Exam 39: Relativity

A supertrain (rest-length = 100 m)travels at a speed of 0.950 c as it passes through a tunnel (rest-length 50.0 m).As seen by a trackside observer,is the train ever completely within the tunnel? If so,by how much?

A satellite moves east,taken as the positive x axis direction,at a speed of 0.5 c and a spaceship moves toward it (to the west)at a speed of 0.8 c as measured by an observer on the Earth.The speed of the satellite measured by an observer in the spaceship is

A starship navigator measures the distance between the Earth and the sun.If the ship is moving at a speed of 0.90 c,instead of obtaining 93 million miles,the navigator measures a distance (in millions of miles)of

An electron has a kinetic energy that is twice its rest energy.Determine its speed.

An astronaut traveling with a speed v = 0.90 c holds a meterstick in his hand.If he measures its length,he will obtain a value of

A boat has an initial velocity of 2 m/s in the y direction on a stream which is moving in the x direction at 1 m/s.The boat is accelerating in its direction of motion at 1 m/s².What is the acceleration of the boat (in m/s²)relative to the water?

The first intergalactic spaceship is headed toward the Magellanic Clouds at a speed of 0.8c.The spaceship is 1 000 m long.Clocks at the front and the rear of the spaceship both read 3:00 P.M.Can it be 3:00 P.M.simultaneously at the front and the back of the spaceship?

The period of a pendulum is 2.0 s in a stationary inertial frame of reference.What is its period when measured by an observer moving at a speed of 0.60 c with respect to the inertial frame of reference?

In a color television tube,electrons are accelerated through a potential difference of 20000 volts.With what velocity do the electrons strike the screen?

Assume a gram of a substance marketed as "Pure Energy" is annihilated by a gram of a second substance "Anti-Pure Energy." How long would the energy released power a city which uses 10⁹ watts of power?

The 500 m-long spaceship Springbrake is at rest on the planet Hitest for refueling.Another spaceship,Summerbrake,passes parallel to Springbrake at 0.600c.The crew on Springbrake measure the length of Summerbrake as it passes and find that the length they measure is exactly the same as the known 500 m rest length of Springbrake.If Summerbrake were at rest next to Springbrake,its length would then be measured to be

When 1.0 gram of hydrogen combines with 8.0 grams of oxygen,9.0 grams of water is formed.But is this true? During the reaction 2.86 × 10⁵ J of energy is released.How much mass is actually lost in this reaction?

Find the momentum and speed of a proton whose kinetic energy equals its rest energy.(The mass of a proton is 938.3 MeV/c²).

Captain Ray,on the Galactic Explorer,sets off bright signal lights at the two ends of his spaceship so that they are seen as flashing simultaneously by General Kay,who is watch the ship go by.General Kay concludes that she was next to the midpoint of the ship at the instant when the lights flashed in her reference frame.This can only happen if Captain Ray,at the center of the Galactic Explorer,

The half-life of a muon is 2.20 μs as measured in a stationary reference frame.What is the half life of the muon (in μs)when it is moving with a speed of v = 0.800 c?

Captain Jirk reports to headquarters that he left the planet Senesca 1.88 × 10⁴ seconds earlier.Headquarters sends back the message: "Was that spaceship proper time?" It will be spaceship proper time if it was

The quantity which does not change in magnitude from that observed in system S when observed in system S' moving away from system S at speed v is

Two spaceships traveling in opposite directions along parallel lines measure their own and the other spaceship's length while passing one another.The crew on spaceship A says that their ship is 1000 m long and that ship B is 800 m long.The crew on ship B says that their ship is 1000 m long and that ship A is 800 m long.At what speed does each crew say that the other ship is traveling relative to their own ship?

Energy is released during a nuclear reaction due to a conversion between mass and energy.Mass is not conserved.The initial and final amounts are different.If a total of 1.0 gram of mass is "missing",how much energy has been released?

A spaceship leaves Earth and maintains a constant force by means of a nuclear engine.As the speed of the spaceship increases,an observer on Earth finds that relative to her the magnitude of the spaceship's acceleration is