# Thread: Newton's Third Law and Collisions

1. Hi,

Hopefully someone can help me understand the following problem.

So, according the Newton's third law we now that for every action there is an equal and opposite reaction.

Let's look at three scenarios. We'll have four marbles, all the same size, but different masses.
Marbles A and B: both 20g
Marble C: 2g
Marble D: 2000g
Speed X: 10cm/s

Scenario #1: (Using Marble A and B)
Marble A rolls at speed X towards Marble B that is at rest. Marble A hits Marble B. This causes Marble A to stop moving and Marble B to move at speed X.

Scenario #1: (Using Marble A and B)
Marble A rolls at speed X towards Marble C that is at rest. Marble A hits Marble C. This causes Marble A to slow down and Marble B to move fast (more than speed X).

Scenario #1: (Using Marble A and B)
Marble A rolls at speed X towards Marble D that is at rest. Marble A hits Marble D. This causes Marble A to bounce back and Marble B to hardly move.

What I don't understand is that in all three scenarios Marble A hit Marbles B, C and D with the same force. I understand why Marbles B, C and D react differently (because of their different masses). What I don't understand is why Marble A behaves differently: either stopping, slowing down or bouncing back. According the Newton's third law, since it hits the three marbles with the same force, the opposite force on Marble A is the same in all three situations. I understand that momentum is conserved, but I would like to deal with the forces issue only. Basically, why does Marble A behave differently to the same reaction force. The behavior of the marbles that it hits seems to influence its own behavior.

Any thoughts would be appreciated,
Shar

2. In those types of collisions both momentum and kinetic energy are conserved.
momenta are proportional to velocity times mass, and are vectors (velocity is sign sensitive)
kinetic energies are proportional to velocity squared times mass, and are scalars.

Set up some sketches of before and after. Define a positive direction. Create two equations. Solve for the two unknowns.

3. Thanks for the reply. I understand that energy is conserved. I'm trying to understand the influence of the forces separately. If in each of the three situations, let's say a 5N force pushed back on Marble A, why did the marble behave differently?

4. If the masses are the same it it possible for the marble to transfer ALL the energy and momentum to the other marble. If the masses are different it it just not possible to conserve both if the momentum of A afterwards is zero.

5. All I'm saying is that in the three situations the same reaction force (e.g. 5 N) caused Marble A to either slow down, stop or bounce back. Is this because of time of impact? Does the marble have a longer impact time with the larger mass, so that the force causes a great change in motion. I'm wondering.

6. It is a consequence of conservation of energy and momentum. Imagine a small bullet hitting an infinitely strong target so it doesn't get absorbed. If the bullet is much lighter than the target it will bounce off. If the mass of the target is much less than the bullet, the bullet will keep going along with the target. There is a situation in the middle where the bullet just stops - that is when the mass of the bullet and target target are equal.

7. Hi Jilan,

I like your example. Would you agree that in all three situations the bullet hit its target with the same force, and that an equal force hit it in return? If this is so, without thinking about the energy concepts, how would you explain that each bullet behaved differently after impact. If you're purely thinking about Newton's third law, how would you explain this? - that the bullet reacted differently to the same force.

8. Force is a funny concept in collisions. In a perfect collision the time of it would be zero so the force would be infinite! So it's best not to think in those terms!

9. As I understand so far, the magnitude of the reaction force is meaningless, only the direction of the force is significant. As in your example, the bullet either slows down, stops or bounces back, all in reaction to the same magnitude of force.

10. Take a look at this. Fascinating fun. Momentum, Magnets & Metal Balls - Sixty Symbols

11. The video doesn't answer my question, but it is pretty cool - thanks for the link.

I surmised your OP was well answered in the posts that said the momentum and KE are conserved in perfectly elastic collisions. The best and simplest way to understand this is through momentum and KE. Also answered was that using forces, pressures, times etc is not practical with that type of problem.

Maybe Hooke's Law , Young's Modulus , Plasticity , Creep , Stress Relaxation , Deformation and strain , Stress can shed some light on how materials respond to forces, pressure, tension etc.

It's a long haul beyond first year simplifications.

13. I've thought about this a bit more, and realized that the forces must be different in each situation. For example, as in the original example at the top, if Mass A traveling at speed X hits Mass B (both same masses), let's say with a force of 4 N, then in return Mass B will hit Mass A also with a force 4N in the opposite direction, causing Mass A to stop. BUT, if Mass A traveling at the same speed hits Mass C which has a smaller mass, then it cannot successfully hit it with a force of 4N. A 4N force will not be accepted by the smaller mass and therefore the reaction force on Mass A will be less than 4N, and the mass will not stop as it did when it hit Mass B.
Now, when Mass B hits Mass D, which is heavier than Mass B, I am thinking that it does accept the 4N force and causes a reaction force of 4N, and then maybe due to spring action or something an additional force is applied to Mass B causing it to bounce back.

Does this make sense?

14. As has been posted: The force is a function of the interaction. It is a result of how the materials interact. No interactions means no forces. A 5 m/s collision between two 1 kg balls made of brass, steel, india rubber, wood, or glass will all have different forces. It's a material science situation. Engineering type maths show this in a clearer fashion than lengthy prose.

15. Originally Posted by Shar200
Hi,

Hopefully someone can help me understand the following problem.

So, according the Newton's third law we now that for every action there is an equal and opposite reaction.

