I am trying to prove the efficiency of crumple zone in a presentation, but I think that I'm am doing something wrong. Basically I'm a grade 12 physics student, and I am suppose to present crumple zone. I understand that we need to impulse and momentum in here, and I tried setting up a problem that proves the effectiveness of crumple zone.
In one case, I show a car of mass 4000 kg that has a rigid front and travels in uniform motion of 30 m/s and it hits the wall. the front only crumples by 10 cm (this is an assumption that I'm making, based on nothing really) and I compare it to the same car, driving at the same velocity but with crumple zone at the front, making the crumple 30 cm.
The question is, am I making a good assumption? or am I suppose to account some other factors as well?
FΔt = Δp.
The Attempt at a Solution
For the first case I am using the formula Δd=vΔt-(1/2)aΔt^2, where i substitute "a" with (v2-v1)/Δt, which results in 6.67*x10^-3 seconds to decelerate from 30 to 0.next I am using the equation FΔt = Δp to calculate the force that is exerted on the passengers, which results in 120000/6.67x10^-3 = 1.8x10^7 N.
I am doing the same calculation for the second case:
0.3=-(1/2)(-30)Δt = 0.02 seconds
120000/0.02 = 6x10^6N.
which proves that crumple zone (in this case) is reducing the force on the passengers by 66%.
But I am not sure if that is the force that the people are experiencing or the force that the car absorbs. Any suggestions.