Particle decay: Relativistic or classical?

In summary, the conversation revolved around a competitive exam question in India that involved momentum conservation in the classical sense and 4 momentum conservation. The problem initially seemed to have a straightforward solution, but it was later discovered that the question contained incorrect information about the energies of the two pieces involved. It was ultimately determined that the problem was a classical momentum problem and not one involving special relativity.
  • #1
Isomorphism
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This question was asked in an competitive exam in India.

The relevant equations are momentum conservation in the classical sense and the 4 momentum conservation.

My attempt: Classical momentum conservation would seem inaccurate since the kinetic energies are high. However, a straightforward application of it yields option (a). I think it is wrong since we end up with more energy than we started with. Initial energy is 3GJ, but final energy is 10 GJ since C has 8GJ of energy.

I wanted to know how to solve it using special relativity. It looks like information about the masses is missing.(I know that I cannot use conservation of masses.) So I am wondering whether it is possible to solve this problem with relativistic corrections and whether the answer still remains 30 degrees.

Thanks,
 
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  • #2
Isomorphism said:
The following question was asked in an competitive exam in India:https://www.physicsforums.com/attachments/108398

The relevant equations are momentum conservation in the classical sense and the 4 momentum conservation.

My attempt: Classical momentum conservation would seem inaccurate since the kinetic energies are high. However, a straightforward application of it yields option (a). I think it is wrong since we end up with more energy than we started with. Initial energy is 3GJ, but final energy is 10 GJ.

I wanted to know how to solve it using special relativity. It looks like information about the masses is missing.(I know that I cannot use conservation of masses.) So I am wondering whether it is possible to solve this problem with relativistic corrections and whether the answer still remains 30 degrees.

Thanks,

It's got nothing to do with Relativity. The piece that went off at right angles should have ##1 GJ## not ##2 GJ##.
 
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  • #3
How did you know that it is a classical momentum problem apriori?

The energies of the two pieces are 8GJ and 2GJ.

I have updated my original post.

PeroK said:
It's got nothing to do with Relativity. The piece that went off at right angles should have ##1 GJ## not ##2 GJ##.
 
  • #4
Isomorphism said:
How did you know that it is a classical momentum problem apriori.

The energies of the two pieces are 8GJ and 2GJ.

If it was a SR problem, it would have said "relativistic velocity", not "high velocity".
 
  • #5
Isomorphism said:
How did you know that it is a classical momentum problem apriori?
1 GJ might sound like a lot, but if you calculate the equivalent amount of mass, you find ##m = \frac{10^9}{(3\times10^8)^2}= 1.1\times 10^{-8}\text{ kg}.## The mass of the missile is many orders of magnitude above that.
 
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  • #6
vela said:
1 GJ might sound like a lot, but if you calculate the equivalent amount of mass, you find ##m = \frac{10^9}{(3\times10^8)^2}= 1.1\times 10^{-8}\text{ kg}.## The mass of the missile is many orders of magnitude above that.

Or, if the missile had a mass of ##1 kg## then its velocity would be less than ##8 \times 10^4 m/s##
 
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  • #7
Thanks for that clarification.

If it is classical, how has the total energy increased?
 
  • #8
Isomorphism said:
Thanks for that clarification.

If it is classical, how has the total energy increased?

That would be a mistake in the question, as pointed out in post #2.
 
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1. What is particle decay?

Particle decay is a process in which a subatomic particle transforms into one or more different particles. This can occur spontaneously or as a result of interactions with other particles.

2. What is the difference between relativistic and classical particle decay?

Relativistic particle decay occurs at high speeds and considers the effects of special relativity, such as time dilation and mass-energy equivalence. Classical particle decay occurs at low speeds and does not take these effects into account.

3. How does particle decay relate to the laws of physics?

Particle decay is governed by the laws of quantum mechanics and the standard model of particle physics. These laws describe the behavior and interactions of subatomic particles.

4. Can particle decay be observed in everyday life?

No, particle decay typically occurs at the subatomic level and cannot be observed in everyday life. However, scientists can recreate and study particle decay in high-energy particle accelerators.

5. What are the practical applications of studying particle decay?

Studying particle decay can help us understand the fundamental properties of matter and the universe. It also has practical applications in fields such as nuclear energy, medical imaging, and particle physics research.

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