SDilation Equations

Topics: On this worksheet you will practice using these basic dialation formulas from Special Relativity.

Page Directions The numerical values in this worksheet are randomly generated allowing students the opportunity to conveniently practice, and drill, common situations.

Before beginning any given worksheet, please look over all of the questions and make sure that there are no duplicate answers shown for the same question. If duplicates are present simply refresh the page until every answer is unique.

In order to check an answer (even when you are just starting the worksheet on Question 1) it is necessary to omit

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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 0.65c?

1.27 x 10^-27 kg2.2 x 10^-27 kg1.09 x 10^-27 kg2.57 x 10^-27 kg

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Question 2 How much energy would be released if the rest mass of 97.5 grams of wood were to be entirely converted into energy?

8.78 x 10²¹ J8.78 x 10¹⁸ J8.78 x 10¹⁶ J8.78 x 10¹⁵ 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 0.999999975c, how long would it view the beam's tunnel?

2.236 x 10^-3 m2.5 x 10^-2 m8.5 x 10^-5 m7.603 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 4834.5 meters according to an observer moving with the muons If the muons, if they can travel on average at 0.8c?

1.209 x 10^-5 sec2.014 x 10^-5 sec7.252 x 10^-6 sec7.735 x 10^-6 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?

0.00180.09160.02220.0549

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Question 6 If an alpha particle has a velocity of 1.95 x 10⁸ m/sec, what is its relativistic kinetic energy? The rest mass of an alpha particle is 6.644 x 10^-27 kilograms.

1.92 x 10^-10 J1.89 x 10^-10 J1.26 x 10^-10 J5.98 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 0.75c m/sec. How fast does each car's speed sensor 'detect' the opposing car oncoming velocity?

0.750c1.500c0.960cstanding 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 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.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.