Can you help with my classroom debate? (Impulses in car crashes)

[Xian Maynor]

My classmates and I were discussing the impulse-momentum theorem and how they correlate.

The example problem consisted of two cars running into solid surfaces at the same velocity. One car ran into a brick wall and came to a complete stop. The other car ran into a haystack and came to a complete stop. This was done so to where the change in momentums were the same between the two cars.

A question was then arisen as to whether the impulse of the two surfaces were the same, as impulse and momentum are considered to always be equal to each other mathematically. My teacher began to say that the impulses were different because the surfaces were different, however, I stated that if the change in momentums were equal between the two cars, then the impulses between the two cars would also be the same.

Who's right?

 

[ZapperZ]

My classmates and I were discussing the impulse-momentum theorem and how they correlate.

The example problem consisted of two cars running into solid surfaces at the same velocity. One car ran into a brick wall and came to a complete stop. The other car ran into a haystack and came to a complete stop. This was done so to where the change in momentums were the same between the two cars.

A question was then arisen as to whether the impulse of the two surfaces were the same, as impulse and momentum are considered to always be equal to each other mathematically. My teacher began to say that the impulses were different because the surfaces were different, however, I stated that if the change in momentums were equal between the two cars, then the impulses between the two cars would also be the same.

Who's right?

Read this:

http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html

Do you think the stopping time is the same for both scenarios?

Zz.

 

[berkeman]

My classmates and I were discussing the impulse-momentum theorem and how they correlate.

The example problem consisted of two cars running into solid surfaces at the same velocity. One car ran into a brick wall and came to a complete stop. The other car ran into a haystack and came to a complete stop. This was done so to where the change in momentums were the same between the two cars.

A question was then arisen as to whether the impulse of the two surfaces were the same, as impulse and momentum are considered to always be equal to each other mathematically. My teacher began to say that the impulses were different because the surfaces were different, however, I stated that if the change in momentums were equal between the two cars, then the impulses between the two cars would also be the same.

Who's right?

Welcome to the PF.

Impulse and momentum have slightly different definitions. Can you show us the equations for each?

EDIT -- Oops, Zz beat me to it!

 

[Xian Maynor]

Read this:

http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html

Do you think the stopping time is the same for both scenarios?

Zz.

Yes, the stopping times were the same for both vehicles.

 

[Xian Maynor]

Welcome to the PF.

Impulse and momentum have slightly different definitions. Can you show us the equations for each?

EDIT -- Oops, Zz beat me to it!

There were no equations because they were conceptual multiple choice. We were talking about the change in momentum and impulse and whether they were the same.

 

[ZapperZ]

Yes, the stopping times were the same for both vehicles.

Really? One stops almost immediately, while the other is spread out over the crumpling of the haystack. One changes momentum very quickly, while the other has its momentum change over a period of time.

Think again!

Zz.

 

[Xian Maynor]

Really? One stops almost immediately, while the other is spread out over the crumpling of the haystack. One changes momentum very quickly, while the other has its momentum change over a period of time.

Think again!

Zz.

That was the problem that I had. However, my teacher told me to envision a situation where they had the same stopping time, even though the surfaces are different. I personally feel that she butchered this question.

 

[ZapperZ]

That was the problem that I had. However, my teacher told me to envision a situation where they had the same stopping time, even though the surfaces are different. I personally feel that she butchered this question.

Look at the link I gave you. You (or your teacher) may not want to consider any "equation", but that is the ONLY guide one has to view this, even conceptually.

Zz.

 

[Xian Maynor]

Look at the link I gave you. You (or your teacher) may not want to consider any "equation", but that is the ONLY guide one has to view this, even conceptually.

Zz.

I think I better understand. While the impulses would be the same, the amount of force exerted to stop the car is equally proportional to the amount of time it took the car to stop. Therefore, when multiplied together, they come to the same amount of impulse, even though they are different surfaces?

 

[ZapperZ]

I think I better understand. While the impulses would be the same, the amount of force exerted to stop the car is equally proportional to the amount of time it took the car to stop. Therefore, when multiplied together, they come to the same amount of impulse, even though they are different surfaces?

You are not quite there.

The force applied is inversely-proportional to the time it takes to stop the car. The shorter the time, the larger the applied force to stop the car. This is an opposite relationship, not "equally proportional".

Zz.

 

[Xian Maynor]

You are not quite there.

The force applied is inversely-proportional to the time it takes to stop the car. The shorter the time, the larger the applied force to stop the car. This is an opposite relationship, not "equally proportional".

Zz.

My bad, that's what I meant. I meant it as in if the wall had a force of 3 and the time was 2, and the haystack had a force of 2, but a time of 3, then the impulse would be 6 for both, making the impulses equal.

 

[ZapperZ]

My bad, that's what I meant. I meant it as in if the wall had a force of 3 and the time was 2, and the haystack had a force of 2, but a time of 3, then the impulse would be 6 for both, making the impulses equal.

Then you have it.

Zz.

 

[Xian Maynor]

You are not quite there.

The force applied is inversely-proportional to the time it takes to stop the car. The shorter the time, the larger the applied force to stop the car. This is an opposite relationship, not "equally proportional".

Zz.

Thank you, that really helps me to better understand this.