Exam 35: Relativity

A set of twins,Bobby and Betty,are born on the Earth.Bobby sets off to a distant planet at high speed,arrives,and heads back to Earth.Betty remains on Earth.In Bobby's frame he is at rest and Betty is moving so,according to Einstein,he has aged 20 years while Betty has aged only 2.In Betty's frame she is at rest,so she has aged 20 years and Bobby has only aged 2.Who will be older when Bobby and Betty meet again?

What is the difference in time-of-flight (the elapsed time)required for pions (rest mass 139.5 MeV/c²)and kaons (rest mass 497 MeV/c²)each with momentum 150 MeV/c to travel 55 cm? Use 3.0 x 10⁸ for the speed of light.

A rectangular box in a rocket travelling past the Earth at 0.50 c appears to people on the Earth to be a perfect cube,0.50 m on a side.What is the proper volume of the box?

A cosmic ray muon travels down through the atmosphere,travelling from the top of a 5.0-km tall mountain to sea level in 17 $\mu$ s as measured by astronomers on Earth.What height would one travelling with the muon observe the mountain to be? Use 3.0 * 10⁸ for the speed of light.

The International Space Station orbits 350 km above the Earth's surface at a speed of 27700 km/hr.It takes approximately 1.5 hours to complete each orbit.At the same moment in 2008,two clocks mark the ten year anniversary of the Station orbiting the Earth.Both clocks are accurate to 1 ms,but one is on the Earth and the other is on the Station itself.How does the reading on the Station's clock compare with that of the Earth-based clock,which reads exactly 10 years?

Sam sees two events as simultaneous: i.event A occurs at the point (0,0,0)at the instant 0:00:00 Universal time; ii.event B occurs at the point (x_B,0,0)at the same moment. Tim,moving past Sam with a velocity of (0.998 c)",also observes the two events and sees that event B happened 3.74 µs after event A. Then x_B is

Right before takeoff,a passenger on a plane flying from town A to town B synchronizes his clock with the clock of his friend waiting for him in town B. The plane flies without interruption at a constant velocity of 280 m/s. The moment the plane touches the ground the two friends check simultaneously the indication of their clocks.The clock of the passenger on the plane shows that it takes exactly 7.50 h to travel from A to B. Ignoring any effects of acceleration,the difference between the readings of the clocks B and A is

A new particle is discovered at Stanford Linear Accelerator whose rest mass is 12.0 GeV/c².If the total energy of the particle is 17.0 GeV,what is the momentum of this new particle?

A spacecraft travels a distance of 10^-3 light-years in 20 hours as measured by an observer stationed on Earth.How long does the journey take as measured by the captain of the spacecraft?

How much energy is released when a neutron (rest mass 939.6 MeV/c²)decays into a proton (rest mass 938.3 MeV/c²),an electron (rest mass 0.511 MeV/c²)and an anti-electron neutrino (rest mass approximately zero)?

An observer on the Earth sees the U.S.S.Enterprise approaching from one direction at 0.60 c and a Klingon Battle Cruiser approaching from the opposite direction.According to Mr.Spock,who is aboard the Enterprise,the Klingon Battle Cruiser is approaching the Enterprise,that 0.80 c.What is the speed of the Klingon Battle Cruiser as observed from Earth?

A beam of pions (a pion with rest mass 139.5 MeV/c²)travels down a beam pipe in a laboratory such that the pions have kinetic energy equal to half their rest energy.The pion lifetime is 26 ns.Given this information,how far,on average,will the pions travel in the lab before decaying? Use 3.0 x 10⁸ for the speed of light.

A spacecraft travels along a straight line from the Earth to the Moon a distance of 3.84 * 10⁸ m.Its speed measured on Earth is 0.70 c.How long does the trip take according to a clock on the spacecraft?

Two stationary space stations are separated by a distance of 20 light-years as measured by someone on one of the space stations.A spaceship traveling at 0.90 c relative to the space stations passes by one of the space stations heading directly towards the other one.How long will it take to reach the other space station as measured by someone on the spaceship?

An observer on the Earth sees the U.S.S.Enterprise approaching from one direction at 0.600 c and a Klingon Battle Cruiser approaching from the opposite direction at 0.800 c.According to Mr.Spock,who is aboard the Enterprise,what is the speed of the Klingon Battle Cruiser?

An electron travelling is at 2.968 * 10⁸ m/s,what is the new speed of the electron if its energy is increased by150%? The speed of light is 2.9979 * 10⁸ m/s.

If spaceship A is travelling at 70% the speed of light relative to an observer at rest,and spaceship B is travelling at 90% the speed of light relative to an observer at rest,which of the following have the greatest velocity as measured by an observer in spaceship B?

A new particle is discovered at Stanford Linear Accelerator whose rest mass is 12.0 GeV/c².If the momentum of this new particle was 5.00 GeV/c,then what would be its total energy?

A wedge-shaped space ship has a width of 20 m and a length of 50 m and is shaped like and isosceles triangle.What is the angle between the base of the ship and the side of the ship as measured by a stationary observer if the ship is travelling by at a speed of 40% the speed of light?

An astronaut on the space shuttle traveling at a speed of 0.70 c is holding a meter stick parallel to the direction of motion.If an observer on Earth could observe the meter stick,what length of the meter stick would he measure?