Laboratory 5

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Laboratory 5: Impulse and Momentum Manuelle Toro mtoromar@vols.utk.edu Purpose: In our daily lives, we experience several collisions either it being like bumping into someone or having to break rapidly and our seatbelts holding us down, these are the changes in momentum, where opposing forces act against each other in a short amount of time, creating impulses we most time can perceive. For this lab we wish to become more familiar with this and understand how different materials colliding with one another affect the outcome of the impulse as well as how changes in velocity and elasticity play a role in the momentum observed. Experiment 1: Bumper block Aluminum Wood High-density foam Low-density foam Maximum force 12.21N 11.655N 9.435N 7.77N Collision time 0.09s 0.1s 0.12s 0.15s Impulse F avg *∆t 0.54945kg* m/s 0.58275kg* m/s 0.5661kg*m/ s 0.58275kg*m/s  Compare the impulse using the four different bumper blocks. Is this what you expected? What significance might this have in a real car collision? Explain. o Overall, this does make my expectation, as since the collision time, as well as the forces, are increasing and decreasing respectively across the materials, we would expect the impulse to remain similar. As for a vehicle we could see that with aluminum there is a smaller impulse meaning, that in a car collision, the individuals in a vehicle colliding with an aluminum surface will experience much lesser forces than those colliding with other materials.

 Compare maximum forces and the interaction times for the four different collisions. Is this what you expected? What significance might this have in a real car collision? Explain! o Overall we see higher maximum forces in a shorter amount of time and lower maximum forces in a larger amount of time, simply comparing these factors we see that in the case of a real- life collision, one that happens in a shorter collision time will yield higher forced to all involved drivers, while giving much ample time of collision yields a lesser force to all drivers, based just on this we would then favor a collision involving low-density foam Experiment 2 Note: the” –“ sign on top of the numbers in some cells means that the value is negative, I’ve tried everything to make it so that the “–“ sign is attached to the value, but it doesn’t seem to work Video 1: Displaceme nt (cm) before the collision: Frame 11 to frame 21 Displaceme nt (cm) after the collision: Frame 25 to frame 35 Velocity before the collision : (cm/s) Velocit y after collisi on: (cm/s) Moment um before the collision (kg cm/s) Moment um after the collision :(kg cm/s) Cart 2 (Left) mass = 0.5 kg 5.5cm -7.5cm 16.487c m/s - 22.47 5cm/s 8.2435k g*cm/s - 11.2375 kg*cm/s Cart 1 (right) mass = 0.5 kg -7.5cm 5.5cm - 22.482c m/s 16.48 2cm/s - 11.241k g*cm/s 8.241kg *cm/s Total momentum before and after the collision: - 2.9975k g*cm/s - 2.9965k g*cm/s Video 2: Displaceme nt (cm) before the Displaceme nt (cm) after the Velocity before the Velocit y after collisi Moment um before Moment um after

collision: Frame 12 to frame 22 collision: Frame 31 to frame 41 collision : (cm/s) on: (cm/s) the collision (kg cm/s) the collision :(kg cm/s) Cart 2 (left) mass = 0.5 kg -5.5cm -14cm - 1.8353c m/s - 4.670 4cm/s - 0.918kg *cm/s - 2.3352k g*cm/s Cart 1 (right) mass = 0.5 kg -14cm -5.5cm - 4.6718c m/s - 1.834 8cm/s - 2.3359k g*cm/s - 0.9174k g*cm/s Total momentum before and after the collision: - 3.2539k g*cm/s - 3.2526k g*cm/s Video 3: Note: I noticed the table in the video portal for this said to review frames 16 to 25, but when I looked at the instructions, they wanted us to review 10 frames in 1/3 second so I did frames 16 to 26 and got the same results as I’ve done with video 1 and 2 *I’m not sure if it’s a typo in the website or not* Displaceme nt (cm) before the collision: Frame 2 to frame 12 Displaceme nt (cm) after the collision: Frame 16 to frame 26 Velocity before the collision : (cm/s) Velocit y after collisi on: (cm/s) Moment um before the collision (kg cm/s) Moment um after the collision :(kg cm/s) Cart 2 (left) mass = 0.5 kg 7.5cm -2cm 2.503c m/s - 0.672 cm/s 1.2515k g*cm/s - 0.336kg *cm/s Cart 1 (right) mass = 0.5 kg -11.5cm -2cm - 3.838c m/s - 0.672 cm/s - 1.919kg *cm/s - 0.336kg *cm/s Total momentum before and after the collision - 0.6675k g*cm/s - 0.672kg *cm/s

