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 0.84c?
1.99 x 10
^{-27}
kg
1.4 x 10
^{-27}
kg
9.06 x 10
^{-28}
kg
3.08 x 10
^{-27}
kg
omit
Question 2
How much energy would be released if the rest mass of 126 grams of wood were to be entirely converted into energy?
1.13 x 10
^{16}
J
1.13 x 10
^{19}
J
1.13 x 10
^{17}
J
1.13 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 0.999999966c, how long would it view the beam's tunnel?
2.608 x 10
^{-3}
m
1.156 x 10
^{-4}
m
3.4 x 10
^{-2}
m
8.866 x 10
^{-1}
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 4785 meters according to an observer moving with the muons If the muons, if they can travel on average at 0.8c?
7.178 x 10
^{-6}
sec
1.196 x 10
^{-5}
sec
7.656 x 10
^{-6}
sec
1.994 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?
0.0019
0.0231
0.0906
0.0544
omit
Question 6
If an alpha particle has a velocity of 2.52 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.
5.04 x 10
^{-10}
J
2.11 x 10
^{-10}
J
5.98 x 10
^{-10}
J
2.29 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 0.66c m/sec. How fast does each car's speed sensor 'detect' the opposing car oncoming velocity?
0.660c
standing still, similar to a person
walking up a down escalator
1.320c
0.919c
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.
Time appears to run more slowly in a frame of reference that is moving relative to an observer in a stationary frame.
The laws of physics are the same in all inertial reference frames.
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