A car travelling 30mph hits a solid wall. Due to its lack of crumple zones the car stops in 0.01 seconds. If the driver weighs 70Kg calculate:
a) The impulse and the force exerted on the seat belt.
b) The impulse and the force exerted on the seat belt if the car had a crumple zone and took 0.2 seconds to stop.

Question

A car travelling 30mph hits a solid wall. Due to its lack of crumple zones the car stops in 0.01 seconds. If the driver weighs 70Kg calculate:
a)	The impulse and the force exerted on the seat belt.
b)	The impulse and the force exerted on the seat belt if the car had a crumple zone and took 0.2 seconds to stop.

anonymous · Answer

what is "impulse"? Acceleration?

anonymous · Answer

no impulse is J=F*t

anonymous · Answer

Now I think that the crumple zone changes the equation, since the crumple zone takes away energy from the impact, so this would decrease the force on the seat belt and on the impulse.

anonymous · Answer

How did you work that out? I need to understand whats happening.

anonymous · Answer

Sorry about that
Ok so the impulse is F*t
Impulse is also the change in momentum, so $$mv-mv$$
Thus, the impulse would be his initial mass * initial velocity
70 kg * 30 mph *.44704 (conversion) and you get $$938.8Nm$$
Because he comes completely to rest, the final impulse is zero because his final velocity is zero.
So the impulse would be 
$$938.8Nm$$

anonymous · Answer

Now we need to find the force, so remember that
$$J=F*t$$
So since the impulse is
$$938.8 Ns$$
We can set that equal to F*t
$$938.8 Ns=F*.01s$$
which is the time it takes him to stop.
So $$F=93880 N$$

anonymous · Answer

sorry the impulse units are N*s not N*m

anonymous · Answer

Thank you for the excellent response, That makes sense to me now. :)

anonymous · Answer

no problem :)
I can try to answer the one about the crumple zone also.
I believe that the impulse would be the same, since the change in momentum is the same. This is because the initial velocity and the final velocity do not change.
So, 
$$J=938.8 Ns$$
Now the force will change because of the crumple zone. The crumple zone has changed the time it takes to slow down to zero.
Recall that $$J=F*t$$
And that now, the time it takes to stop is $$.2 seconds$$
So, 
$$938.8 Ns=F*.2s$$
So $$F=4694 N$$

anonymous · Answer

This makes sense because the crumple zone is slowing down the amount of time during the accident, so the force on the seatbelt is less than the immediate impact.