- 2

- 0

Anyway the math:

m1 = 1600kg the jeep

v1 = 20m/s jeep's initial velocity

m2 = 18000kg the bus

v2 = -25m/s the bus's initial velocity. This is supposed to be negative because the two are approaching right?

tf = 175ms :: 0.175s I looked at the force curves on sled tests (the accelerometer used to study car accidents at the curves tended to return to 0 between 150 and 200 milliseconds

ti = 0ms

m{1+2-debris} = 1600kg + 18000kg - 100 kg :: 19,500kg ((NOTE: typical weight of windows in car is 45kg)) the mangled remains of the two entangled automobiles

(m1v1)/(tf-ti) + (m2v2)/(tf-ti) = (m{1+2-debris}v3)/(tf-ti)

solving for v3

(m{1+2-debris}v3)/(tf-ti) = (m1v1)/(tf-ti) + (m2v2)/(tf-ti)

(m{1+2-debris}v3) = [(m1v1)/(tf-ti) + (m2v2)/(tf-ti)] * (tf-ti)

v3 = ([(m1v1)/(tf-ti) + (m2v2)/(tf-ti)] * (tf-ti)) / m{1+2-debris}

v3 = ([(1,600kg * 20m/s) / 0.175s] + [(18,000kg * -25m/s) / 0.175s]) * 0.175s) / 19,500kg

v3 = [(182,857kgm/s^2 + -2,571,428kgm/2^2) * .175s] / 19,500kg

v3 = (-2,388,571kgm/s^2 * .175s) / 19,500kg

v3 = -418,000kgm/s / 19500kg

v3 = -21.4m/s

_____________________________________________

F1 = [m1*(v3-v1)]/(tf-ti)

F1 = ([1,600kg * (-21.4m/s - 20m/s)] / .175s)

F1 = [(1,600kg * -41.4m/s) / .175s]

F1 = (-66,240kgm/s / .175s)

|F1| = |378,514Newtons|

F2 = [m2*(v3-v1)]/(tf-ti)

F2 = ([18,000kg * (-21.4m/s - -25m/s)] / .175s)

F2 = [(18,000kg * 3.6m/s) / .175s]

F2 = 370,285N

F(lux) = [mlux*(v3-v1)]/(tf-ti)

F(lux) = 45kg * -41.4m/s / .175s

F(lux) = 45kg * 24.12g

F(lux) = 10,650N <----Is this way too low?

F(passanger) = [mpassanger*(v3-v2)]/(tf-ti)

F(passanger) = (100kg * 3.6m/s) / .175s

F(passenger) = 100kg * 2.1g

F(passenger) = 2,060N :: a solid but not professional punch is ~3,000N

In a head on collision with a bus, while inside a jeep, my numbers are suggesting a passenger would experience 10,000 Newtons. This is significant but not catastrophic. Head on collisions are frequently fatal aren't there? Shouldn't the newtons be much higher? What am I doing wrong here?

Sorry this is such a word wall. I wanted to write this out as completely as possible in hopes somebody might catch my error(s).