Exam 37: Relativity

System has a velocity u = +0.45c relative to system S,as shown in the figure.The clocks of S and are synchronized at t = = 0 when the origins O and coincide.An event is observed in both systems.The event takes place at x = 600 m and at time t = 1.9 μs,as measured by an observer in S.What is the -coordinate of the event,measured by an observer in ?

An electron is accelerated from rest through a potential difference of 50.0 kV.What is the TOTAL energy of the electron? (c = 3.00 × 10⁸ m/s,e = 1.60 × 10^-19 C,

An astronaut in an inertial reference frame measures a time interval Δt between her heartbeats.What will observers in all other inertial reference frames measure for the time interval between her heartbeats?

How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 10⁸ m/s)

A particle is moving at 0.75c relative to a lab on Earth.By what percentage is the Newtonian expression for its momentum in error? (The percentage error is the difference between the erroneous and correct values,divided by the correct one).

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy.What is the TOTAL energy of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 10⁸ m/s,m_proton = 1.67 × 10^-27 kg)

Two spaceships are approaching one another,each at a speed of 0.28c relative to a stationary observer on Earth.What speed does an observer on one spaceship record for the other approaching spaceship?

Two space stations are at rest relative to each other and are 6.0 × 10⁷ m apart,as measured by observers on the stations.A spaceship traveling from one station to the other at 0.90c relative to the stations passes both of them,one after the other.As measured by an observer in the spaceship,how long does it take to travel from one station to the other?

A navigational beacon in deep space broadcasts at a radio frequency of 50 MHz.A spaceship approaches the beacon with a relative velocity of 0.40c.What is the frequency of the beacon radio signal that is detected on the ship?

An electron has a speed of 0.643c.Through what potential difference would the electron need to be accelerated (starting from rest)in order to reach this speed? (c = 3.00 × 10⁸ m/s, ,m_el = 9.11 × 10^-31 kg)

You are a passenger on a spaceship.As the speed of the spaceship increases,you would observe that

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

A navigational beacon in deep space broadcasts at a radio frequency of 50 MHz.A spaceship approaches the beacon with a relative velocity of 0.40c.The spaceship passes the beacon and departs from it with a DIFFERENT relative velocity.The beacon signal is now detected at a frequency of 40 MHz.What is the new velocity of the spaceship relative to the beacon?

A spaceship approaches the earth with a speed 0.50c.A passenger in the spaceship measures his heartbeat as 70 beats per minute.What is his heartbeat rate according to an observer that is at rest relative to the earth?

As measured in Earth's rest frame,a spaceship traveling at takes to travel between planets.How long does the trip take as measured by someone on the spaceship?

A spacecraft is measured by an observer on the ground to have a length of 53 m as it flies toward the earth with a speed 1.7 × 10⁸ m/s.The spacecraft then lands and its length is again measured by the observer on the ground,this time while the spacecraft is at rest on the launchpad.What result does he now get for the length?

Astronaut Mark Uri is space-traveling from planet X to planet Y at a speed of relative to the planets,which are at rest relative to each other.When he is precisely halfway between the planets,a distance of 1.0 light-hour from each one as measured in the planet frame,nuclear devices are detonated on both planets.The explosions are simultaneous in Mark's frame.What is the difference in the time of arrival of the flashes from the explosions as observed by Mark?

During a nuclear reaction,1.7 × 10^-4 J of energy is released.What is the resulting change in mass of the particles involved? (c = 3.00 × 10⁸ m/s)

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

Assume that a certain city consumes electrical energy at an average rate of 2.0 × 10⁹ W.What would be the mass change in producing enough energy to keep this city running for 21 weeks?