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					Practice questions


                                                  Chapter 23
                                               Space-time Physics

                                       For speeds close to the speed of light use:
                                                                              1
                                                                 
                                                                            v2
                                                                          1 2
                                                                            c

                                       For speeds much smaller than the speed of light you
                                       should use the approximation:

                                                                         v2
                                                                     1 2
                                                                         2c
                                                       2          2
                                       Ek = γm0c – m0c
                                                                                 -31
                                       Rest mass of the electron = m0 = 9.11 x 10 kg
                                                 8    -1
                                       c = 3 × 10 m s

    1. A distant quasar is moving away from us at half the speed of light.
        a At what speed does light from the quasar reach Earth?
              .....................................................................................................................................

              ............................................................................................................................... [1]

        b What effect, in general, does the quasar's relative speed have on the light we receive?
              .....................................................................................................................................

              ............................................................................................................................... [2]

                                                                                                                                   [Total: 3]

    2. The data at the start of this Questions section give two versions of a formula for the
       Lorentz factor γ. How much of an error is introduced in a simple calculation by using the
       approximate formula for speeds up to 0.2c?
              .....................................................................................................................................

              .....................................................................................................................................

              ............................................................................................................................... [5]

                                                                                                                                   [Total: 5]




                                                                        1(5)
3. a Michelson and Morley attempted to detect absolute motion by investigating whether or
     not the speed of light in a direction parallel to the Earth's motion differs from the speed
     of light perpendicular to the Earth's motion. Outline briefly what resulted from this
     experiment and what was concluded.
        .....................................................................................................................................

        .....................................................................................................................................

        .....................................................................................................................................

        ............................................................................................................................... [4]

   b In a science fiction novel, a space rocket leaves the Earth in year 2100 and travels out
     of the Solar System to a distant star at a speed of 0.85c, where c is the speed of light in
     vacuo, to a star 25 light years from the Earth.

        i    How many years, in the frame of reference of the Earth, does the spacecraft take
             to reach the star?
        .....................................................................................................................................

        ............................................................................................................................... [2]

        ii   What is the distance, in the frame of reference of the spacecraft, between the
             Earth and the star?
                    ........................................................................................................................

        ............................................................................................................................... [2]

        iii A member of the crew is 18 years old when the rocket leaves the Earth. How old
            is this crew member on arrival at the star?
        .....................................................................................................................................

        .....................................................................................................................................

        ............................................................................................................................... [3]

                                                                                                                           [Total: 11]

4. Calculate:
   a the relativistic mass of an electron travelling at a speed of 0.9c
        .....................................................................................................................................

        ............................................................................................................................... [2]

   b its momentum.
        .....................................................................................................................................

        ............................................................................................................................... [2]

                                                                                                                             [Total: 4]




                                                                  2(5)
5. a Einstein's theory of special relatively has two postulates.
     State and explain what they are.
        .....................................................................................................................................

        .....................................................................................................................................

        .....................................................................................................................................

        ............................................................................................................................... [4]
                                                                               -28                                              -6
   b A stationary muon has a rest mass of 1.88 x 10                                  kg and a half-life of 2.2 x 10 s.
     Calculate:

        i    the mass of a muon travelling at 0.99c, where c is the speed of light in a vacuum,
        .....................................................................................................................................

        .....................................................................................................................................

        ............................................................................................................................... [3]

        ii   the distance, in a laboratory frame of reference, travelled in one half-life by a
             muon
        .....................................................................................................................................

        .....................................................................................................................................

        ............................................................................................................................... [3]

                                                                                                                           [Total: 10]

6. Certain particles have a half-life of 1.52 μs when at rest. Such particles, created in the
   upper atmosphere travel towards the Earth at a speed approximately equal to that of light.
     A particle detector, suspended by a balloon at an altitude of 2280 m, detects 5800
     particles in 12 minutes. A similar detector at sea level, vertically below the balloon,
     detects 650 particles in the same interval of time.
   a Assuming the particles travel at the speed of light, calculate the time of travel between
     the two detectors, as measured by a person on Earth.
             ................................................................................................................................

        ............................................................................................................................... [2]

   b Using your answer to a and assuming that the fast-moving particles also have a half-life
     of 1.52 μs, calculate the number of particles which would be expected at sea-level in
     the twelve-minute period.
        .....................................................................................................................................

        ............................................................................................................................... [2]

   c By reference to the actual number comment on your answer.
        .....................................................................................................................................

        ............................................................................................................................... [2]

                                                                                                                             [Total: 6]



                                                                  3(5)
7. a At what relative speed must a clock travel to make it run at half the rate of a clock
     at rest?
        .....................................................................................................................................

        .....................................................................................................................................

        ............................................................................................................................... [3]

   b At this speed, how long would a metre stick appear to be to

        i    a traveller with the stick,
        ............................................................................................................................... [1]

        ii   an observer at rest?
        ............................................................................................................................... [1]

                                                                                                                               [Total: 5]

                                                                                                                          10
8. The cosmic rays with the highest energies are protons with kinetic energy 10 GeV. (1
           9
   GeV = 10 eV.) This energy is much greater than the proton's rest-mass energy.
                                                                                         10
   a Show that the value of γ for such a proton is about 10 .
        .....................................................................................................................................

        ............................................................................................................................... [3]

   b Write down the speed of this proton to one significant figure.
        .....................................................................................................................................

        ............................................................................................................................... [2]
                              5
   c Our galaxy is 10 light years in diameter. How wide is it from the point of view of the
     proton?
        .....................................................................................................................................

        ............................................................................................................................... [2]

   d How long would the proton take to cross the galaxy

        i    as observed by us,
        ............................................................................................................................... [1]

        i    as measured in the proton's reference frame'?
        ............................................................................................................................... [1]

                                                                                                                               [Total: 9]




                                                                  4(5)
9. Electrons in a TV tube (Cathode ray tube, as used in old TV’s) are accelerated by a
   potential difference of 25 kV.
   a How much work in joules is done in accelerating an electron?
        .....................................................................................................................................

        ............................................................................................................................... [2]

   b How much kinetic energy does the electron gain?
        ............................................................................................................................... [1]

   c The tube works to a tolerance of 0.2 per cent. Does the tube design need to take
     account of a relativistic increase in mass of the electrons? If so what aspect of the
     design would be affected'?
        .....................................................................................................................................

        .....................................................................................................................................

        .....................................................................................................................................

        ............................................................................................................................... [4]

                                                                                                                             [Total: 7]
                                                                                                                [Overall total 60]




                                                                  5(5)

				
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posted:9/18/2012
language:French
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