Frame of reference, energy and momentum of particle

[SL_1719]

Homework Statement

In a certain reference frame, a particle with momentum of 4 MeV/c and a total energy of 5 MeV
(a) Determine the mass of the particle.
(b) What is the total energy of the particle in a reference frame in which its momentum is 4 MeV/c?
(c) What is the relative speed of the two reference frames?

Homework Equations

E²=p²c²+(mc²)²
E=mc²/(1-(u²/c²))^1/2
u_x=(u'_x+v)/(1+vu'_x/c²)
u/c=pc/E
(u just another form of velocity)

The Attempt at a Solution

So I was able to find the answer to a and b, which are 5.3 MeV 6.64MeV respectively. I am just struggling finding to find an answer. Working on a practice problem I was coming nowhere close to the answer it had. I am just completely lost. I tried on the practice problem doing u/c=pc/E=> 4/5=.8 and 3/4.24=.707, but from there any combination I used got me nowhere. For the practice problem original frame momentum=4MeV/c, total energy=5MeV, mass is 3 MeV, total energy in frame 2=4.24MeV and momentum=3MeV/c. Anything helps, pointing me in the right direction or equations I am missing.

 

[anathema]

Thank you!

Hi there,

First, let's define some variables for easier understanding:
m = mass of the particle
p = momentum of the particle
E = total energy of the particle
c = speed of light
u = velocity of the particle in the original reference frame
u' = velocity of the particle in the new reference frame
v = relative speed between the two reference frames

a) To determine the mass of the particle, we can use the equation E^2 = p^2c^2 + (mc^2)^2. Plugging in the given values, we get:
(5 MeV)^2 = (4 MeV/c)^2 * c^2 + m^2c^4
m = 3 MeV/c^2

b) In the new reference frame, the momentum is still 4 MeV/c, but the total energy is different. We can use the equation E = mc^2/(1-(u'^2/c^2))^(1/2). Plugging in the values, we get:
E = (3 MeV/c^2)*c^2/(1-(4 MeV/c)^2/c^2)^(1/2)
E = 4.24 MeV

c) To find the relative speed between the two reference frames, we can use the equation u/c = pc/E. Plugging in the values, we get:
(4 MeV/c)/c = (4 MeV/c)(3 MeV/c^2)/(4.24 MeV)
u = 0.894c

I hope this helps! Let me know if you have any further questions.