Energy and Momentum - GRE Subject Test: Physics
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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?
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:
For a relativistic particle, momentum is given by:
from which we can solve for gamma:
Total energy of a relativistic particle is given by:
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The rest mass energy 
of a particle with mass 
is one quarter of its total energy 
. What is the of the particle's momentum, in units of 
?
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 
, we find:
Which, in units of mc, gives us the correct answer.
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.
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The relativistic momentum of a particle with mass 
is 
. What is the total energy 
of the particle, given in units of the rest mass energy 
?
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:
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:
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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?
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 
is defined as:
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 
, so 
is not a possible answer.
Making the approximation that
Combining this with the first equation:
From beta, we can find the velocity:
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:
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A particle in an accelerator has a total energy 
and a relativistic momentum 
. What is the rest mass of the particle, in units of 
?
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.
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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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?
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?
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.
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.
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