Impulse and Momentum Lab

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Northeastern University *

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393

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Electrical Engineering

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Dec 6, 2023

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Allen Ye Period 1 Impulse and Momentum DATA TABLE Mass of cart 0.516kg Filename for thin band 3 Filename for thick band 1 Trial Final Velocity v f (m/s) Initial Velocity v i (m/s) Change of Velocity Δ v (m/s) Impulse (area under curve) (N ⋅ s) Δ t of Impulse (s) Average Force (calculate d ) (N) F max (from graph) (N) Thin Elastic a 0.5877 -0.7465 1.3342 0.695 0.44 1.58 2.446 b 0.6159 -0.7494 1.3653 0.7088 0.46 1.54 2.54 Thick Elastic a 0.5602 -0.7368 1.297 0.6758 0.38 1.78 3.871 b 0.565 -0.7209 1.2859 0.6697 0.34 1.97 3.807 Trial Area under curve (from table above) (N ⋅ s) m∆v (calculated ) (kg ⋅ m /s) % difference (See analysis step #3) Thin Elastic a 0.695 0.516 * 1.3342 = 0.688 1.012 b 0.7088 0.516 * 1.3653 = 0.704 0.679

Thick Elastic a 0.6758 0.516 * 1.297 = 0.669 1.011 b 0.6697 0.516 * 1.285 = 0.664 0.854 ANALYSIS 1. Calculate the change in velocities and record in the data table. From the mass of the cart and change in velocity, determine 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. 2. If you personally experience a change in momentum, are you interested in the effects on your body of the average force or the maximum force? Explain why. ● I would be more interested in the effects on my body of the max force because the max force will determine the largest extent of the injury on my body. 3. If the impulse-momentum theorem is correct, the calculated mΔv will equal the area under the force vs. time graph 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, and then multiply by 100 to get percent (%). How close are your values, percentage-wise? Do your data support the impulse-momentum theorem? ● The percent error for all the trials are below 1.02%, which is an extremely small margin of error and indicates that the values are very close percentage-wise. As a result, the data does support the impulse-momentum theorem. 4. Look at the shape of the last force vs . time graph. 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 maximum force? ● Yes it is significantly different. The peak value of the force is 3.807N while the average value is 2.088N. You could deliver the same impulse with a much smaller maximum force if you have the force be applied for a longer duration. 5. Would you change your answers to the Preliminary Questions in light of your work with the impulse-momentum theorem? How? ● I believe my preliminary question answers were correct, so I would not change my answers. For number 2, the rubber ball does apply a larger impulse.

6. When you use different elastic materials, what changes occurred in the shapes of the graphs? Is there a correlation between the type of material and the shape? If so, explain the correlation and provide an explanation. Include 2 force vs. time graphs - one from each type of band in your report. Use trials that have similar initial velocities. In LoggerPro, adjust the x and y axes so that they are the same scale and align them vertically on the same page to make them easily comparable. Be sure to include the area under the graph in your printed graph. ( Choose Analyze ►Integral ► Force) Thick 1A Thin 3A ● Using different elastic materials resulted in different durations of the force and the peak value of the force. There does seem to be a correlation between the elasticity of the material and the shape of the graph. The thick band had a higher max force but smaller force duration while the thin band had a lower max force but longer force duration. However, the integral for both trials were similar. 7. When you used the thicker band (which is a tighter elastic material), what effect did this have on the duration of the impulse? What affect did this have on the maximum size of the force? Can you develop a general rule from these observations?

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● The thicker and more elastic band had a smaller impulse duration and a larger maximum force size. From my observations I can conclude that in general, the thinner the band and the less tight the elastic material, there will be a longer impulse duration and smaller maximum peak force. 8. When comparing graphs from the two different bands, why is it important that the starting velocities be similar? If the thinner band had a much larger initial velocity than the thicker band, why would it be difficult to compare the results? ● It is important that the starting velocities are similar so that the impulses are constant. The initial velocity is used to calculate the change in total velocity and m∆v, so having it as a constant variable in the experiment is important to being able to make correct observations. If the thinner band had a much larger initial velocity compared to the thicker band, then the impulse would be larger which would be confusing.