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

I got m1'+m2' = 2.25 MeV/c^2.In summary, a particle with mass 1 MeV/c2 and kinetic energy 2 MeV collides with a stationary particle of mass 2 MeV/c2, and after the collision, the particles stick together. To find the speed of the first particle before the collision, the total energy of the first particle before the collision, and the initial total momentum of the system, the equations p_0=(m_1'+m_2')v\gamma and E_0=(m_1'+m_2')c^2\gamma are used. However, when solving for m1'+m2' and substituting,
  • #1
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,

[tex]p_0=(m_1'+m_2')v\gamma[/tex]

Total energy must be conserved too:

[tex]E_0=(m_1'+m_2')c^2\gamma[/tex]


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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  • #2
Show more work.
What did you do when you worked these out?
 
  • #3
I solved for m1'+m2'. And substituted.
 

1. What is a relativistic collision?

A relativistic collision is a type of collision that occurs between particles at high speeds, close to the speed of light. This type of collision takes into account the principles of special relativity, which describe how the laws of physics apply in different frames of reference.

2. How does a relativistic collision differ from a non-relativistic collision?

In a non-relativistic collision, the speeds of the particles involved are much lower than the speed of light. This means that the effects of special relativity can be ignored. In a relativistic collision, the speeds are close to the speed of light, so special relativity must be taken into account.

3. What is the equation for calculating the relativistic energy of a particle?

The equation for calculating the relativistic energy of a particle is E = mc2 / √(1 - v2/c2), where E is the energy, m is the mass of the particle, v is the velocity, and c is the speed of light. This equation takes into account the increase in energy that occurs as a particle's speed approaches the speed of light.

4. Can a relativistic collision result in the creation of new particles?

Yes, a relativistic collision can result in the creation of new particles. This is due to the high energies involved in the collision, which can be converted into mass according to Einstein's famous equation, E=mc2. This phenomenon is observed in particle accelerators, where particles are collided at high speeds to create new particles.

5. How does a relativistic collision affect the mass and length of a particle?

In a relativistic collision, the mass of a particle increases as its speed increases. This is known as relativistic mass, and it is a result of the particle's increased energy. The length of the particle also contracts in the direction of motion, a phenomenon known as length contraction. These effects are both consequences of special relativity and are only significant at high speeds close to the speed of light.

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