Exam 29: Electromagnetic Induction

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

Velocity addition: Three spaceships A, B, and C are in motion, as shown in the figure. The commander on ship B observes ship C approaching with a relative velocity of 0.78c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.31c. What is the velocity of ship C, relative to an observer on ship A?

Kinetic energy: 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, e = 1.60 × 10^-19 C, m_el = 9.11 × 10^-31 kg)

Time dilation: A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship which travels away from Earth at a speed of 0.60c for five years (as measured by Courtney), then immediately turns around and comes back at 0.60c. When Andrea returns, Courtney is 20 years old. How old is Andrea upon her return?

Doppler effect: 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?

Total energy: As a spaceship is moving toward Earth, an Earthling measures its length to be 325 m, while the captain on board radios that her spaceship's length is 1150 m. (c = 3.00 × 10⁸ m/s) (a) How fast is the rocket moving relative to Earth? (b) What is the TOTAL energy of a 75.0-kg crewman as measured by (i) the captain in the rocket and (ii) the Earthling?

Total energy: A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the momentum 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)

Total energy: 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? (c = 3.00 × 10⁸ m/s)

Kinetic energy: An electron is accelerated from rest through a potential difference of 50.0 kV. What is the speed of the electron? (c = 3.00 × 10⁸ m/s, e = 1.60 × 10^-19 C, m_el = 9.11 × 10^-31 kg)

Velocity addition: 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 to the right (both of these speeds are measured in Earth's rest frame), how fast are the particles moving with respect to each other?

Length contraction: 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? (c = 3.00 × 10⁸ m/s)

Lorentz transformation: System S' has a velocity u = +0.45c relative to system S, as shown in the figure. The clocks of S and S' are synchronized at t = t' = 0 when the origins O and O' 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 x'-coordinate of the event, measured by an observer in S'?

Velocity addition: A star is moving towards the earth with a speed at 90% the speed of light. It emits light, which moves away from the star at the speed of light. Relative to us on earth, what is the speed of the light moving toward us from the star?

Length contraction: Relative to the frame of the observer making the measurement, at what speed parallel to its length is the length of a meterstick 60 cm?

Velocity addition: A spaceship approaching an asteroid at a speed of 0.60c launches a rocket forward with a speed of 0.40c relative to the spaceship. At what speed is the rocket approaching the asteroid as measured by an astronaut on the asteroid?

Length contraction: 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? (c = 3.00 × 10⁸ m/s)

Velocity addition: A spaceship is moving away from the earth with a constant speed of 0.80c. The spaceship fires a 28-kg missile with a speed of 0.50c relative to the spaceship. What is the speed of the missile measured by observers on the earth if the missile is fired (a) away from the earth? (b) toward the earth?

Total energy: 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)

Simultaneity: 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?

Length contraction: An astronaut leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth. The astronaut's destination is a star system 14.4 light-years away. (One light-year is the distance light travels in one year.) According to the astronaut, how long does the trip take?