Exam 9: Relativity

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

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).

A spaceship from another galaxy passes over the solar system directly above a radial line from the sun to the Earth.(We measure that distance to be 1.5 *10¹¹ m. )On Earth,the spaceship is observed to be traveling at a speed of 0.80 c,for which $\gamma$ = 5/3.As measured on Earth it takes the spaceship 625 seconds to travel from the sun to Earth.When a scientist in the spaceship measures the Earth-sun distance and the time it takes her to travel that distance,she finds the results are respectively

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 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 30-year-old woman takes a trip on a rocket,leaving her 20-year-old brother behind.She travels at a speed of 0.8 c,and is gone 20 years,according to the younger brother.When she returns,how many years older/younger is she than her brother?

A 1 000-kg automobile moving with a speed of 24 m/s relative to the road collides with a 500-kg automobile initially at rest.If the two stick together,what is the velocity in m/s of the two cars after the collision according to an observer in a truck moving 10 m/s in the same direction as the moving cars?

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 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?

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 1 000-kg automobile moving with a speed of 24 m/s collides with a 500-kg car initially at rest.If the two stick together,what is the velocity (in m/s)of the two cars after the collision relative to an automobile moving in the same direction at 15 m/s?

The half-life of a muon is 2.2 $\mu$ s.How fast is it moving relative to an observer who says its half-life is 4.4 $\mu$ s?

In a classroom on the first spaceship to an extrasolar planet--there are children because the trip will take 200 years--a teacher is showing charge Q uniformly distributed along a conducting rod of length L₀ to produce linear charge density $\lambda$ ₀.As observed on Pluto when the spaceship passes it at 0.800 c,the linear charge density $\lambda ^ { \prime }$ is

In a color television tube,electrons are accelerated through a potential difference of 20 000 volts.With what velocity do the electrons strike the screen?

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?

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 1 000 m long and that ship B is 800 m long.The crew on ship B says that their ship is 1 000 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?

A spaceship moving past the Earth with a speed of 0.800 c signals to the Earth with pulsed laser photons emitted at 10.0-second intervals according to the spaceship's clock.According to observers on Earth who see the flashes,the time interval they measure is

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

A proton has a total energy of 2.5 *10 ^{- 10} J.How fast is it moving? (M = 1.67 *10 ^{- 27} kg)