the velocity before and after the impulse. Choose an interval corresponding to a time when the elastic was initially relaxed, and the cart was moving at approximately constant speed away from the Force Sensor. Drag the mouse pointer across this interval. Click the Statistics button, , and read the average velocity. Record the value for the initial velocity in your data table. In the same manner, choose an interval corresponding to a time when the elastic was again relaxed, and the cart was moving at approximately constant speed toward the Force Sensor. Drag the mouse pointer across this interval. Click the statistics button and read the average velocity. Record the value for the final velocity in your data table. 12. Now record the time interval of the impulse. On the force vs. time graph, drag across the impulse, capturing the entire period when the force was non-zero. Find the average value of the force by clicking the Statistics button, , and also read the length of the time interval over which your average force is calculated. This can be found at the bottom of the force graph as the  x. 13. Perform a 3 more trials by repeating Steps 10 – 12. Try to make the force a little different each time. Record the information in your data table. 20 - 4 Physics with Computers

Impulse and Momentum Data Table The mass of the cart was measured to be 490.6 grams which is converted to 0.4906 kilograms. Mass of cart + weights 0.4906 kg Trial Final Velocity vf (m/s) Initial Velocity vi (m/s) Average Force F (N) Duration of Impulse Δ t (s) 1 1.027 -1.151 0.9394 1.148 2 0.7280 -0.8525 0.7501 1.061 3 0.8380 -0.9902 0.5915 1.077 4 0.8677 -1.001 0.6030 1.074 5 0.7733 -0.8980 0.8082 1.036 Physics with Computers 20 - 5

Experiment 20 Analysis 1. From the mass of the cart and change in velocity, determine the final and initial momentum and 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 found at the end of this section. 2. 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? Do your data support the impulse-momentum theorem? We calculated the percentage difference between the change in momentum and impulse to see how closely they match. The percentage difference is small in trial 1 and trial 5, this means the change in momentum and impulse are close supporting the theorem. But in trials 2,3 and 4 there was a big difference between the change in momentum and impulse, around a 30 to 35% difference. This shows that the data might not fully support the term possibly due to measurement error, and other factors. 4. Look at the shape of the force vs . time graph of your last trial. 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? The peak value of the force is different from the average force. This means the force applied during impact is not consistent. It starts strong and then gets weaker. To deliver the same impulse with a smaller force we can make the collision last longer by spreading the force over time. This will reduce the peak force while still giving the same push. 5. Revisit your answers to the Preliminary Questions in light of your work with the impulse-momentum theorem. After you have completed your calculations in the table as well as answered all of the prelab and analysis questions (in a different color of text) be sure to submit your handout to your instructor. Calculations Table 20 - 6 Physics with Computers

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Impulse and Momentum Trial Final Momentum m vf Initial Momentum m vi Change in momentum Δ mom Impulse F Δ t Average of change in momentum & Impulse ( Δ mom + F Δ t)/2 Difference between change in momentum & Impulse |( Δ mom - F Δ t)| % difference between Impulse and Change in momentum |( Δ mom - F Δ t)| * 100 Average units (kg ⋅ m/s) (kg ⋅ m/s) (kg ⋅ m/s) or (N ⋅ s) (N ⋅ s) (N ⋅ s) (N ⋅ s) % 1 0.504 -0.564 1.068 1.078 1.073 0.01 0.93% 2 0.357 -0.418 0.775 0.796 0.786 0.21 26.72% 3 0.411 -0.486 0.897 0.637 0.767 0.26 33.90% 4 0.427 -0.491 0.918 0.648 0.783 0.27 34.48% 5 0.379 -0.441 0.82 0.837 0.829 0.017 2.05% After you have completed your calculations in the table as well as answered all of the prelab and analysis questions (in a different color of text) be sure to submit your handout to your instructor. Physics with Computers 20 - 7