Exam 27: Relativity

Two stars are at rest relative to each other. In their common rest frame, these stars are 90.0 light-years apart. If they are measured to be $68.7 \text { light-years }$ apart by the navigator of a spaceship traveling between them, how fast is the spaceship moving relative to these stars?

A spaceship traveling at 0.50c away from Earth launches a secondary rocket in the forward direction at 0.50c relative to the spaceship. As measured by Earthlings, how fast is the secondary rocket moving away from Earth?

Observer A sees a ruler moving by in a relativistic rocket and measures its length to be L_A. Observer B moves along with the rocket and measures the length of the ruler to be L_B. What is true about these two length measurements?

A star is moving toward Earth at 90% the speed of light. The star emits light, which moves away from the star at the speed of light. What do Earth-based astronomers measure for the speed of this light?

A spaceship approaching an asteroid at a speed of 0.60c launches a scout rocket with speed 0.40c relative to the spaceship. At what speed is the scout rocket approaching the asteroid?

In a nuclear plant, 10¹⁷ J of energy is available from mass conversion. How much mass of fuel was lost to produce this energy? (c = 3.0 × 10⁸ m/s)

A satellite with a rest mass of 200 kg and a speed of 0.800c and a second satellite with a rest mass of 100 kg and a speed of 0.600c are traveling toward each other in deep space. The satellites collide and somehow manage to stick together. What is the rest mass of the combined object after the collision?

In a certain chemical reaction, 8.1 × 10^-19 J of energy is released per molecule formed. What is the difference in mass per molecule between the sum of the masses of the molecules of the reagents before the reaction and the mass of the molecules produced by the reaction? (c = 3.0 × 10⁸ m/s)

Astronaut Rob leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth. Rob's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year). Relative to a frame of reference that is fixed with respect to Earth, how long does it take Rob to complete the trip?

You are moving at a speed 2/3 c toward Randy when shines a light toward you. At what speed do you see the light approaching you?

A person with an initial mass of 70 kg climbs a stairway and thereby rises 6.0 m in elevation. By how much does his mass increase by virtue of his increased potential energy? (c = 3.0 × 10⁸ m/s)

Two satellites with equal rest masses are traveling toward each other in deep space. One is traveling at 0.550c and the other at 0.750c. The satellites collide and somehow manage to stick together. What is the speed of the combined object after the collision?

A spaceship enters the solar system moving toward the sun at a constant speed relative to the sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is 50.0 minutes. As measured in the coordinate system of the sun, how long did it take for the spaceship to travel that distance? The radius of the orbit of Jupiter is 778 × 10⁹ m, and that of the orbit of Mars is 228 × 10⁹ m.

An alpha particle has a mass of 6.64 × 10^-27 kg and a charge of 3.20 × 10^-19 C, and it is traveling at 0.9650c. (c = 3.00 × 10⁸ m/s), 1 eV = 1.60 × 10^-19 J) (a) What is its rest energy (in GeV)? (b) What is its total energy (in GeV)? (c) What is its kinetic energy (in GeV)?

An object with a rest mass of 0.456-kg is moving at 1.20 × 10⁸ m/s. What is the magnitude of its momentum? (c = 3.00 × 10⁸ m/s)

Calculate the amount of energy needed to accelerate an electron from $0.8880$ to $0.991 \mathrm { c }$ Express your answer in $\mathrm { MeV }$ The rest mass energy of an electron is 0.511 MeV.

A spaceship, traveling at 0.100c away from a stationary space platform, launches a secondary rocket towards the station, with a speed of 0.560c relative to the spaceship. What is the speed of the secondary rocket relative to the space platform?

If a typical city consumes electrical energy at a rate of $2.0 \mathrm { GW }$ how many kilograms of matter would have to be converted entirely into electrical energy in order to keep this city running for $14 \text { weeks? }$ $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space. They have identical speeds of 0.600c. The satellites collide and somehow manage to stick together. What is the rest mass of the combined object after the collision?

A particle is moving at 0.86c. By what magnitude percentage is the Newtonian expression for momentum in error? (The percentage error is the difference between the erroneous and correct expressions, relative the correct one).