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before the collision After the collision p cart 2 p cart 1 p total p cart 2 p cart 1 p total Video 1 8.2435kg* cm/s - 11.241kg*c m/s - 2.9975kg*c m/s - 11.2375 kg*cm/s 8.241k g*cm/s - 2.9965k g*cm/s Video 2 - 0.918kg*c m/s - 2.3359kg*c m/s - 3.2539kg*c m/s - 2.3352k g*cm/s - 0.9174 kg*cm/ s - 3.2526k g*cm/s Video 3 1.2515kg* cm/s - 1.919kg*c m/s - 0.6675kg*c m/s - 0.336kg *cm/s - 0.336k g*cm/s - 0.672kg *cm/s  Does the total momentum of the carts change in the elastic collision experiments? Refer to your data. o Yes but not significantly, although the values are not identical we can see there is only a difference in total momentum (- 2.9975kg*cm/s in video 1 before minus -2.9965kg*cm/s for video 1 after) of 0.001kg*cm/s in video 1 and (-3.2539kg*cm/s for video 2 before minus -3.2526kg*cm/s for video 2 after) 0.0013kg*cm/s in video 2 before and after the collision, meaning that overall they are identical, we can attribute this insignificant difference due to friction in the track and possible air resistance that might be in between the car’s path  Does the total momentum of the carts change in the inelastic collision experiment? Refer to your data. o Similarly to the elastic results we see that although there is a change is very insignificant, as we can see a difference in total momentum (-0.6675kg*cm/s for video 3 before minus - 0.672kg*cm/s for video 3 after) of 0.0045 kg*cm/s before and after the collision, which again can be attributed to friction in the track and/or Air resistance in the path of the cars.  Did your experiments reproduce the expected results? If not, speculate on the reasons for any discrepancies. o Yes, we can certainly say these results fall within our expectations, as we hoped we could visualize the conservation of momentum, as seen in the lecture when objects collide with each other it is expected the transfer of momentum from one object to another; without any forces escaping the system; to be even across each other. As such we can expect that the impulses before and after the collision would be equal, and as seen in our calculation for all three videos (both elastic and inelastic) we say the impulses were equal with only insignificant differences that

can be attributed to incontrollable factors, the experimental design accounted for but couldn’t exclude. Experiment 3  Place a wide textbook on the floor and stand on it. Then jump off the book onto the floor two different times. The first-time land normally, allowing your knees to bend. The second time land stiff-legged, not allowing your knees to bend. Do these jumps feel different to you? Explain! o When allowing the knees to bend I noticed the forced felt on my legs was much weaker than when I didn’t let my knees bend, we could explain this as a transfer of momentum, when we allow the knees to bend we create a larger collision time meaning our impulse would be lesser, and thus allow our body to have a smaller maximum force, while if we remained stiffed-legged we reduce the collision time by a greater amount causing the impulse to be much higher and thus I experience I higher maximum force  Open the Phyphox app on your phone. Lay your phone flat on a table. Start measuring "Acceleration (without g)". Maximize the "Linear Acceleration z" graph, and while holding your phone with the screen facing up, repeat the jumps, while recording the acceleration. Examine the graphs. o Jump while bending knees:  overall, we see that the acceleration while bending the knees makes it so that

the difference in acceleration over time is smaller, observable in the peaks around seconds 1, 1.5, and 2, and as such this proves our point of us having a weaker impulse due to the ample time allowed while bending, and therefore the weaker maximum force we experience.  Jump while stiffed-legged: In this case when not allowing our knees to bend we see that the difference in acceleration is much higher, due to the high peak we can see around second 1.5 as such we can

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prove our point that while being stiffed-legged we make it so that the time of collision is much smaller and thus we experience a higher impulse.  What can you say about the maximum forces, the interaction times, and the total impulses given to the jumper in the two different kinds of landings? o In both scenarios, we see it took me around 2-3 seconds to finish the recording, but unlike each other in the first fall when we allowed the knees to bend, we say that the peaks are much broader giving us a collision time of around 1 second, while in the measurement with the stiffed legs we saw the collision time to be around 0.5 seconds. In addition, we see that the peaks experienced are much different than one another in the first scenario we can estimate the changes in acceleration to be

around 17m/s 2 out of simple visual estimates, while in the second scenario, we see a difference in acceleration of around 45m/s 2 multiplied by my constant mass in both scenarios of 58kg we get a maximum force of 986N for scenario 1 and 2610N for scenario 2, using these values to determine the impulse of each scenario given the estimated collision times we see a value of 986kg*m/s for scenario 1 and 1305kg*m/s for scenario 2. Thus, we can then prove that bending our knees when jumping will lead to a much easier landing in the sense of force and impulse. Reflection: This lab was interesting, we saw how both different materials can affect the impulse received by a car, and as such could conclude low-density would be ideal when comparing the collision time and maximum force, while aluminum will be ideal when only considering impulse, secondly, we evaluated the differenced in elastic and inelastic impulses, overall we see conservation of momentum proven by how our numbers remained fairly similarly, we can also visualize how the small differenced in the values could be all accounted for in the sense of external forces interfering in our experiment. Lastly, we saw a significant experiment that allowed me to use all the skills learned in the lab to try to bring reason into why the way we land affects the forces we perceive, overall using the formulas given as well as values I could estimate I was able to prove, bending the knees will be a much better way of landing. To conclude I feel this lab allowed us a perspective into the world of momentum and gave us to tools to understand all the forces that collide against us and the conservation of such.

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