Test #2          Physics 262     S04      Name________KEY_______

 

1.      What is special relativity? (2pts)

 

The study of the physics of bodies moving at velocities that are an appreciable

fraction of the speed of light.  It includes views from different frames of reference, and discussion of space-time.

 

2.     What are the main postulates of special relativity? (2)

 

The laws of physics are the same for observers in all inertial frames of reference.  No frame is preferred.

The speed of light, c, in a vacuum is the same in all directions and in all inertial frames of reference.  It is the speed limit.

 

3.     What is a postulate?  (What does the word mean?) (1)

 

A postulate is a proposition taken for granted and used as a starting point for a chain of reasoning.

 

4.     What is an invariant? (2)

 

In special relativity, an invariant is a quantity that is the same in all inertial frames of reference.

 

5.  If a rocket goes by us at .4c and we see its tail pass x=1200 km at t=0.01s, at which time a light flashes (at that point), what does the observer on the rocket see?  Assume we synchronized at x=x’=0,  t=t’=0 as the rocket passed.

(4)

The observer on the ship sees the 1200 km as 1100 km  gamma=1.09

Since this problem was not formulated correctly, I allowed a number of different answers—as long as the approach was logical.

 

 

6.    If you look through a telescope at a clock (identical to your clock) on a moving satellite, what will you observe? (2)

 

You may see the clock running faster than yours or slower than yours depending on the direction the satellite is moving with respect to you.

This is due to Doppler effect.

 

7.    The proper time between two events is measured by clocks at rest in a frame in which the two events ___ (1)

                                                        occur at the same place

 

8.    And electron is moving at 0.6 c.   (e mass = 9.11 e-31 kg)  Calculate is energy classically and with relativity.  Comment on the difference. (4)

 

Classical:  KE = ˝ mv2

 

Relativistic:  KE = (gamma – 1) moc2       gamma = 1.25

 

Relativistic KE is slightly larger; in this case because the velocity is large enough that there is a large effective increase in the mass (energy).

 

9.    And observer notes a moving clock is running slow by a factor of 8.  At what speed is the clock moving? (2)

 

t = gamma to   thus gamma = 8   calculate v from equation for gamma

 

10.                        A quasar is observed from a spaceship that is traveling at 0.2 c with respect to the Earth.  The ship reports to Earth that they observe a spectral line shifted from 450nM to a wavelength of 1200nM.  What is the velocity of the quasar with respect to the Earth? (in terms of c)

 

Diagram is very useful on this problem.  Frame of ship is moving at .2c wrt Earth.  Quasar velocity in frame of ship is determined by Doppler shift equation:  eqn 38-30 in text      Then add velocity of Doppler shift to velocity of ship wrt Earth using eqn 38-28.  ux = 0.826c

           

11. A rocket of rest length 100 meters moves at o.8 c past a timing device that records the time interval between passage of the nose and tail of the ship.  What will be the time interval measured? (3)

 

As the ship passes the timing device, it will have an observed length of 60 m.  Travelling at 0.8c the passage will take  0.25 microseconds.  Gamma = 1.66

 

12.                        If a rocket has a mass of 3 e6 kg and is moving at 0.63c, what is its relativistic kinetic energy? (3)

 

Relativistic KE = (gamma-1) moc2      gamma = 1.29    KE = 7.8 x 1022 Joules

 

13.                        If the kinetic energy of a proton is equal to four times its rest energy, what is the speed the particle is moving? (3)

 

Etotal = KE + moc2    Etotal = 4 moc2  + moc2    = 5 moc2     gamma = 5

 

Calculate velocity from equation for gamma    v = 0.98c

 

14.                        What is the relativistic momentum of the particle in (13)?  (Both in SI and energy units) (2)

 

prel = gamma m ov     Get gamma v from above problem.  Solve with SI units.

 

15.                        A particle has a momentum of 7 MeV/c.  What is its energy in MeV?

                 (1)

 Use equation E2  = (pc) 2  + (mc2 ) 2       7.04 MeV  

 If you have a photon or a very light particle like an electron, the energy will essentially be 7 MeV.  But for a heavier particle, the rest energy will add to the kinetic energy that gives the momentum.

 

16.                        If the particle in (15) is an electron, what is its speed? (2)

 

If total energy is 7.04 MeV—use equation for relativistic KE  = (g-1) mo c2

Rest energy of electron is 0.511MeV.  therefore     (g-1) =12.8

Velocity for this gamma is 0.994 c

 

End of test.