How Can I Apply Theoretical Physics Concepts to Practical Exam Questions?

[starlooney]

Hi, I'm really hoping somebody can help me. basically i have an exam coming up very shortly and from my revision thought i was doing ok with the relativity section. When i have come to look at past exam question i have discovered that although i know my theory i haven't a clue how to actually apply it to any of the situations given. What I'm hoping is that someone might read this and might be able to provide the starting blocks to answer the questions.

Here are 2 examples from the past two years:
(1) Consider two stars, one with mass m 0 and velocity 0.8 c and another one with mass 3mo and at rest in the reference of a distant observer. Suppose that the two stars collide and merge into one star.
(a) What is the initial total linear momentum of the system?
(b) What is the initial total energy of the system?
(c) What is the velocity of the system after merging?
(d) What is the rest mass of the resulting star?

(2) A pion is produced by the collision of a cosmic ray particle with a nucleon in the upper atmosphere. The pion rapidly decays into a muon, and the muon then decays into an electron and a neutrino. The rest mass of a muon mu is about 106 MeV, and the muon-decay timeseale is 2.2 x 10 .6 s.
(a) If the muon is produced at a height of 18 km above the sea level with a total energy of 30 GeV and it travels downward vertically, what are the Lorentz factor and relativistic parameter of the muon?
(b) What is the expected time of flight that the muon takes to reach sea level?
(c) What is the probability that the muon can reach sea level?

I am obviously not asking anyone to answer the above questions i am really just hoping to find the starting blocks for each question so that i could apply my knowledge to other situations. Thank you very much for your help!

 

[OlderDan]

Hi, I'm really hoping somebody can help me. basically i have an exam coming up very shortly and from my revision thought i was doing ok with the relativity section. When i have come to look at past exam question i have discovered that although i know my theory i haven't a clue how to actually apply it to any of the situations given. What I'm hoping is that someone might read this and might be able to provide the starting blocks to answer the questions.

Here are 2 examples from the past two years:
(1) Consider two stars, one with mass m 0 and velocity 0.8 c and another one with mass 3mo and at rest in the reference of a distant observer. Suppose that the two stars collide and merge into one star.
(a) What is the initial total linear momentum of the system?
(b) What is the initial total energy of the system?
(c) What is the velocity of the system after merging?
(d) What is the rest mass of the resulting star?

(2) A pion is produced by the collision of a cosmic ray particle with a nucleon in the upper atmosphere. The pion rapidly decays into a muon, and the muon then decays into an electron and a neutrino. The rest mass of a muon mu is about 106 MeV, and the muon-decay timeseale is 2.2 x 10 .6 s.
(a) If the muon is produced at a height of 18 km above the sea level with a total energy of 30 GeV and it travels downward vertically, what are the Lorentz factor and relativistic parameter of the muon?
(b) What is the expected time of flight that the muon takes to reach sea level?
(c) What is the probability that the muon can reach sea level?

I am obviously not asking anyone to answer the above questions i am really just hoping to find the starting blocks for each question so that i could apply my knowledge to other situations. Thank you very much for your help!

You might want to look here for a refresher on relativistic momentum and energy. Problems like your collision problem are usually transformed into the center of mass frame of reference and then transformed back to express the results.

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html

Your second problem is based on an actual experiment that was performed to verify the predictions of length contraction and time dilation. Imagine riding along on the muon. What would the 18 km distance an Earth observer sees look like to you? The lifetime of the muon assumes the rest frame of the muon. How would the moun's "clock" appear to be running to an Earth observer?

 

[thepatientmental]

Hello there,

I can definitely provide some tips on how to approach these types of exam questions. The key to success in these types of questions is to understand the theory and concepts behind them, and then apply them to the specific scenarios given.

For the first example, you will need to apply the principles of conservation of linear momentum and conservation of energy. Remember that in a closed system, the total linear momentum and total energy remain constant. So for part (a), you will need to calculate the initial total linear momentum of the two stars before they collide. This can be done by multiplying the mass of each star by its velocity and adding them together. For part (b), you will need to calculate the initial total energy of the system by using the equation E=mc^2, where E is energy, m is mass, and c is the speed of light. For part (c), you will need to use the conservation of momentum equation to calculate the velocity of the system after merging. And for part (d), you will need to use the equation E=mc^2 again to calculate the rest mass of the resulting star.

For the second example, you will need to apply the principles of special relativity and decay processes. For part (a), you will need to use the equation γ=1/√(1-v^2/c^2) to calculate the Lorentz factor, where v is the velocity of the muon and c is the speed of light. The relativistic parameter can be calculated using the equation β=v/c. For part (b), you will need to use the equation d=vt, where d is the distance traveled, v is the velocity, and t is the time. And for part (c), you will need to use the equation P=1-e^(-t/τ), where P is the probability, t is the time, and τ is the decay time.

I hope these tips will help you get started on these questions. Remember to always understand the theory behind the questions and apply it to the specific scenarios given. Good luck on your exam!