Energy of two colliding particles

In summary, when two identical particles are smashed together with the same energy E, the energy measured for one of them by an observer in the rest system of the other is 5 orders of magnitude greater than the energy for an individual particle. This can be found using the Lorentz transformation equations or by considering the dot product of the 4-momenta in the center of mass frame and the rest frame of one of the particles. This dot product is a Lorentz invariant.
  • #1
Dawei
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Homework Statement


Two identical particles are smashed together. They each have the same energy E. What is the energy measured for one of them by an observer in the rest system of the other?

Homework Equations



E = γmc2
E = γ(E' + vp)

The Attempt at a Solution



I've already found the speed of each particle, which is .99998C . Obviously I can't just double that since it would give me a non-real value for gamma. I know that the answer is 5 orders of magnitude greater than the energy for an individual particle.
 
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  • #2
Hi Dawei! :smile:

You should be able to get this directly from the Lorentz transformation equations.

Alternatively, see http://en.wikipedia.org/wiki/Addition_of_Velocities_Formula" [Broken] :wink:
 
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  • #3
Dawei said:
Two identical particles are smashed together. They each have the same energy E. What is the energy measured for one of them by an observer in the rest system of the other?
You do not need a Lorentz transformation. Hints: What does the dot product of the 4-momenta tell you in the CM frame (in terms of energy and mass)? What does it tell you in the rest frame of one of the particles (in terms of energy and mass)? Is this dot product a Lorentz invariant?
 
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1. What is the definition of energy in the context of two colliding particles?

Energy in the context of two colliding particles refers to the total amount of kinetic and potential energy possessed by the particles before and after the collision. This energy can be transferred between the particles during the collision.

2. How is the energy of two colliding particles calculated?

The energy of two colliding particles can be calculated using the equation E = 1/2mv^2, where m is the mass of the particle and v is its velocity. This equation takes into account both the kinetic energy (1/2mv^2) and potential energy (mgh) of the particles.

3. What factors affect the energy of two colliding particles?

The energy of two colliding particles can be affected by the mass and velocity of the particles, as well as the angle and type of collision (elastic or inelastic). Other factors such as external forces and friction can also influence the energy of the particles.

4. How does the law of conservation of energy apply to two colliding particles?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. In the context of two colliding particles, the total energy before the collision is equal to the total energy after the collision, demonstrating the conservation of energy.

5. What is the difference between elastic and inelastic collisions in terms of energy?

In an elastic collision, the kinetic energy of the particles is conserved, meaning the total energy before and after the collision remains the same. In an inelastic collision, some of the kinetic energy is converted into other forms of energy such as heat or sound, resulting in a decrease in the total energy. However, in both cases, the law of conservation of energy still applies.

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