math help please

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Originally Posted by BigTyla

I was operating under the assumption that this was an academic question. Since it's a real-world problem, we can do a little more hand-waving.

Perfectly inelastic means that the truck stuck with the car throughout the collision, ie the car didn't bounce off the truck.

Let's assume one-dimensional since it was likely that the car was rear-ended, and we will assume that the collision was square enough with the rear to cancel out effects from the two other dimensions.

Was the car also at a 15 degree decline?

Momentum of the truck is easy. p = mv = 14000 lb x 40 mi/hr = 560000 lb-mi/hr

Momentum must be conserved, and hence transfered to the car assuming an elastic collision. But we still need the speed of the truck after the collision to find the velocity of the car after impact, since:

mass of truck * velocity of truck (before collision) = mass of truck * velocity of truck + mass of car * velocity of car (after collision)

Once finding the velocity of the car, you would need to assume a reasonable number for the friction coefficient of the car with brakes applied. Then you would have to use the energy equation to determine the distance the car would travel with these assumptions, taking into account the 15 degree decline by factoring in potential energy.

In other words, this isn't as easy as you think.

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Found an estimate COR of .15 and COF 0.9 static, 0.7 kinetic if you feel like doing the math.

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Originally Posted by vroom4

Disclaimer: Please dont reference me in a court case where you totalled 3 cars.

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I knew this was going to be the case. There are crazy complex simulation codes to do what you want us to do on an internet forum for free.

I laughed when I read it was IRL. Think of some poor soul trying to account for all the shit in the back of a fully loaded utility truck during an impact :lo5l:

I think its safe to say your gf would've needed 4-5 car lengths between her and the next vehicle.

I figured it would have to be something ridiculous like that. Something no one would do unless they knew it was going to happen. I am just doing this for kind of my own knowledge gain, and semi help with math. Thank you for the help.

There are so many variables to this problem in the real world it'd take forever to figure out. You have to know how the car crumples to find the energy absorbed from that, the friction forces, even the amount of energy absorbed by the springs in every vehicle as they get hit.

My dynamics professor was asked to do something very similar to this to prove the client couldn't have gotten whiplash from a rear ending and he declined it.

lol at this whole thread

force = M*A

that's the first thing you have to figure out. 15 degree slope doesn't matter if the speed is constant at 40mph. its just a function of the speed and the mass behind it. everything else will follow that.