Relativistic Energy and Velocity

In summary, to calculate the speed, momentum, and total energy of a 1760 MeV proton, you can use the equations E= mc^2 (Rest Energy), E= Ɣmc^2 (Total Energy), p= Ɣmv (momentum), and KE= mc^2(Ɣ-1) (Kinetic Energy). By assuming the kinetic energy to be 1760 MeV, the problem can be solved and the speed, momentum, and total energy of the proton can be determined.
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PhysicsInNJ
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Homework Statement


A proton has a mass of 938 MeV/c2. Calculate the speed, momentum, and total energy of a 1760 MeV proton.

Homework Equations


E= mc^2 (Rest Energy)
E= Ɣmc^2 (Total Energy)
p= Ɣmv (momentum)
KE= mc^2(Ɣ-1) (Kinetic Energy)

The Attempt at a Solution


I'm not sure how the last number given (1760 MeV) is relevant, as in, I don't know what to do with it in order to start solving the problem. I know it isn't rest energy/mass because that is given as 938 MeV/c^2. It also is not the total energy because that is asked for in the question and the answer is not 1760 MeV.
 
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Normally I would think they meant the total energy, but perhaps they meant the kinetic energy. Try assuming the kinetic energy is 1760 MeV and see what you get.
 
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Lucas SV said:
Normally I would think they meant the total energy, but perhaps they meant the kinetic energy. Try assuming the kinetic energy is 1760 MeV and see what you get.
You're right. that worked. Thank you!
 
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Related to Relativistic Energy and Velocity

1. What is relativistic energy?

Relativistic energy is the energy that an object has due to its mass and velocity, taking into account the effects of special relativity. It is described by the famous equation E=mc^2, where E is energy, m is mass, and c is the speed of light. This equation shows that as an object's velocity approaches the speed of light, its energy also increases significantly.

2. How does relativistic energy differ from classical energy?

Classical energy, also known as Newtonian energy, is based on the laws of classical mechanics and does not take into account the effects of special relativity. It only considers an object's mass and velocity at low speeds, while relativistic energy considers an object's mass and velocity at any speed, including speeds close to the speed of light.

3. What is the relationship between relativistic energy and velocity?

Relativistic energy and velocity are directly related, meaning that as an object's velocity increases, its relativistic energy also increases. This is due to the fact that as an object's velocity approaches the speed of light, its relativistic mass also increases, resulting in a larger amount of energy being required to accelerate the object further.

4. How does special relativity affect an object's velocity?

Special relativity states that the laws of physics are the same for all observers in uniform motion, regardless of their relative velocities. This means that an object's velocity can appear different to different observers, depending on their relative velocities. Additionally, as an object's velocity approaches the speed of light, its mass increases and it becomes more difficult to accelerate it further.

5. What are the implications of relativistic energy and velocity in practical applications?

Relativistic energy and velocity have significant implications in various practical applications, such as nuclear power, particle accelerators, and space travel. In nuclear power, the conversion of small amounts of mass into energy results in a large amount of energy being produced, as described by the equation E=mc^2. In particle accelerators, scientists use the principles of special relativity to accelerate particles to incredibly high velocities in order to study their properties. In space travel, the effects of special relativity must be taken into account in order to accurately calculate the energy and velocity required for a spacecraft to reach its destination.

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