How can I prove with physics equations that a 7 point seatbelt would be safer than the average 3 pointer
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How can I prove with physics equations that a 7 point seatbelt would be safer than the average 3 pointer

[From: ] [author: ] [Date: 11-06-08] [Hit: ]
So in terms of physics equations you need to examine the impulse (http://en.wikipedia.org/wiki/Impulse_%28physics%29)which factors into your bodys momentum. if the impulse I = F*t (or an integral Int(F*dt) for a force that changes with time, that will determine your total change in momentum Delta P(I = Delta P). The change in momentum is the negative of your mass times the velocity of the car when the crash begins because at the end of the crash you are sitting still so no momentum.......
Well it depends on how you define "safe". When you stop in a crash, the belt applies a force to your body where it contacts. This force is what slows you down with the car so you don't fly out the windshield. That force it applies to stop your entire mass is divided between the different lines of contact over your body. If you have fewer places where the seat belt meets your body then those lines of contant will have more force. If you have more harnesses then less force is applied along each one but still totals the force required to stop you (over the time of the crash). You would also need to examine where those belts lie on the human body. A seat belt around your neck for example isn't a good idea because your hear would still fly forward but your neck would get a force holding it back so you would choke the person as the crash happens.

So in terms of physics equations you need to examine the impulse (http://en.wikipedia.org/wiki/Impulse_%28physics%29) which factors into your body's momentum. if the impulse I = F*t (or an integral Int(F*dt) for a force that changes with time, that will determine your total change in momentum Delta P (I = Delta P). The change in momentum is the negative of your mass times the velocity of the car when the crash begins because at the end of the crash you are sitting still so no momentum. Delta P = -m*v

so if the impulse assuming a constant force F is I = F*t = Delta P = -m*v then
the force applied to the person equals:
F = -(m*v)/t where t is the time it took to stop.

You'll notice that first of all as the time required to stop goes up, the force on the person in the crash is small (since you're dividing by t). This means anything that extends the crash in time reduces the shock on the body. Airbags serve this purpose by creating a cushion of air to slow the person more slowly than say a restrictive belt, but that's not really what you asked. You'll want to argue that you can also reduce the force by distributing it over the persons body more evenly. A 7 point seatbelt ususally joins the belts at the persons center of mass as well which is an ideal place so the person stops more uniformly. A lap belt or 3 pointer would have more force over the fewer belts and they may not be ideally positioned to minimize biological stress while stopping the person's body.

Okay I can't say I have much else to give you since this question could probably be answered better by a crash test engineer, but I hope it got you thinking in the right direction. (Or totally wrong direction if I'm way off).
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