What is the correct calculation for total kinetic energy after the collision?

AI Thread Summary
The discussion centers on calculating the total kinetic energy after a collision between two particles, one moving and one stationary. The user successfully completed parts of the problem regarding the speed and total energy of the first particle, as well as the initial momentum of the system. However, they express confusion over calculating the total kinetic energy after the collision, emphasizing the need for conservation of momentum and energy. They attempted to derive expressions for momentum and energy but did not arrive at the correct value. The thread highlights the complexities of applying conservation laws in relativistic collisions.
Gyroscope

Homework Statement


••• A particle of mass 1 MeV/c2 and kinetic
energy 2 MeV collides with a stationary particle of mass
2 MeV/c2. After the collision, the particles stick together. Find
(a) the speed of the first particle before the collision, (b) the
total energy of the first particle before the collision, (c) the ini-
tial total momentum of the system, (d) the total kinetic energy
after the collision, and (e) the mass of the system after the
collision.

I could do (a,b) and (c).

My doubts are on (d).
I know momentum must be conserved.
So,

p_0=(m_1'+m_2')v\gamma

Total energy must be conserved too:

E_0=(m_1'+m_2')c^2\gamma


If I work out these too expressions, I don't find the correct value. :smile:

What am I doing wrong.

Homework Equations





The Attempt at a Solution

 
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Show more work.
What did you do when you worked these out?
 
I solved for m1'+m2'. And substituted.
 
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