Special relativity momentum and energy conservation

[Taylor_1989]

Homework Statement

Two identical particles of mass m travel towards each other at speed v; they combine and form a single new particle. By employing conservation of momentum and conservation of energy, what is the mass of this new particle in

Homework Equations

Relativistic momentum and total energy , possibly lorentz velocity transformation

The Attempt at a Solution

I am completely lost to where to start with this, because of two reasons. I can see if I need to use a frame of reference, I not sure if the v<<c and do I take the velocity as a vector?

I know the momentum and total energy are consevered in relativity but in the question I see that if the final momentum is equal to the sum of the initial surely this 0 because they are moving at the same speed and they are the same mass, so how can they even move at a speed after the collision. My lecture has not explained this very well in his notes and I am very lost could someone please help me.

Also tell me what the latex tags are for the physics forum. Big thanks in advance.

 

[PeroK]

Homework Statement

Two identical particles of mass m travel towards each other at speed v; they combine and form a single new particle. By employing conservation of momentum and conservation of energy, what is the mass of this new particle in

Homework Equations

Relativistic momentum and total energy , possibly lorentz velocity transformation

The Attempt at a Solution

I am completely lost to where to start with this, because of two reasons. I can see if I need to use a frame of reference, I not sure if the v<<c and do I take the velocity as a vector?

I know the momentum and total energy are consevered in relativity but in the question I see that if the final momentum is equal to the sum of the initial surely this 0 because they are moving at the same speed and they are the same mass, so how can they even move at a speed after the collision. My lecture has not explained this very well in his notes and I am very lost could someone please help me.

Also tell me what the latex tags are for the physics forum. Big thanks in advance.

I think it's safe to assume that "towards each other" means a head-on collision. So, momentum before the collision is 0, as you suspected.

Latex in line $E = mc^2$ or isolated: $$E = mc^2$$

 

[phinds]

Homework Statement

Two identical particles of mass m travel towards each other at speed v; they combine and form a single new particle. By employing conservation of momentum and conservation of energy, what is the mass of this new particle in

Homework Equations

Relativistic momentum and total energy , possibly lorentz velocity transformation

The Attempt at a Solution

I am completely lost to where to start with this, because of two reasons. I can see if I need to use a frame of reference, I not sure if the v<<c and do I take the velocity as a vector?

I know the momentum and total energy are consevered in relativity but in the question I see that if the final momentum is equal to the sum of the initial surely this 0 because they are moving at the same speed and they are the same mass, so how can they even move at a speed after the collision. My lecture has not explained this very well in his notes and I am very lost could someone please help me.

Also tell me what the latex tags are for the physics forum. Big thanks in advance.

Something to think about to clarify your thinking on the velocity and Lorentz transform: would the answer be any different if you were to use a reference frame in which one of the particles is at rest?

 

[PeroK]

Something to think about to clarify your thinking on the velocity and Lorentz transform: would the answer be any different if you were to use a reference frame in which one of the particles is at rest?

Personally, I would prefer the centre-of-momentum frame for his one!

 

[Taylor_1989]

Thank for the response guy, I just had another look and it dawned on me. I mean momentum would be 0 and then I could total energy of the system is equal to the rest energy hence \(\displaystyle E=mc^2[\math]\)

 

[Buffu]

Thank for the response guy, I just had another look and it dawned on me. I mean momentum would be 0 and then I could total energy of the system is equal to the rest energy hence \(\displaystyle E=mc^2[\math]\)

\(\displaystyle

You have to enclose the math in side two # or two $
eg:
#`# e = mc^2 #`#
or $`$ e = mc^2 $`$

just don't put ` in between.It is to stop the rendering of math.\)

 

[Ray Vickson]

Thank for the response guy, I just had another look and it dawned on me. I mean momentum would be 0 and then I could total energy of the system is equal to the rest energy hence \(\displaystyle E=mc^2[\math]\)

\(\displaystyle

No. If the collision is perfectly inelastic (all kinetic energy converted to mass) then the mass afterwards would NOT be $2m$ in the relativistic case. (In the classical case we would not have conservation of energy because mass end energy are not equivalent in that regime.)\)