GRE Subject Test: Physics : Energy and Momentum
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Example Questions
Example Question #1 : Energy And Momentum
A relativistic particle of mass m has a total energy 37 times its rest energy. What is the momentum of the particle, in units of mc?
144
37
98
52
21
37
The total energy E of a relativistic particle is related to its rest mass energy Eo by:
Where gamma is related to the momentum by:
Combining the equations and solving for p, we get:
Which, in the units specified, is 37.
Example Question #2 : Special Relativity
A particle of mass m traveling at a relativistic speed has a momentum of 50 mc. What is the total energy E of the particle, expressed in units of the rest mass energy Eo?
For a relativistic particle, momentum is given by:
from which we can solve for gamma:
Total energy of a relativistic particle is given by:
Example Question #6 : Special Relativity
The rest mass energy 
The question tells us:
Where the rest mass energy of a particle is:
Using the equation for the total energy of a particle, we can substitute:
Solving this for 
Which, in units of mc, gives us the correct answer.
Example Question #2 : Energy And Momentum
The relativistic momentum of a particle with mass 
The total energy of a relativistic particle is given by:
Substituting the momentum, we get:
Because the rest mass energy of a particle is given by:
The total energy is:
Example Question #7 : Special Relativity
A scientist measures the spectrum of relativistic jet emitted from a black hole. He finds that the a particular spectral line, which has a stationary wavelength of 212.5 nm, has a Doppler shifted wavelength of 643.7 nm. What is the radial velocity of the relativistic jet?
The relativistic Doppler shift equation is given by:
Where 
Because the stationary wavelength is shorter than the moving wavelength, the object must be receding from the Earth, eliminating two answers.
The speed of light is approximately 
Making the approximation that
Combining this with the first equation:
From beta, we can find the velocity:
Example Question #1 : Energy And Momentum
A particle in an accelerator has a total energy 
The total energy of a relativistic particle is given by:
Solving for the rest mass 
Which, in the units specified, gives the answer 3.
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