Exam 27: Relativity

Assume that a typical city consumes electrical energy at a rate of 2.0 × 10^-9 W.How many kilograms of matter would have to be converted entirely into energy in order to keep this city running for 21 weeks?

Explain why it is impossible for an object to travel at the speed of light.

Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y,while an astronaut on the spaceship says that the trip took 6.27 y.Find the velocity of the spaceship in terms of the speed of light.

The special theory of relativity predicts that there is an upper limit to the speed of a particle.It thus follows that there is also an upper limit on the following property of a particle:

An astronaut on a spaceship moving at 0.927 c says that the trip between the two stars took 4.26 y.How long does this journey appear to take to someone in the rest frame of the two stars?

Calculate the kinetic energy of an electron moving at 0.737 c.Express your answer in keV.

The rest mass of a particle depends upon how fast it is moving.

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

Calculate the speed at which a 0.272 kg object has the same momentum as a 1.30 kg object moving 0.515 c.

As measured in Earth's rest frame,a spaceship traveling at 0.964 c takes 11.2 y to travel between planets.How long does the trip appear to take for someone on the spaceship?

An electron has a speed of 0.643 c.Through what potential difference would the electron need to be accelerated in order to reach this speed? Assume that the electron was initially at rest.

A star is moving toward Earth with a speed of 0.9 c (90% the speed of light).It emits light,which moves away from the star at the speed of light.Relative to us on Earth,the speed of the light moving toward us (emitted by the star)is

A spaceship is moving between two distant stars at 0.932 c.To someone in the ship,the distance between the two stars appears to be 26.4 ly.What is the distance between the stars in the stars' rest frame?

A hydrogen atom and a neutron fuse to form deuterium.If the energy released is 3.6 × 10^-13 J,what is the mass of the deuterium? Take the H atom nucleus as a single proton.

A right-angled construction frame ABC,when measured at rest,has dimensions as follows: AB = 28.00 m,AC = 10.00 m,and BC = 26.15 m.The frame is given a velocity of 0.80 c,relative to the space platform,in a direction parallel to AC.The dimensions of the moving frame are measured simultaneously by observers on the platform.In the figure,the length AB measured by these observers is closest to:

A rocket is moving at 1/4 the speed of light relative to Earth.At the center of this rocket,a light suddenly flashes.To an observer at rest on Earth,the light will reach the front of the rocket at the same instant that it reaches the back of the rocket.

Calculate the amount of energy needed to accelerate an electron from 0.888 c to 0.991 c.Express your answer in MeV.

Assume that it takes you one week to read a book in your own rest frame.Would it appear to you to take longer to read this book if you were in a spaceship moving at a constant speed of 0.98 c than it would if you read the same book while sitting in a chair at home?

The kinetic energy of a particle of mass M traveling at 1/2 the speed of light is Mc²/8.

Astronauts travel to a star 2000 light-years from Earth in a spaceship capable of speeds approaching,but not exceeding,the speed of light.Is it possible that the original astronauts will still be alive when the spaceship reaches the star? Why or why not?