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AS03A - Gamma Factor, Length Contraction, Time Dilation, Mass Increase 1. Determine the gamma factors to 5 significant digits for the following relativistic speeds V (c Y 0.01 c or 1% the speed of light 0.10 c or 10% the speed of light 0.25 c or 25% the speed of light 0.50 c or 50% the speed of light 0.75 c or 75% the speed of light 0.90 c or 90% the speed of light 0.99 c or 99% the speed of light 0.999 c or 99.9% the speed of light 0.9999 c or 99.9% the speed of light Show a sample calculation for a row of your choice: Sketch a graph of gamma factor vs speed for 0.25 c to 0.99 c. YA 0.0 0.10 0.50 V ( c ) 2. If a space ship is 100 m long at rest and 20 m high and 40 m wide, then what are its dimensions at 99% of c forward? 3. If superman masses 250 kg at rest then determine his mass if he is moving at 0.90 c. 4. If it takes 1 hour for a volcano to erupt on the planet Earth, then how long does it appear to take for an alien in a spaceship passing by the Earth at 25% of the speed of light? 5. If it takes 15 min for Wonderwoman to eat lunch on her invisible jet flying at 0.999 c, then how long has passed at Justice League headquarters which is at rest?6. If Thor masses 1.014 metric tonne while flying at 98.9% the speed of light, then determine his rest mass. 7. Spiderwoman is normally 1.8 m tall when at rest. How fast would she have to fly upwards at to contract to a length of 1.0 m? 8. Draw the following shapes as they would appear at various relativistic velocities. At rest 0.50 . Im 50 cm ) 0.75 60 cm o . 10 m 10m or 0.90 0.99 Assignment 03B Relativistic Velocity 1. The Roadrunner has a velocity of 0.9 [North] and Speedy Gonzales has a velocity of 0.8 [South]. If they are approaching each other, then determine their relative velocity. 4 |4 J'JJ..; Pl 2. Supergirl is flying at 0.9 [East] and The Flash has a velocity of 0.99 [East]. If The Flash is catching up to Supergirl from behind Supergirl then determine their relative velocity. 3. Black Widow is travelling at 0.5 [East] and Loki has a velocity of 0.4 [West]. If they are receding from one another, then determine their relative velocity. x & 4. The Enterpnise is travelling at 0.999 [East] and the Star Destroyer has a velocity of 0.99 [East]. If they are receding from one another then determine their relative velocity. 5. If the Tardis space-time-ship has a velocity of 0.5 [E] and The Heart of Gold starship also travelling [E] has a relative velocity of 0.1 [receding] then determine the velocity of the Heart of Gold starship. 6. If the Prometheus space exploration vessel has a velocity of 0.99 [E] and the starship Daedalus has a relative velocity of 0.999 [approaching head-on from the E] then determine the velocity of the starship Daedalus. Assignment 03C Relativistic Kinetic Energy & Momentum (*** = Tough Question Give it a good try and do not worry if you can't finish it) 1. Protons normally have a rest mass of 1.67x10" kg. In the Large Hadron Accelerator at CERN in Europe protons were accelerated to 99.9997% of the speed of light in 2014, Determine the relativistic momentum and kinetic energy of one of these protons. 2. Ifthe Flash masses 100 kg at rest and then runs across the Atlantic Ocean at 99% the speed of light then determine his relativistic kinetic energy and relativistic momentum. Compare them to classical mechanics kinetic energy and momentum. What is the percentage error if we naively use classical mechanics? " ***3, If Storm normally masses 60 kg at rest and she somehow manages to reach a relativistic momentum of 4.5 trillion N s then determine her relativistic velocity. 4. Marvin the Martian's UFO has a rest mass of 100 tonnes. He accidently calculates his kinetic energy to be 4.5