Question on Momentum, Force and Impulse

[Chan1993]

Car makers build in many safety features to their cars. Some advertise these features a great deal so that many people will have heard of 'crumple zones' and 'rigid steel safety cage'. Seat belts have also lead to increased safety.

The crumple zone in a car are the engine compartment and the boot. These are designed so that they crumple or collaspe in a serious collison so that the impact is spread over a longer time. The safety cage is a cage of strong steel bars around the passenger space which is hidden in the body of the car.

a) A car of mass 9.00 x 10² kg traveling at 10ms^-1 when it skids off the road and into a concrete wall. If the car does not have crumple zones, it is stopped in 0.0500s; if it does have crumple zones, the slowing down process, is 0.900s longer

i) What is the momentum of the car before it hits the wall?
ii) What is the momentum after the collision?
iii) What is the change of momentum?
iv) How big is the force stopping the car if it does not have crumple zones?
v) How big is the force if it does not have crumple zones?
vi) Comment on your answers for (iv) and (v).

• Momentum: p = mv
• Ft= mv-mu
• F=ma

Momentum before= p = 900 x 10 = 9000kgms

sigh that's all I can do...

I think you're also suppose to use $$\Sigma$$Before = $$\Sigma$$After

 

[skand]

I think you should think that since an impulsive force has acted on car,we cannot use Conservation of Momentum.The final momentum is $0$.

Change in momentum is same in both the cases,but 'rate of change of momentum' is different and thus,the forces are different.

 

[nlightner]

i) The momentum of the car before it hits the wall is 9000 kg*m/s.
ii) After the collision, the momentum will be 0 kg*m/s since the car comes to a complete stop.
iii) The change in momentum is 9000 kg*m/s.
iv) The force stopping the car without crumple zones is F = (9000 kg*m/s) / (0.0500 s) = 180,000 N.
v) With crumple zones, the force stopping the car is F = (9000 kg*m/s) / (0.9500 s) = 9473.68 N.
vi) The force stopping the car is significantly reduced with the presence of crumple zones, which allows for a longer deceleration time and spread out the impact force over a longer period of time. This helps to reduce the overall force exerted on the passengers and minimize potential injuries.