Let's look at three scenarios. We'll have four marbles, all the same size, but different masses.
Marbles A and B: both 20g
Marble C: 2g
Marble D: 2000g
Speed X: 10cm/s

Scenario #1: (Using Marble A and B)
Marble A rolls at speed X towards Marble B that is at rest. Marble A hits Marble B. This causes Marble A to stop moving and Marble B to move at speed X.
So, A acts with a force upon B and puts B in motion with speed X. (Why X? You can find this ONLY by writing the equations of energy/momentum conservation) *
B acts upon A with an equal and opposite force and makes A stop. (How do you know this? You guessed it, you will need to .....write the equations of energy/momentum conservation).
The two balls have reversed roles, in perfect symmetry. Do you have a problem with this explanation so far?

--------------------------------------------------------------------------------------------------
*

If the above becomes:

so:

=> . Only the solution is acceptable, so .

16. Originally Posted by Shar200
As I understand so far, the magnitude of the reaction force is meaningless, only the direction of the force is significant. As in your example, the bullet either slows down, stops or bounces back, all in reaction to the same magnitude of force.
This is not true, the magnitude of the force and the mass of the particle are key.
"A" acts with force F on "B".
"B" (re)acts with force -F on "A"

The acceleration of the two particles is equal if and only if their masses are equal, otherwise it is not:

if then

This explains why

Scenario #1: (Using Marble A and B)
Marble A rolls at speed X towards Marble C that is at rest. Marble A hits Marble C. This causes Marble A to slow down and Marble B to move fast (more than speed X).
You certainly must mean:

"Scenario #2: (Using Marble A and C)
Marble A rolls at speed X towards Marble C that is at rest. Marble A hits Marble C. This causes Marble A to slow down and Marble C to move fast (more than speed X)."

This is because , see above. This implies , see above.

17. I'm liking this because you have the right idea. In a perfectly elastic collision between two balls of the same mass the moving ball will stop dead. If it's heavier is will keep going, albeit slower. If it is lighter than what it is colliding with it will bounce back. However thinking of it in terms do forces will lead to issues because how long the objects are in contact is very dependent on the materials involved. You need to consider just the momentum and the energy conservation. You might enjoy this video.

18. Originally Posted by Jilan
I'm liking this because you have the right idea. In a perfectly elastic collision between two balls of the same mass the moving ball will stop dead. If it's heavier is will keep going, albeit slower. If it is lighter than what it is colliding with it will bounce back. However thinking of it in terms do forces will lead to issues because how long the objects are in contact is very dependent on the materials involved. You need to consider just the momentum and the energy conservation. You might enjoy this video.
Good video, all you need to do is to be able to write the equations of energy/momentum conservation that explain the video.

19. Thanks for the video. Gives to me a lot to think about. I'm going to play around with some math over the weekend and see if I can find force patterns. What I seem confident about is that different forces are exerted on different masses, even if they are all the same material. (I'm talking about Marble A hitting any size mass) Also, there is a maximum amount of force an object can exert enabling it to bounce back (at the same speed it hit an object). So for example, a 1 kg ball travelling at 1 m/s will have a maximum impact of 2 N. I might be wrong about this, but I think this is the right direction.

20. Originally Posted by Shar200
So for example, a 1 kg ball travelling at 1 m/s will have a maximum impact of 2 N.
Nope, 1N.

21. Originally Posted by Shar200
Thanks for the video. Gives to me a lot to think about. I'm going to play around with some math over the weekend and see if I can find force patterns. What I seem confident about is that different forces are exerted on different masses, even if they are all the same material. (I'm talking about Marble A hitting any size mass) Also, there is a maximum amount of force an object can exert enabling it to bounce back (at the same speed it hit an object). So for example, a 1 kg ball travelling at 1 m/s will have a maximum impact of 2 N. I might be wrong about this, but I think this is the right direction.
You will have extreme difficulties. Forces are best applied in situations where the forces are constant. In collisions they are not.

22. So, I played around with with this Phet simulation (Collision&#32;Lab 2.01).
I created a 1kg mass traveling at 1 m/s that collided with other different masses. So, as predicted, the smaller the collided mass, the smaller the change in momentum. Also I noticed that there is a maximum change of momentum of 2.0 km x m/s (or N x s) when hitting larger masses.

So, I think I'm back to square one. I'm not sure if a larger force is applied on a larger mass, or if the time of impact is longer, or is it both. I can't find anything on the web that correlates time of impact versus mass.

23. Originally Posted by Shar200
So, I played around with with this Phet simulation (Collision Lab 2.01).
I created a 1kg mass traveling at 1 m/s that collided with other different masses. So, as predicted, the smaller the collided mass, the smaller the change in momentum. Also I noticed that there is a maximum change of momentum of 2.0 km x m/s (or N x s) when hitting larger masses.

So, I think I'm back to square one. I'm not sure if a larger force is applied on a larger mass, or if the time of impact is longer, or is it both. I can't find anything on the web that correlates time of impact versus mass.
Did you read any of the explanations that I wrote for you?

24.

25. Interesting study. I am only able to read the abstract, but I think it's enough. It's not a surprise that golf balls made of different materials have different impact times. Would you assume that longer impact time would allow greater acceleration of a golf ball, since the golfer can apply a given force for a longer period of time?

It's also interesting to learn that the duration of impact was reduced with speed of club. So, they are saying that if the impact force is larger due to speed (they're not talking about mass), then the force affects the golf ball for a shorter amount of time then a smaller force from a slower club.

... I wonder if there are other studies with similar results.

26. Careful. Perfectly elastic also means absolutely no loss of energy into the environment. No noise, no heat, no everything in or out of those two balls. The P and KE equations hold perfectly.
Very good elastic collisions are quite easy to create. The P and KE equations do not quite hold but are a good approximation, the loss may be undetectable with ordinary do it yourself measurements.

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