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 0.76c?

2.57 x 10^-27 kg2.2 x 10^-27 kg1.09 x 10^-27 kg1.27 x 10^-27 kg

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Question 2 How much energy would be released if the rest mass of 114 grams of wood were to be entirely converted into energy?

1.03 x 10¹⁹ J1.03 x 10¹⁷ J1.03 x 10¹⁶ J1.03 x 10²² 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 0.999999974c, how long would it view the beam's tunnel?

8.84 x 10^-5 m2.6 x 10^-2 m2.28 x 10^-3 m7.753 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 4829 meters according to an observer moving with the muons If the muons, if they can travel on average at 0.8c?

7.244 x 10^-6 sec7.726 x 10^-6 sec2.012 x 10^-5 sec1.207 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?

0.09150.02230.00180.0549

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Question 6 If an alpha particle has a velocity of 2.28 x 10⁸ m/sec, what is its relativistic kinetic energy? The rest mass of an alpha particle is 6.644 x 10^-27 kilograms.

1.73 x 10^-10 J5.98 x 10^-10 J2.24 x 10^-10 J3.22 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 0.74c m/sec. How fast does each car's speed sensor 'detect' the opposing car oncoming velocity?

1.480cstanding still, similar to a person
walking up a down escalator0.956c0.740c

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

The laws of mechanics are the same in all reference frames.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.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.