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Miami-Dade College PHY2053 L Impulse and Momentum INTRODUCTION: It takes an impulse to change the momentum of an object, momentum is mass in motion. This is just another statement for Newton’s Second Law of motion. For this experiment, a dynamics cart will roll along a level track. Its momentum will change as it stretches an elastic tether cord, much like a horizontal bungee jump. The force applied by the cord is measured by a Force Sensor. The cart velocity throughout the motion is measured with a Motion Detector. Using Logger Pro to find the area under the force-time graph for the interval of time where the momentum change happened. Motion Detector Force Sensor Elastic cord OBJECTIVES: • Determine the mathematical relationship between impulse and change in momentum as to find the mass of the object experiencing the change in momentum; • Measure a cart’s momentum change and compare to the impulse it receives; • Compare average and peak forces in impulses; MATERIALS computer Vernier computer interface Logger Pro Vernier Motion Detector Vernier Force Sensor dynamics cart and track clamp elastic cord (rubber bands) string 500 g mass PRELIMINARY QUESTIONS 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? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2. You want to close a door by throwing a 400 g lump of clay or a 400 g rubber ball at it. You throw both objects with the same speed, the rubber ball bounces straight back 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? Explain. PROCEDURE 1. Measure the mass of your dynamics cart and record the value in the data table. 2. Connect the Motion Detector to DIG/SONIC 1 of the interface. If the Motion Detector has a switch, set it to Track. Connect the Force Sensor to Channel 1 of the interface. If your Force Sensor has a range switch, set it to 10 N. 3. Place the track on a level surface. Use the leveler to confirm that the track is level. It should not roll. If necessary, adjust the track. 4. Attach a rubber band to the cart and the Force sensor with a paper clips. Make sure the cart can roll freely with the rubber ban slack and stays in the tracks as the rubber band stretches. Clamp the Force Sensor so that the string and cord, when taut, are horizontal and in line with the cart’s motion. 5. Place the Motion Detector 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 0.15 m to the detector. 6. Click , select Force Sensor from the list, and click to zero the Force Sensor. 7. 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. 8. 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. 9. Once you have made a run with good position, velocity, and force graphs, collect your data and complete tables I and II. • Your instructor will demonstrate how to collect the final and initial velocities and the impulse experienced by the object. 10. Add a second rubber band and repeat Steps 7–9, record the information in your data table. 14. Repeat for four more rubber bands. DATA TABLES: Mass of cart Kg 0.264 TABLE I Rubber bands Trial one vf (m/s) vi (m/s) Trial two vf (m/s) vi (m/s) Trial three vf (m/s) vi (m/s) 1 2.65 -2.15 2.68 -2.17 2.62 -2.19 2 3 4 5 6 2.89 3.28 3.57 3.96 4.19 -2.25 -2.2 -2.23 -2.3 -2.25 2.92 3.31 3.53 4.01 4.28 -2.23 -2.21 -2.25 -2.32 -2.2 2.93 3.19 3.61 3.98 4.26 -2.26 -2.24 -2.26 -2.33 -2.24 TABLE II Rubber bands 1 2 3 4 5 6 Impulse (Ns) Trial Trial One Two 1.25 1.28 1.36 1.34 1.45 1.48 1.53 1.55 1.65 1.66 1.71 1.73 Average Trial Three 1.27 1.39 1.46 1.52 1.68 1.72 Average vf (m/s) vi (m/s) Vf-Vi m/s (Ns) TABLE III Rubber bands 1 2 3 4 5 6 Average (Ns) Average vf (m/s) vi (m/s) ANALYSIS 1. Create an additional table (Table III) of Impulse vs. change in velocity. 2. From Table I, determine the average change in velocity fill out in the data table 1 and recorded in Table III. 3. Determine the average impulse for each trial on dtat table 2 and record these values in your data Table III. 4. Use Logger Pro and graph the data in Table III, Average Impulse on the y-axis and change in velocity on the x-axis. 5. Obtain the mathematical regression for the relationship between impulse and change in velocity; 6. Interpret the mathematical meaning of the slope and y-intercepts. What are the units of the slope express in basic units? 7. Determine the mass of the car. 8. Determine the percentage error for your lab related to the mass : %𝑒𝑟𝑟𝑜𝑟 = |𝑟𝑒𝑎𝑙 − 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑|/𝑟𝑒𝑎𝑙 × 100% 9. During the experiment was determine that the average time of interaction was 0.18 seconds. For the first row in the data table III determine the average force acting on the cart(using the change of Impulse . To do this, you will need, the real mass of the cart, the initial and final velocities, the time interval of the charge in velocity. 𝐹 ⃗_𝑎𝑣𝑒 = 𝑚(𝑣 ⃗_𝑓 − 𝑣 ⃗_𝑖 )/∆𝑡 10. For the same first row in the data table III, but now using the average impulse determine the average force acting on the cart. To do this, you will apply the formula : (The time is 0.18 s) 𝐹 ⃗_𝑎𝑣𝑒 = 𝐼 ⃗/∆𝑡 11. Compare the % difference of the average forces for calculations in point 9 and 10. 0 ⁄ 0 𝑑𝑖𝑓𝑓 = |𝐸_1 − 𝐸_2 |/((𝐸_1 + 𝐸_2)/2) Show your formulas and calculations when needed. Write the goal and conclusions.

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