How Do Momentum and Kinetic Energy Influence Collision Outcomes?

[Mohamad]

Suppose object1 with mass m and velocity v has collided with a block. Also, object2 that has identical shape and dimensions with mass m/2 and velocity 2v has collided to that block. Since the momenta of two objects are identical but the kinetic energy of object2 is twice:

1. Are the forces between objects and block at the moment of collision different?
2. Are the results of collisions different? I want to know which of them - momentum or energy - has influence on the result of collision.

PS, in another situation we can suppose the mass of object2 is 4m and the velocity is v/2, so the kinetic energy is similar to object1 but the momentum is twice.

 

[PeroK]

Summary: Which of them has influence on the result of a collision? Change in momentum, change in kinetic energy or both?

Suppose object1 with mass m and velocity v has collided with a block. Also, object2 that has identical shape and dimensions with mass m/2 and velocity 2v has collided to that block. Since the momenta of two objects are identical but the kinetic energy of object2 is twice:

1. Are the forces between objects and block at the moment of collision different?
2. Are the results of collisions different? I want to know which of them - momentum or energy - has influence on the result of collision.

Have you ever heard of Newton's third law?

 

[Mohamad]

Have you ever heard of Newton's third law?

I asked the difference between force of object1 and force of object2 on the block? They are two different situations. I can't understand the relationship with Newton's third law!

 

[PeroK]

I asked the difference between force of object1 and force of object2 on the block? They are two different situations. I can't understand the relationship with Newton's third law!

Okay. What's stopping you doing the calculations yourself?

 

[Mohamad]

Okay. What's stopping you doing the calculations yourself?

I don't know how to compute the force between objects, given mass and velocity.

 

[PeroK]

I don't know how to compute the force between objects, given mass and velocity.

You can't. The force depends on the materials involved and how long the actual collision takes. Hard objects would have high forces and springlike objects would have low forces.

You can, however, calculate changes in energy and momentum that occur as a result of the collision.

 

[Mohamad]

The force depends on the materials involved

In both situations that I said, materials are identical, so it doesn't matter. I don't want an actual number for amount of force. I only want a comparison between forces in these two situations.

calculate changes in energy and momentum

Suppose we don't know anything about the after of collison. Can we do a comparison between the collisions of these two situations:

• The energy of object2 is equal to object1 but the momentum is different. (object1 and object2 collide to an identical block)
• The momentum of object2 is equal to object1 but the energy is different. (object1 and object2 collide to an identical block)

 

[PeroK]

In both situations that I said, materials are identical, so it doesn't matter. I don't want an actual number for amount of force. I only want a comparison between forces in these two situations.

Suppose we don't know anything about the after of collison. Can we do a comparison between the collisions of these two situations:

• The energy of object2 is equal to object1 but the momentum is different. (object1 and object2 collide to an identical block)
• The momentum of object2 is equal to object1 but the energy is different. (object1 and object2 collide to an identical block)

You need to post your best attempt at these problems.

As I said before, the actual forces depend on assumptions about the materials and how they deform when they collide. You're better off looking at impulse in these cases.

Alternatively, you could model the collision using an elastic spring.

 

[Motore]

Perhaps this link can give you some insight:
http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html

 

[Dale]

Alternatively, you could model the collision using an elastic spring.

This is the approach that I would recommend. It will get you a "first order" answer at a minimum.

In both situations that I said, materials are identical, so it doesn't matter.

Actually, modeling the force of a collision the details matter very much. In fact, simply saying "same material" is insufficient. You actually have to describe the structure a bit. The key is to get an overall spring constant that you can use to model the force as a function of the compression distance. However, that does not only depend on the material, but also the shape of the structure. The same material has the same density, so to make a different amount of mass requires a different volume.

If the large mass is a solid sphere, then is the small mass a solid sphere of a smaller radius or is it a hollow sphere? The resulting spring constants will be different.

If the masses are cylindrical are they made to have the same length but different diameter (more massive will have higher spring constant) or are they made to have the same diameter but different length (more massive will have lower spring constant) or are they made to differ in both diameter and length such that their spring constants are the same?

 

[russ_watters]

1. Are the forces between objects and block at the moment of collision different?
2. Are the results of collisions different? I want to know which of them - momentum or energy - has influence on the result of collision.

To me, these questions have simple but not particularly useful answers:

1. Probably yes.
2. Yes; both.

The problem here in my opinion is that "results of collisions" doesn't mean anything. What results? Most often for simple physics problems, the "results" are momentum and kinetic energy. Force is not often as useful. But it is kind of up to you what you want - and for you to define.

 

[Mohamad]

Thanks a lot, I understood the faults and oversimplifications in my question.

 

[sophiecentaur]

forces between objects and block at the moment of collision

It should be remembered that there is never a 'moment' of a collision. Collisions are never instantaneous; they always take some time. The shorter the time, the greater the forces involved. Two steel balls colliding will have greater forces between them than two rubber 'super balls' and two 'perfect' sponges would have even lower forces between them - because the times are so different.