Conservation of relativistic momentum

In summary, the conversation discusses the calculations and signs involved in determining relativistic momentum before and after a collision, specifically in the y-component. It is mentioned that velocity does not always follow conservation laws in collisions and further clarification is requested on what is trying to be shown.
  • #1
VVS2000
150
17
Homework Statement
Given a collision, I have to verify that the y component of the collision remains the same in the given reference frames(photos are attached) which differ only by x components of velocity(berkeley physics course pg 375)
Relevant Equations
P=Mv/(1-v^2/c^2)
TM = total momentum
15941503875305250151553508138034.jpg
15941496202457519876965809938172.jpg
15941496613308007361789658812793.jpg
15941503875305250151553508138034.jpg
 
Physics news on Phys.org
  • #2
Before the collision, particle 1 has a negative y'-component of momentum. But it looks like you wrote it as having a positive y'-component. Similarly, check your signs for after the collision.

In the definition of relativistic momentum, the denominator is ##\sqrt{1-v^2/c^2} = \sqrt{1-\left(v_x^2+v_y^2\right)/c^2}##.
In the primed frame, this is ##\sqrt{1-{v '}^2/c^2} = \sqrt{1-\left({v_x '}^2+{v_y '}^2 \right)/c^2}##. So, for particle 1 in the primed frame you need to include ##{v_x '}^2## as well as ##{v_y '}^2## in the denominator.
 
  • Like
Likes VVS2000
  • #3
Yeah you're right about the signs. But what if I want to show only for the y component if the velocity is conserved?
 
  • #4
VVS2000 said:
Yeah you're right about the signs. But what if I want to show only for the y component if the velocity is conserved?
It's not clear to me what you are trying to show. Velocity is not something that obeys a conservation law in general collisions. Can you describe precisely what you want to show?
 

What is the conservation of relativistic momentum?

The conservation of relativistic momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant in all inertial reference frames. This means that the total momentum of all the objects involved in a collision or interaction will be the same before and after the event, regardless of the speed or direction of the objects.

Why is the conservation of relativistic momentum important?

The conservation of relativistic momentum is important because it is a fundamental law of nature that helps us understand and predict the behavior of objects in motion. It is also a key principle in many areas of physics, including particle physics, astrophysics, and cosmology.

How does the conservation of relativistic momentum differ from classical momentum?

The conservation of relativistic momentum differs from classical momentum in that it takes into account the effects of special relativity, which describes the behavior of objects moving at speeds close to the speed of light. In classical physics, momentum is calculated using the equation p = mv, where m is an object's mass and v is its velocity. In relativistic physics, the equation for momentum is p = mv/√(1-v^2/c^2), where c is the speed of light.

What is an example of the conservation of relativistic momentum in action?

An example of the conservation of relativistic momentum in action is a collision between two particles in a particle accelerator. Before the collision, the total momentum of the two particles is equal to the sum of their individual momenta. After the collision, the particles may have changed direction or speed, but the total momentum of the system will remain the same.

Are there any exceptions to the conservation of relativistic momentum?

No, there are no known exceptions to the conservation of relativistic momentum. This principle has been extensively tested and has been found to hold true in all observed physical interactions. However, in extreme cases such as black holes or the Big Bang, where the laws of physics may break down, the conservation of relativistic momentum may not apply.

Similar threads

  • Introductory Physics Homework Help
Replies
15
Views
852
  • Introductory Physics Homework Help
Replies
4
Views
742
  • Introductory Physics Homework Help
Replies
2
Views
753
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
23
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
621
  • Introductory Physics Homework Help
2
Replies
47
Views
636
  • Introductory Physics Homework Help
Replies
2
Views
919
  • Introductory Physics Homework Help
Replies
6
Views
614
  • Introductory Physics Homework Help
Replies
7
Views
1K
Back
Top