Exam 26: Special Relativity

You are riding in a spaceship that has no windows,radios,or other means for you to observe or measure what is outside.You wish to determine if the ship is stopped or moving at constant velocity.How can you do this?

A certain unstable particle has a mean lifetime of 1.52 × 10^-6 s.This is the time interval between its creation in a nuclear process and its extinction into decay products,as measured in a frame of reference at rest with respect to the particle.An average such particle is observed by a scientist on Earth to travel 342 m in its lifetime.What is the speed of the particle relative to Earth? (c = 3.00 × 10⁸ m/s)

If the kinetic energy of a particle is 3.00 times its rest energy,the speed of the particle is closest to which of the following values?

In an "atom smasher," two particles collide head on at relativistic speeds.If the velocity of the first particle is 0.741c to the left,and the velocity of the second particle is $0.543 c$ to the right (both as measured in the lab rest frame),how fast are the particles moving with respect to each other?

One of Einstein's postulates in formulating the special theory of relativity was that the laws of physics are the same in reference frames that

As an electron slows down from 0.9980c to 0.5000c,how much momentum does it lose? (c = 3.0 × 10⁸ m/s,m_electron = 9.11 × 10^-31 kg)

A satellite,initially at rest in deep space,separates into two pieces,which move away from each other.One piece has a rest mass of 190 kg and moves away with a speed 0.500c,and the second piece has a rest mass of 250 kg and moves in the opposite direction.What is the speed of the second piece?

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)

An electron has a speed of 0.783c.Through what potential difference would the electron need to be accelerated from rest in order to reach this speed? The rest mass energy of an electron is 0.511 MeV.

You are moving past the Earth at 0.990c and notice your heart beating 88 beats per minute. (a)If a doctor on Earth measures your heart rate as you zip past,what will the measured rate be? (b)If you had been moving 99.99% the speed of light,what rate would you have observed your heart beats?

A rocket is traveling away from Earth at 90% the speed of light.The captain turns on a laser light.What is the speed of the light as measured by an Earth-based astronomer if the captain aims the laser (a)directly forward or (b)directly backward?

Two spaceships,each 100 m long in its own rest frame,approach Earth from opposite directions,with equal speeds relative to Earth.As measured by a passenger in one of the spaceships,the other spaceship is 96 m long.What is the speed of the spaceships relative to Earth?

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 speed of the combined object after the collision?

If the mass of a 1.0-kg book could be entirely converted into electrical energy,how many kW ∙ h of energy would that generate? (c = 3.0 × 10⁸ m/s)

The energy released by a certain reaction is enough to totally evaporate 125 kg of water at its boiling point.How much mass was lost during this reaction? (L_F = 334,000 J/kg for water,c = 3.00 × 10⁸ m/s)

A set of twins,Andrea and Courtney,are initially 10 years old.While Courtney remains on Earth,Andrea rides on a spaceship that travels away from Earth at a speed of 0.60c for 10 years (as measured by Courtney).At the end of the trip,Courtney is 20 years old.How old is Andrea?

Two spaceships are approaching one another,each at a speed of 0.31c relative to a stationary observer on Earth.What speed,in terms of the speed of light,does an observer on one spaceship record for the other approaching spaceship?

How much mass is lost during a reaction in which 1.7 × 10⁸ MeV of energy is released? (c = 3.0 × 10⁸ m/s,1 eV = 1.6 × 10^-19 J)

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?

A spaceship visits a star that is 4.5 light-years from Earth,and the spaceship travels at one-half the speed of light for the entire trip. (a)How long did the trip take according to an observer on Earth? (b)How long did the trip take according to an observer on the spaceship?