# Chapter 1 by tQ7Cr31i

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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?
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b What effect, in general, does the quasar's relative speed have on the light we receive?
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............................................................................................................................... [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?
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[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.
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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?
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ii   What is the distance, in the frame of reference of the spacecraft, between the
Earth and the star?
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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?
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............................................................................................................................... [3]

[Total: 11]

4. Calculate:
a the relativistic mass of an electron travelling at a speed of 0.9c
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b its momentum.
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[Total: 4]

2(5)
5. a Einstein's theory of special relatively has two postulates.
State and explain what they are.
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-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,
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ii   the distance, in a laboratory frame of reference, travelled in one half-life by a
muon
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............................................................................................................................... [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.
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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.
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............................................................................................................................... [2]

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

i    a traveller with the stick,
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ii   an observer at rest?
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[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 .
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b Write down the speed of this proton to one significant figure.
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5
c Our galaxy is 10 light years in diameter. How wide is it from the point of view of the
proton?
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d How long would the proton take to cross the galaxy

i    as observed by us,
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i    as measured in the proton's reference frame'?
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[Total: 9]

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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?
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b How much kinetic energy does the electron gain?
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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'?
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[Total: 7]
[Overall total 60]

5(5)

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