Exam 37: Relativity

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:

A distant star has a transverse speed (perpendicular to our line of sight) of 30,000 km/s with respect to Earth. Its spectrum has an absorption line at a frequency of 5.00 x 10¹⁴ Hz. What is the frequency of that line as observed on Earth?

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:

A certain automobile is 6.0 m long if at rest. If it is measured to be 4.8 m long while moving, its speed is:

If the kinetic energy of a free particle is much less than its rest energy then its kinetic energy is proportional to:

A meter stick moves sideways (that is, in a direction perpendicular to its length) at 0.95c. According to measurements taken in the laboratory, its length is:

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:

A particle with rest mass m moves with speed 0.6c. Its kinetic energy is:

An electron (m = 9.11 *10^-31 kg) has a speed of 0.95c. The magnitude of its momentum is:

The length of a meter stick moving at 0.95c in the direction of its length with respect to the laboratory is measured by simultaneously marking its ends on an axis which is stationary in the laboratory. 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:

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

A meson when at rest decays 2 $\mu$ s after it is created. If moving in the laboratory at 0.99c, its lifetime according to laboratory clocks would be:

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:

A basic postulate of Einstein's theory of relativity is:

A spectral line of a certain star is observed to be "red shifted" from a wavelength of 500 nm to a wavelength of 1500 nm. Interpreting this as a Doppler effect, the speed of recession of this star is:

An observer notices that a moving clock runs slow by a factor of exactly 10. The speed of the clock is:

An electron is moving at 0.6c. If we calculate its kinetic energy using (1/2)mv², we get a result which is:

A train traveling very fast (v = 0.6c) has an engineer (E) at the front, a guard (G) at the rear and an observer (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':

Two events occur 100 m apart with an intervening time interval of 0.37 $\mu$ s. The speed of a clock that measures the proper time between the events is:

A rocket ship of rest length 100 m is moving at speed 0.8c past a timing device which records the time interval between the passage of the front and back ends of the ship. This time interval is: