SDilation Equations

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

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Question 1 A proton has a rest mass of 1.67E-27 kg. What is its relativistic mass when it is travelling at 0.83c?

2.01 x 10^-27 kg1.39 x 10^-27 kg2.99 x 10^-27 kg9.31 x 10^-28 kg

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Question 2 How much energy would be released if the rest mass of 124.5 grams of wood were to be entirely converted into energy?

1.12 x 10¹⁶ J1.12 x 10²² J1.12 x 10¹⁷ J1.12 x 10¹⁹ J

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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 0.999999970c, how long would it view the beam's tunnel?

2.449 x 10^-3 m1.02 x 10^-4 m3 x 10^-2 m8.328 x 10^-1 m

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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 4807 meters according to an observer moving with the muons If the muons, if they can travel on average at 0.8c?

7.691 x 10^-6 sec2.003 x 10^-5 sec7.211 x 10^-6 sec1.202 x 10^-5 sec

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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?

0.00180.05460.09100.0227

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Question 6 If an alpha particle has a velocity of 2.49 x 10⁸ 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 J2.06 x 10^-10 J2.3 x 10^-10 J4.74 x 10^-10 J

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Question 7 Two 22nd century cars are travelling in opposite directions. Each car is moving at moving towards each other at 0.7c m/sec. How fast does each car's speed sensor 'detect' the opposing car oncoming velocity?

1.400c0.940c0.700cstanding still, similar to a person
walking up a down escalator

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Question 8 Which of the following statements is NOT a postulate of special relativity?

The speed of light is always equal to 1/µ_oε_o = 3 x 10⁸ m/sec regardless of the relative motion of the observor or the source.The laws of physics are the same in all inertial reference frames.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.