Momentum in special relativity problem

[sapz]

Homework Statement

Hi there.

I added a question as an image, what is the right way to find the momentum?

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

what is the right way to find the momentum?

You use the energy-momentum relationship.

$E^2 = m^2c^4 + p^2c^2$

The kinetc energy is $K=(\gamma -1)mc^2$ and $E=\gamma mc^2$

 

[sapz]

Im aware of that. However could you please address the question in the picture? Which way is wrong, and why?

 

[Simon Bridge]

I was[/] addressing the pic.
The pic includes the question "What is the momentum of the moving particle?"
You wanted to know the right way to go about it - I told you.

It seems I misunderstood.
Define "right way". (What makes you think there is a wrong way in there?)
The pic shows you how to solve for two contexts in relation to the center-of-mass.

 

[Nickie]

In special relativity, momentum is defined as the product of an object's mass and its velocity. This can be expressed mathematically as p = mv, where p is the momentum, m is the mass, and v is the velocity. However, in order to properly calculate momentum in special relativity, we must also take into account the effects of time dilation and length contraction. This can be done using the Lorentz transformation equations.

To find the momentum of an object in a specific reference frame, we must first determine the object's velocity in that frame. This can be done by using the Lorentz transformation formula for velocity, v' = (v + u)/(1 + (vu/c^2)), where v' is the velocity in the new frame, v is the velocity in the original frame, u is the relative velocity between the two frames, and c is the speed of light.

Once we have the velocity in the new frame, we can then use the equation p = mv to calculate the momentum. It is important to note that in special relativity, momentum is a relativistic quantity and is not conserved in all reference frames. Therefore, it is essential to use the correct equations and transformations when calculating momentum in special relativity problems.