PhysicsLAB 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
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?
Question 2  How much energy would be released if the rest mass of 135 grams of wood were to be entirely converted into energy?
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 0.999999976c, how long would it view the beam's tunnel?
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 4840 meters according to an observer moving with the muons If the muons, if they can travel on average at 0.8c?
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?
Question 6  If an alpha particle has a velocity of 2.7 x 108 m/sec, what is its relativistic kinetic energy? The rest mass of an alpha particle is 6.644 x 10-27 kilograms.
Question 7  Two 22nd century cars are travelling in opposite directions. Each car is moving at moving towards each other at 0.76c m/sec. How fast does each car's speed sensor 'detect' the opposing car oncoming velocity?
Question 8  Which of the following statements is NOT a postulate of special relativity?

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