Relevistic energy problem : part 2

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In summary, the conversation discusses a relativistic Heavy Ion collider at Brookhaven, colliding fully ionized gold nuclei accelerated to an energy of 200 GeV per nucleon. The speed and momentum of each nucleus just before collision are calculated, and the equations used include Lorentz transformation equations and the relativistic velocity addition formula.
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Benzoate
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Homework Statement



relavtivistic Heavy Ion collider at brookhaven is colliding fully ionized gold(Au) nuclei accelerated to an energy of 200 GeV per nucleon. each Au nucleus contains 197 nucleons . a) What is the speed of each Au nucleus just before collision b)What is the momentum of each at that instant? c) What energy and momentum would be measured for one of the Au nuclei by an observer in the rest system of the other Au nucleus

Homework Equations


Possible equations: For Lorentz transformation equations, E=gamma*mc^2 ;p(x)=gamma*m*u(x) , u(x) being the velocity of the Au nucleon in the x dirrection.

The Attempt at a Solution



I don't have trouble with part a, I'm only having trouble with parts b and c. I calculated the velocity to be , u= .999999999717c. and that's the correct velocity according to the back of my textbook. If you want to see how I calculated the velocity, go see my other posts titled relavistic energy problem In part b), since the value of u is extremely closed to the speed of light , I would used p=gamma*m*u. Therefore, p(x)=4152.27*(3.28e-25 kg)*(.99999999717*c)=4.09e-13 kg *m/s
E=gamma*mc^2= 4152.27*(3.28e-25 kg)*(.99999999717*c)^2 = 1.226e-4 joules
For part c) , I will have to used the Lorentz transformations for energy and momentum . I assumed the directions of y and z are zero, I think I'm supposed to find p'(x) and p'(x)= gamma*(p(x-vE/c^2) = 4152.27*(4.09e-13 kg*m/s-v(1.226e-4 joules))/c^2) and E'(x)=gamma*(E-v*p(x))= 4152.27*(1.226-4 Joules-v(4.09e-13 kg*m/s). I'm having trouble finding v. On second thought, wouldn't v=0 since the observer is in the rest system ?
 
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  • #2
Benzoate said:

Homework Equations


Possible equations: For Lorentz transformation equations, E=gamma*mc^2 ;p(x)=gamma*m*u(x) , u(x) being the velocity of the Au nucleon in the x dirrection.

I replied to your other post. These appear to be correct, but I think the velocity is somewhat less (as these things go) than you found.

The Attempt at a Solution



I'm having trouble finding v. On second thought, wouldn't v=0 since the observer is in the rest system ?

I think you will want to use the relativistic velocity addition formula to find the velocity of one nucleus as seen in the rest frame of the other. Keep in mind that, since we are setting up a collision, the velocities of the two nuclei will be in *opposite* directions.
 
  • #3
And wouldn't p(x)=p(x') and E(x)=E(x').

I would suggest double checking your calculations and equations to ensure accuracy. It is also important to note that in relativity, velocity is relative and can be different depending on the observer's frame of reference. In this case, the observer in the rest system of the other Au nucleus would measure a different velocity and momentum than the one calculated in part b. Additionally, the equations for Lorentz transformations of energy and momentum are more complex and involve factors such as the angle of collision and the Lorentz factor. It may be helpful to consult a textbook or seek guidance from a teacher or colleague.
 

1. What is the "Relevistic energy problem" and why is it important in science?

The "Relevistic energy problem" refers to the discrepancy between the predicted amount of energy in the universe based on the theory of relativity and the observed amount of energy. This problem is important in science because it challenges our understanding of the fundamental laws of physics and the nature of the universe.

2. What was the solution proposed in "Relevistic energy problem : part 1" and why was it not accepted?

In "Relevistic energy problem : part 1", the solution proposed was the existence of dark energy, a mysterious force that counteracts the effects of gravity and causes the expansion of the universe to accelerate. However, this solution was not accepted because it is still a theoretical concept and there is not enough evidence to support its existence.

3. What is the main focus of "Relevistic energy problem : part 2" and how does it address the previous solution?

The main focus of "Relevistic energy problem : part 2" is the study of alternative theories of gravity that could potentially explain the observed acceleration of the universe's expansion without the need for dark energy. This addresses the previous solution by exploring other possibilities and expanding our understanding of the universe.

4. How does the "Relevistic energy problem" relate to the concept of dark matter?

The "Relevistic energy problem" is closely related to the concept of dark matter, as both involve discrepancies between predicted and observed energy in the universe. However, dark matter refers specifically to the missing mass in the universe, while the "Relevistic energy problem" encompasses a broader range of energy discrepancies.

5. What are the potential implications of solving the "Relevistic energy problem"?

If the "Relevistic energy problem" is solved, it could lead to a better understanding of the laws of physics and the true nature of the universe. It could also have practical applications such as improving our understanding of energy sources and potentially finding ways to manipulate and harness energy for various purposes.

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