Special relativity collisions problem

So In summary, the two particles p1 and p2, with masses m and energy E, respectively, annihilate to produce two particles of mass 100m. The minimum initial energy of collision in the LAB frame is such that the CM frame energy is just enough to create the particles without any remaining momentum. This means that the particles will coalesce in the LAB frame or any other frame.
  • #1
deadringer
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Homework Statement


We have two particles mass m called p1 and p2. P1 is stationary, p2 has energy E. They annihilate to produce to particles of mass 100m. We need to find the min value of E


Homework Equations





The Attempt at a Solution


I suspect that the minimum initial energy of collision in the LAB frame is such that the CM frame energy is just enough to create the particles i.e that they are stat afterwards. In which case they would coalesce in the LAB frame (or any other). Is this true?
 
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  • #2
Right. You need 100m in the CM frame (where total momentum=0).
 

FAQ: Special relativity collisions problem

What is special relativity and how does it relate to collisions?

Special relativity is a theory proposed by Albert Einstein that describes the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion, and the speed of light is constant regardless of the observer's frame of reference. In collisions, special relativity is used to calculate the effects of high speeds and the resulting energy changes.

How does special relativity affect the conservation of momentum in collisions?

Special relativity states that the total energy of a system must be conserved in all frames of reference. This includes both kinetic energy and rest energy. In collisions, the conservation of momentum is still valid, but the total energy of the system may change due to relativistic effects, such as an increase in mass or energy.

Can special relativity explain why objects appear to have different lengths when moving at high speeds?

Yes, special relativity predicts that objects moving at high speeds will appear shorter in the direction of motion due to the contraction of length. This is known as length contraction and is a result of the time dilation effect in special relativity.

How does special relativity affect the concept of time in collisions?

In special relativity, time is relative and can appear to pass at different rates for different observers depending on their relative velocities. This means that in collisions, the time experienced by different objects may vary, leading to different perceptions of the same event.

Can special relativity explain the concept of mass-energy equivalence?

Yes, special relativity is the basis for the famous equation E=mc², which shows the equivalence between mass and energy. This means that mass can be converted into energy and vice versa, and the amount of energy produced is proportional to the mass of the object.

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