Exam 37: Relativity

A millionairess was told in 1992 that she had exactly 15 years to live. However, if she travels away from the Earth at 0.8 c and then returns at the same speed, the last New Year's day the doctors expect her to celebrate is:

Two flashes of light occur simultaneously at t = 0 in reference frame S, one at x = 0 and the other at x = 600 m. They are observed in reference frame S', which is moving at 0.95c in the positive x direction. The origins of the two frames coincide at t = 0 and the clocks of S' are zeroed when the origins coincide. In S' the coordinate where the leading edges of the two light flashes meet and the time when they meet are:

While emitting light of proper frequency f₀, a source moves to the right with speed c/4 relative to reference frame S. A detector, to the left of the source, measures the frequency to be f, which is greater than f₀. This means:

Spaceship A, traveling past us at 0.7c, sends a message capsule to spaceship B, which is in front of A and is traveling in the same direction as A at 0.8c relative to us. The capsule travels at 0.95c relative to us. A clock that measures the proper time between the sending and receiving of the capsule travels:

A meter stick moves in the direction of its length through a laboratory. According to measurements taken in the laboratory, its length is 0.31 m. The speed of the meter stick relative to the laboratory is:

A source at rest emits light of wavelength 500 nm. When it is moving at 0.90c away from an observer, the observer detects light of wavelength:

According to the theory of relativity:

A meson moving through a laboratory of length x at a speed v decays after a lifetime T as measured by an observer at rest in the laboratory. If the meson were at rest in the laboratory its lifetime would be:

Observer A measures the velocity of a rocket as and a comet as . Here are parallel and in the direction of the observer's positive x axis. The speed of the comet as measured by an observer on the rocket is:

A measurement of the length of an object that is moving relative to the laboratory consists of noting the coordinates of the front and back:

The mass of a particle is m. In order for its total energy to be twice its rest energy, its momentum must be:

Visible light, with a frequency of 6.0 *10¹⁴ Hz, is reflected from a spaceship moving directly away at a speed of 0.90c. The frequency of the reflected waves observed at the source is:

The length of a meter stick moving at 0.95c in the direction of its length is measured by simultaneously marking its ends on a stationary axis. As measured by clocks moving with the stick, the time interval between the making of the back mark and the making of the front mark is:

A console lamp in the cabin of a spaceship appears green when the ship and observer are both at rest. When the ship is moving at 0.90c away from Earth, passengers on board see:

The proper time between two events is measured by clocks at rest in a reference frame in which the two events:

The work that must be done to increase the speed of an electron (m = 9.11*10^-31 kg) from 0.90c to 0.95c is:

As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the rocket and 9 * 10^-8 s later a mark is made on the axis at the back end. The marks are found to be 100 m apart. The rest length of the rocket is:

A train traveling very fast (v = 0.6c) has an engineer (E) at the front, a guard (G) at the rear and an passenger (S') exactly half way between them. Both E and G are equipped with yellow signaling lamps. The train passes a station, closely observed by the station master (S). Both E and G use their lamps to send signals. According to both S and S' these signals arrive simultaneously at the instant S' is passing S. According to S, the signal from E will look ______ and that from G will look _____:

Pi mesons at rest have a half-life of T. If a beam of pi mesons is traveling at a speed of v = $\beta$ c, the distance in which the intensity of the beam is halved is:

Relative to reference frame 1, reference frame 2 moves with speed v in the negative x direction. When the origins of the two frames coincide the clocks in both frames are set to zero. An event occurs at coordinate x₁ and time t₁ as measured in reference frame 1 and at coordinate x₂ and time t₂ as measured in frame 2. If , then the coordinates and times of the event are related by: