Exam 29: Electromagnetic Induction

Time dilation: 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?

Lorentz transformation: System S' has a velocity u = +0.56c 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 = 800 m and at time t = 3.0 μs as measured by an observer in S. What is the time of the event, measured by an observer in S'?

Total energy: A relativistic proton has a momentum of 1.0 × 10^-17 kg ∙ m/s and a rest energy of 0.15 nJ. What is the kinetic energy of this proton? (c = 3.00 × 10⁸ m/s, m_proton = 1.67 × 10^-27 kg)

Kinetic energy: How much work must be done to accelerate a particle of mass from a speed of to a speed of

Length contraction: A particle in a 453 m-long linear particle accelerator is moving at How long does the particle accelerator appear to the particle?

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

Total energy: How fast must a proton move so that its kinetic energy is 80% of its total energy?

Kinetic energy: In a certain particle accelerator, a proton has a kinetic energy that is equal to its rest energy. What is the speed of the proton relative to the accelerator?

Time dilation: 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?

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 0.83c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.48c. As measured by commander on ship B, at what speed is ship A approaching ship C?

Momentum: 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).

Length contraction: A spaceship is moving between two distant stars at 0.932c. To someone in the ship, the distance between the two stars appears to be What is the distance between the stars in the rest frame of the stars?

Simultaneity: Astronaut Spud Nick is space-traveling from planet X to planet Y at a speed of 0.60c 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 each planet. The explosions are simultaneous in the frame of the planets. What is the difference in the time of arrival of the flashes from the explosions as observed by Spud?

Time dilation: An unstable particle is moving at a speed of 2.6 × 10⁸ m/s relative to a laboratory. Its lifetime is measured by a stationary observer in the laboratory to be 4.7 × 10^-6 seconds. What is the lifetime of the particle, measured in the rest frame of the particle? (c = 3.00 × 10⁸ m/s)

Total energy: 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)

Momentum: In the lab, a relativistic proton has a momentum of 1.00 × 10^-19 kg ∙ m/s and a rest energy of 0.150 nJ. What is the speed of the proton in the lab? (c = 3.00 × 10⁸ m/s, m_proton = 1.67 × 10^-27 kg)

Simultaneity: 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,

Simultaneity: 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 in the rocket,

Velocity addition: 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?

Time dilation: 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.