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RWDboy
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July 2002
Re: Physics problem. Sat, 26 March 2005 04:47 Go to previous messageGo to previous message
Okay we want 'equivalent' two-car and car-car accidents, and we both agree that kinetic energy is what determines an accidents 'strength'.

Both cars have mass 'm1' and both cars are travelling at velocity 'v1' relative to the road - and are heading towards each other. And the car hitting the wall has mass 'm1' and velocity 'v2'

So the car-car accident has KE1 = 0.5 * (m1 + m1) * (v1)^2

The car-wall accident has KE2 (== KE1) = 0.5 * (m1) * (v2)^2

So

0.5 * (m1 + m1) * (v1)^2 = 0.5 * (m1) * (v2)^2

Cancel out the 0.5

(2 * m1) * (v1)^2 = m1 * (v2)^2

Now take out the factor of m1

2 * (v1)^2 = (v2)^2

Now take the square root of both sides

sqr(2 * (v1)^2) = sqr((v2)^2)

Square root and square cancel out on the RHS, and on the left hand side we separate it into the product of two sqr roots

so

sqr(2) * sqr((v1)^2) = v2

And using the same square root & square cancelling out we get

sqr(2) * v1 = v2

Ie

1.414 * v1 = v2

Ie in the one car accident it must travel 1.414 times the speed of one of the cars in the two car accident to have an accident with overall equiavlent energy.

Anyway, whatever, I'm sure that you understand what's going on by now but you are too lazy to re-arrange the KE formula and substitute stuff around to prove it to yourself. Now I'm going to go do some fun stuff with my Easter saturday instead of whoring on various forums Smile
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Read Message   Physics problem. SquidThu, 24 March 2005 03:43
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