Exam 12: Special Relativity

Captain Kirk reports to headquarters that he left the planet Senesca 1.88 *104 seconds earlier. Headquarters sends back the message: 'Was that spaceship proper time?' It will be spaceship proper time if it was:

A satellite moves east, taken as the positive x axis direction, at a speed of 0.5 c and a spaceship moves toward it (to the west) at a speed of 0.8 c as measured by an observer on the Earth. The speed of the satellite measured by an observer in the spaceship is:

A 1000-kg automobile moving with a speed of 24 m/s collides with a 500-kg car initially at rest. If the two stick together, what is the velocity (in m/s) of the two cars after the collision relative to an automobile moving in the same direction at 15 m/s?

The period of a pendulum is 2.0 s in a stationary inertial frame of reference. What is its period when measured by an observer moving at a speed of 0.60 c with respect to the inertial frame of reference?

The quantity which does not change in magnitude from that observed in system S when observed in system S' moving away from system S at speed v is:

A proton has a total energy of 2.5 * 10-10 J. How fast is it moving? (M = 1.67 * 10-27 kg)

A boat has an initial velocity of 2 m/s in the y direction on a stream, which is moving in the x direction at 1 m/s. The boat is accelerating in its direction of motion at 1 m/s2. What is the acceleration of the boat (in m/s2) relative to the water?

A supertrain (rest-length 100 m) travels at a speed of 0.950 c as it passes through a tunnel (rest-length 50.0 m). As seen by a trackside observer, is the train ever completely within the tunnel? If so, by how much?

The half-life of a muon is 2.2 $\mu$ s. How fast is it moving relative to an observer who says its half-life is 4.4 $\mu$ s?

The first intergalactic spaceship is headed toward the Magellanic Clouds at a speed of 0.8c. The spaceship is 1000 m long. Clocks at the front and the rear of the spaceship both read 3:00 P.M. Can it be 3:00 P.M. simultaneously at the front and the back of the spaceship?

Many science-fiction stories assume that in the future, humanity will use anti-matter as a source of energy. Assume that in some future power plant, a gram of matter is annihilated by a gram of anti-matter. How long would the energy released power a city that uses 109 watts of power?

In a classroom on the first spaceship to an extrasolar planet - there are children because the trip will take 200 years - a teacher is showing charge Q uniformly distributed along a conducting rod of length L0 to produce linear charge density $\lambda$ 0. As observed on Pluto when the spaceship passes it at 0.800 c, the linear charge density is:

In a colour television tube, electrons are accelerated through a potential difference of 20 000 volts. With what velocity do the electrons strike the screen?

A jet plane travels around the world at 3220 km/hr (894 m/s). Two accurate atomic clocks measure the times of flight, one on board the plane and the second on Earth. If it takes 12 hours to complete the journey, what will the time difference (in $\mu$ s) be?

An electron has a kinetic energy that is twice its rest energy. Determine its speed.

A spaceship from another galaxy passes over the solar system directly above a radial line from the sun to the Earth. (We measure that distance to be 1.5 *1011 m.) On Earth, the spaceship is observed to be travelling at a speed of 0.80 c, for which $\gamma$ = 5/3. As measured on Earth it takes the spaceship 625 seconds to travel from the sun to Earth. When a scientist in the spaceship measures the Earth-sun distance and the time it takes her to travel that distance, she finds the results are respectively:

Find the momentum and speed of a proton whose kinetic energy equals its rest energy. (The mass of a proton is 938.3 MeV/c2).

When 1.0 gram of hydrogen combines with 8.0 grams of oxygen, 9.0 grams of water is formed. But is this true? During the reaction 2.86 *105 J of energy is released. How much mass is actually lost in this reaction?

A spaceship moves at a speed of 0.95 c away from the Earth. It shoots a star wars torpedo toward the Earth at a speed of 0.90 c relative to the ship. What is the velocity of the torpedo relative to the Earth? (The direction in which the spaceship moves is the positive direction.)

A spaceship moving past the Earth with a speed of 0.800 c signals to the Earth with pulsed laser photons emitted at 10.0-second intervals according to the spaceship's clock. According to observers on Earth who see the flashes, the time interval they measure is: