Practice Problems
Dilation Equations
Directions:
On this worksheet you will practice using these basic formulas from Special Relativity.
momentum
mass
time
length
kinetic energy
velocity addition
energy-mass
omit
Question 1
A proton has a rest mass of 1.67E-27 kg. What is its relativistic mass when it is travelling at 0.9c?
1.5 x 10
^{-27}
kg
7.28 x 10
^{-28}
kg
1.86 x 10
^{-27}
kg
3.83 x 10
^{-27}
kg
omit
Question 2
How much energy would be released if the rest mass of 135 grams of wood were to be entirely converted into energy?
1.22 x 10
^{19}
J
1.22 x 10
^{16}
J
1.22 x 10
^{17}
J
1.22 x 10
^{22}
J
omit
Question 3
The Stanford Linear Accelerator (SLAC) is 3.4 kilometers long. When in operation, it could produce beams of electrons that travelled at speeds to within 2 cm/sec the speed of light. If an electron in the beam was travelling at 0.999999979c, how long would it view the beam's tunnel?
6.968 x 10
^{-1}
m
7.14 x 10
^{-5}
m
2.049 x 10
^{-3}
m
2.1 x 10
^{-2}
m
omit
Question 4
Muons (or heavy electrons) are created when cosmic rays collide with molecules in the Earth's upper atmosphere. Calculate the time for them to travel to the Earth's suface, a distance of 4856.5 meters according to an observer moving with the muons If the muons, if they can travel on average at 0.8c?
2.024 x 10
^{-5}
sec
7.77 x 10
^{-6}
sec
7.285 x 10
^{-6}
sec
1.214 x 10
^{-5}
sec
omit
Question 5
If the average halflife for a muon is 2.2E-06 seconds, what percentage (expressed as a decimal) of the muons that start the trip in
Question #4
make it to the surface of the earth?
0.0017
0.0552
0.0218
0.0920
omit
Question 6
If an alpha particle has a velocity of 2.7 x 10
^{8}
m/sec, what is its relativistic kinetic energy? The rest mass of an alpha particle is 6.644 x 10
^{-27}
kilograms.
5.98 x 10
^{-10}
J
2.42 x 10
^{-10}
J
7.74 x 10
^{-10}
J
2.11 x 10
^{-10}
J
omit
Question 7
Two 22nd century cars are travelling in opposite directions. Each car is moving at moving towards each other at 0.79c m/sec. How fast does each car's speed sensor 'detect' the opposing car oncoming velocity?
0.790c
standing still, similar to a person
walking up a down escalator
0.973c
1.580c
omit
Question 8
Which of the following statements is NOT a postulate of special relativity?
The speed of light is always equal to 1/µ
_{o}
ε
_{o}
= 3 x 10
^{8}
m/sec regardless of the relative motion of the observor or the source.
The laws of mechanics are the same in all reference frames.
The laws of physics are the same in all inertial reference frames.
Time appears to run more slowly in a frame of reference that is moving relative to an observer in a stationary frame.
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