Help understanding this collision question

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In summary, the question is asking which vehicle will experience the greatest force of impact, the greater impulse, the greater change in momentum, and the greater deceleration in a head-on collision between a truck and a small car. The answer to these questions relies on Newton's third law, where for every action there is an equal and opposite reaction. This means that the force on impact and the impulse will be equal for both vehicles. However, the change in momentum will be different as the velocities and masses of the vehicles are different. As for the deceleration, it will depend on the distance and time of contact, with the truck likely experiencing a greater deceleration. The result may also vary depending on whether the collision is elastic or
  • #1
urbano
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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.
 
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  • #2
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.
 
  • #3
mfb said:
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!
 
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  • #4
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).
 
  • #5



Hello,

I understand that you are having some confusion with a collision problem involving a truck and a small car. Let me try to clarify some of your questions.

Firstly, in terms of the force of impact, it is true that according to Newton's third law, the truck and car will exert equal and opposite forces on each other. However, this does not mean that the forces experienced by both vehicles will be the same. The force experienced by each vehicle will depend on its mass and acceleration. The truck, with a larger mass, will experience a greater force of impact than the small car.

Regarding impulse, you are correct that it will be equal for both vehicles. This is because impulse is the product of force and time, and since the force and time are the same for both vehicles, the impulse will also be the same.

For change in momentum, it is important to consider the initial and final velocities of each vehicle. In a head-on collision, the initial velocities of both vehicles are opposite in direction. This means that the final velocities will also be opposite, resulting in a change in momentum that is equal in magnitude but opposite in direction for both vehicles.

Lastly, for deceleration, it is true that the small car will experience a greater deceleration as it will be pushed backwards by the truck. This is because deceleration is a measure of how quickly an object's velocity decreases, and the small car will experience a larger decrease in velocity due to being hit by the truck.

I hope this helps to clarify some of your questions. If you have any further questions or need more clarification, don't hesitate to ask. Keep up the good work with your studies!
 

What is a collision?

A collision is an event that occurs when two or more objects come into contact with each other and exert forces on each other. This can result in a change in the objects' motion or shape.

What causes collisions?

Collisions can be caused by a variety of factors, including the movement of objects, forces acting on objects, or external influences such as gravity or friction. In some cases, collisions may also be the result of intentional actions, such as in experiments or sports.

How can collisions be analyzed or understood?

Collisions can be analyzed through the use of physics principles and equations, such as Newton's laws of motion and conservation of momentum. Understanding the properties of the objects involved, such as their mass and velocity, can also help in understanding collisions.

What are the different types of collisions?

There are two main types of collisions: elastic and inelastic. In an elastic collision, energy is conserved and the objects bounce off each other without any loss of energy. In an inelastic collision, some energy is lost and the objects may stick together or deform in some way.

Why is understanding collisions important?

Understanding collisions is important in various fields of science and engineering, such as mechanics, astronomy, and material science. It allows us to predict and control the behavior of objects in motion, and can also help in designing safer and more efficient structures and technologies.

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