Help understanding this collision question

[urbano]

Homework Statement

I've been checking out the ol' truck vs small car in a head on collision problem. The question asks which about which vehicle will experience the greatest force of impact ? The greater impulse? The greater change in momentum ? The greater deceleration.

A number of aspects of it have me second guessing my understanding of what is going on...and even when I feel I may know the answer I don't actually know WHY it is the way it is

Homework Equations

Momentum = m * v
Impulse = F * t , which means a change in momentum = change in m * v

Newtons 3rd law

The Attempt at a Solution

So in terms of the force on impact, I believe if Newton's third law says for each action there is an equal and opposite reaction, then therefore they should impart the same amount of force on each other...although this confuses me. If F= m*a, how can they exert the same force on each other given the truck is likely to have a greater force given its mass ?

The greater impulse ...I believe this would be equal. If they are exerting the same amount of force and in contact for the same amount of time then they both are creating an equal impulse. However, the change in momentum confuses me...if it = m * v, the mass of each vehicle is likely to stay the same and the velocity would stay the same. For example if the truck hits the car and pushes it east, the truck and the car will both travel east and their masses will have remained the same...therefore making the impulse equal for both ?

The change in momentum...as per above wouldn't they both change by equal amounts?

The greater deceleration. .for this I believe it to be the mini (or both) as A= d/t and I'm presuming the mini would end up going backwards.

 

[mfb]

So in terms of the force on impact, I believe if Newton's third law says for each action there is an equal and opposite reaction, then therefore they should impart the same amount of force on each other

Right

If F= m*a, how can they exert the same force on each other given the truck is likely to have a greater force given its mass ?

The truck will have a different acceleration.

The greater impulse ...I believe this would be equal. If they are exerting the same amount of force and in contact for the same amount of time then they both are creating an equal impulse.

Right.

However, the change in momentum confuses me...if it = m * v, the mass of each vehicle is likely to stay the same and the velocity would stay the same.

The velocity will not stay the same. In addition, the velocity differences will be different, too.

For example if the truck hits the car and pushes it east, the truck and the car will both travel east and their masses will have remained the same...therefore making the impulse equal for both ?

Their velocity, not their momentum. In addition, the question asks for momentum transfer (change in momentum), not momentum.

The change in momentum...as per above wouldn't they both change by equal amounts?

Right.

The greater deceleration. .for this I believe it to be the mini (or both) as A= d/t and I'm presuming the mini would end up going backwards.

What is d?
You can use F=ma and the result for the force to answer this question.

 

[urbano]

Right
The velocity will not stay the same. In addition, the velocity differences will be different, too.

.

I don't quite get this...at the moment they collide aren't they both for a very small instant of time starting at 0 velocity, i.e they are not moving ? Then if the truck is in contact with the mini and pushes it backwards aren't they moving in the same direction for the same amount of time ? i.e both have the same velocity ? the mini will keep being pushed backwards so long as the truck keeps moving forwards. so the truck pushes forward 5 meters over 5 seconds, the mini moves 5 meters over 5 seconds as well.

Obviously I'm wrong but I don't know why.

**Update** I just watched an animation on this exact scenario, an depending on if it's elastic or non-elastic then the results vary ...ARGHH!

 

[mfb]

at the moment they collide aren't they both for a very small instant of time starting at 0 velocity

Could happen during the collision (but here you get the additional problem that not all parts of the cars are moving at the same speed), but it does not matter.

Then if the truck is in contact with the mini and pushes it backwards aren't they moving in the same direction for the same amount of time ? i.e both have the same velocity ?

After the collision, if the collision is perfectly inelastic, they move with the same velocity. Before the collision, they do not (otherwise they would not collide).