Exam 26: The Special Theory of Relativity

Two satellites with equal rest masses are traveling toward each other in deep space. One is traveling at 0.550c and the other at 0.750c. The satellites collide and somehow manage to stick Together. What is the speed of the combined object after the collision?

An alpha particle has a mass of $6.64 \times 10 ^ { - 27 } \mathrm {~kg}$ and a charge of $3.20 \times 10 ^ { - 19 } \mathrm { C }$ , and it is traveling at $\left. 0.9650 \mathrm { c } . \left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right) , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} \right)$ (a) What is its rest energy (in $\mathrm { GeV }$ )? (b) What is its total energy (in $\mathrm { GeV } )$ ? (c) What is its kinetic energy (in GeV)?

If an electron in the lab has a kinetic energy equal to twice its rest energy, what is its speed in the lab?

A rocket is traveling away from Earth at 90% the speed of light. The captain turns on a laser light. What is the speed of the light as measured by an Earth-based astronomer if the captain aims the laser (a) directly forward or (b) directly backward?

If the mass of a $1.0 - \mathrm { kg }$ book could be entirely converted into electrical energy, how many $\mathrm { kW } \cdot \mathrm { h }$ of energy would that generate? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

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 $0.82 c$ . The commander also observes ship A, advancing in the rear, with a relative velocity of $0.50 \mathrm { c }$ . What is the speed of ship $\mathrm { C }$ as measured by the captain of ship A?

A tracking station on Earth observes a rocket move away at 0.370c. This rocket is designed to launch a projectile at 0.505c relative to the rocket. What speed (in terms of the speed of light) does the tracking station measure for the projectile if it is fired (a) straight ahead of the rocket or (b) backward from the rocket?

How much mass is lost during a reaction in which $1.7 \times 10 ^ { 8 } \mathrm { MeV }$ of energy is released? $( c = 3.0 \times$ $10 ^ { 8 } \mathrm {~m} / \mathrm { s } , 1 \mathrm { eV } = 1.6 \times 10 ^ { - 19 } \mathrm {~J}$ )

A spaceship enters the solar system moving toward the Sun at a constant speed relative to the Sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is $50.0$ minutes. How fast is the spaceship traveling towards the Sun? The radius of the orbit of Jupiter is $778 \times 10 ^ { 9 } \mathrm {~m}$ , and that of the orbit of Mars is $228 \times 10 ^ { 9 } \mathrm {~m}$ .

Observer A sees a ruler moving by in a relativistic rocket and measures its length to be LA. Observer B moves along with the rocket and measures the length of the ruler to be LB. What is true About these two length measurements?

A spaceship is moving away from an asteroid with a speed of 0.80c relative to the asteroid. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the speed of The missile measured by astronauts on the asteroid if the missile is fired toward the asteroid?

A particle in a 799=m-long linear particle accelerator is moving at 0.875c. How long does the particle accelerator appear to the particle?

During a reaction, a reactant loses $4.8 \times 10 ^ { - 28 } \mathrm {~kg}$ of mass. How many joules of energy are released? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

Consider three galaxies, Alpha, Beta and Gamma. An astronomer in Beta sees each of the other two galaxies moving away from her in opposite directions at $0.70 \mathrm { c }$ . At what speed would an observer in Alpha see the galaxy Beta moving?

A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The length of the train, as measured by a stationary observer on the ground,

You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

You are riding in a spaceship that has no windows, radios, or other means for you to observe or measure what is outside. You wish to determine if the ship is stopped or moving at constant Velocity. How can you do this?

You are moving at a speed 2/3 c toward Randy when shines a light toward you. At what speed do you see the light approaching you?

As shown in the figure, the captain of spaceship A observes spaceship $E$ escaping with a relative velocity of $0.35 c$ . A missile $M$ is fired from ship A directly toward ship $E$ , with a velocity of $0.76 c$ relative to ship A. What does the captain of ship E measure for the velocity of the missile M?

The special theory of relativity predicts that there is an upper limit to the speed of an object. It therefore follows that there is also an upper limit on which of the following properties of the Object? (There could be more than one correct choice.)