# GRE Subject Test: Physics : Energy and Momentum

## Example Questions

### Example Question #2 : Special Relativity

A relativistic particle of mass has a total energy 37 times its rest energy.  What is the momentum of the particle, in units of mc?

52

37

144

98

21

37

Explanation:

The total energy 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 #1 : Special Relativity

A particle of mass m traveling at a relativistic speed has a momentum of 50 mc.  What is the total energy of the particle, expressed in units of the rest mass energy Eo?

Explanation:

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 #1 : Energy And Momentum

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 ?

Explanation:

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.

### Example Question #1 : Energy And Momentum

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 ?

Explanation:

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 #2 : 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?

Explanation:

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:

### Example Question #1 : Energy And Momentum

A particle in an accelerator has a total energy  and a relativistic momentum . What is the rest mass of the particle, in units of  ?