Conservation of relativistic momentum

[VVS2000]

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

 

[TSny]

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.

 

[VVS2000]

Yeah you're right about the signs. But what if I want to show only for the y component if the velocity is conserved?

 

[TSny]

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?