Module 12 Honors Extension
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University of North Carolina, Chapel Hill *
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118
Subject
Aerospace Engineering
Date
Feb 20, 2024
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docx
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3
Uploaded by therealgeorgenotthefake
Module 12 Honors Extension
Football
1.
Excel charts
2.
The net change in momentum is 8.75 kg*m/s
3.
The net change in velocity during the hit is 1.09 m/s a.
Questions: How does the change in velocity of the head + helmet during the hit compare
to a typical walking speed for a person?
i.
The change in velocity of the head + helmet during the hit is typically much smaller than the walking speed for a person. A normal walking speed for a person is in the range of 1 to 2 meters per second (m/s), and the change in velocity during a hit, even a significant one, is usually a fraction of a meter per second. This difference is because the time of an impact is very short, and the change in velocity has to happen rapidly to generate high forces.
b.
Question: How can such a large peak force cause such a small change in velocity?
i.
This is explained because of impulse and momentum. Even though the peak force during a hit is quite large, the small change in velocity occurs because the impact duration is short. The change in momentum (impulse) is equal to the force applied over time. In the case of a hit, the force is large but acts for a very
brief time, resulting in a relatively small change in velocity. This contrasts with actions like walking, where the force is applied over a more extended period, resulting in a significant change in velocity.
4.
The SI for the given data is 8.5, and the SI for the doubled data is 48.05. This increase is SI shows how sensitive SI is based on acceleration. The acceleration for the doubled data is so much higher, suggesting that a relatively small increase in acceleration can result in a substantial increase in injury risk. Given that “values of ~ 400 s typically produce unconsciousness and mild concussion,” I would say that our player is unlikely to be concussed. However, concussions and brain injuries are much more complicated than just this SI, and depending on the placement of the hit, the likelihood of concussion can change drastically. Smartphone
5. A screenshot of a zoomed in time region of your acceleration around the collision. 6.
Report the maximum acceleration during the collision, in g’s.
a.
a
max
=
4.20
g
7.
Report the SI over the collision.
a.
1.37 8.
Discuss the peak acceleration and SI relative to the football data and explain differences in the SI found.
a.
The peak acceleration for the football player is: 27.8 g, with an SI of 8.5, and the peak acceleration of the phone was 4.20 g, with an SI of 1.37. The peak acceleration of the football player is significantly higher, which indicates that the football player had a much more forceful impact. This is corroborated by the fact that the severity index of the football players impact is much higher than that of the smart phone, which means there
is a much higher risk. The differences in SI Can be attributed to the impact duration and mechanics, as well as how SI is calculated. In football, impacts are intense but short, which means a higher peak acceleration and peak force, but small change in velocity. b.
While the SI values give you a quantitative measure of impact, there are lot of external factors when it comes to how a contact injury effects someone. Besides impact placement, as I mentioned earlier, there’s also all the padding that football players wear to distribute the impact force. For the smartphone collision, there’s a lower SI, so a lower numerical chance of injury, but smartphones don’t have all that padding. c.
All in all, it’s very important to consider context for collisions.
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