Exam 26: Special Relativity

Astronaut Jill leaves Earth in a spaceship and is now traveling at a speed of 0.280c relative to an observer on Earth.When Jill left Earth,the spaceship was equipped with all kinds of scientific instruments,including a meter stick.Now that Jill is underway,how long does she measure the meter stick to be?

A person in a rocket ship traveling past the earth at a speed of 0.500c fires a laser gun in the forward direction.With what speed does an observer on Earth measure for the light pulse?

You are a passenger on a spaceship.As the speed of the spaceship increases,you will observe

Consider three galaxies,Alpha,Beta and Gamma.An astronomer in Beta sees each of the other two galaxies moving away from him in opposite directions at 0.70c.At what speed would an observer in Alpha see the galaxy Gamma moving?

Two spaceships,each 100 m long in its own rest frame,approach Earth from opposite directions,each with a speed 0.50c relative to Earth.As measured by a passenger in one of the spaceships,how long is the other spaceship?

A proton,which has a mass of 1.67 × 10^-27, is moving at 0.80c relative to the laboratory.What does a physicist in that lab measure for its momentum? (c = 3.0 × 10⁸ m/s)

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 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).

If the kinetic energy of a proton is 80% of its total energy,what is the speed of the proton?

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

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

A spaceship is moving away from an asteroid with a speed of 0.80c relative to the asteroid.The spaceship then fires a missile with a speed of 0.50c relative to the spaceship.What is the speed of the missile measured by astronauts on the asteroid if the missile is fired toward the asteroid?

Suppose one twin takes a ride in a spaceship traveling at a very high speed to a distant star and then back again,while the other twin remains on Earth.Compared to the twin who remained on Earth,the astronaut twin is

One 20-year-old twin brother takes a space trip with a speed of 0.80c for 30 years according to a clock on his spaceship.At the end of this trip,what are (a)his own age and (b)the age of his Earth-based twin brother?

An electron has a relativistic momentum of 1.1 × 10^-21 kg ∙ m/s.What percent of its total energy is its kinetic energy? (m_electron = 9.11 ×10^-31 kg,c = 3.0 × 10⁸ m/s)

Calculate the speed at which a 0.723-kg object has the same momentum as a 1.30-kg object that is moving 0.515c.

A starship is constructed to be 100 m long in the factory.It is launched and as it coasts by Earth,it is measured to be shortened to 5.48 m long. (a)How fast,in terms of the speed of light,is it moving past Earth? (b)What length does the ship's crew measure for the ship?

An astronaut is resting on a bed inclined at an angle above the floor of a spaceship,as shown in the figure.From the point of view of an observer who sees the spaceship moving near the speed of light parallel to the floor,the angle the bed makes with the floor

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.How fast is the spaceship traveling towards the Sun? The radius of the orbit of Jupiter is 778 × 10⁹ m,and that of the orbit of Mars is 228 × 10⁹ m.

Two spaceships approach Earth from opposite directions.One has a speed of 0.21c and the other a speed of 0.34c,both relative to Earth.What is the speed of one spaceship relative to the other?