Chapter 26 Special Theory of Relativity

A meter stick that is 1.0 m long in its own frame of reference moves past you at a speed of 0.96c. What length would you observe it to be?

0.28 m

A spaceship moves away from the Earth with a speed of 0.80c. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the velocity of the missile measured by observers on the Earth if the missile is fired away from the Earth? From the previous problem, what is the velocity of the missile measured by observers on the Earth if the missile is fired toward the Earth?

0.50c

A spaceship moves away from the Earth with a speed of 0.80c. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the velocity of the missile measured by observers on the Earth if the missile is fired toward the Earth?

0.50c

A meter stick is moving toward you with a speed of 0.80c. What is its length?

0.60 m

A stationary observer sees a spaceship contract to 3/4 of its proper length. How fast is the spaceship moving?

0.66c

How fast should a moving clock travel if it is to be observed by a stationary observer as running at one-half its normal rate?

0.87c

How fast would a rocket ship have to move to contract to half of its proper length (as observed by a stationary object)?

0.87c

What is the speed of a proton if its mass is twice its rest mass?

0.87c

A spaceship, moving away from the Earth at a speed of 0.70c, fires forward a phaser missile at a speed of 0.60c relative to it. What is the velocity of the missile as seen by observers on the Earth?

0.92c

A spaceship moves away from the Earth with a speed of 0.80c. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the velocity of the missile measured by observers on the Earth if the missile is fired away from the Earth?

0.93c

Captain Q of the Spaceship XY; observes the evil Captain Z coming towards him at 0.7c in his ship, the Mx^2. Captain Z fires a missile towards the XY that travels at 0.8c in the Mx^2 frame of reference. What is its speed as measured by Captain Q of the XY?

0.96c

A proton is moving with a kinetic energy that is 80% of its total energy. What is the speed of the proton?

0.98c

The kinetic energy of a proton is 80% of its total energy. What is the speed of the proton?

0.98c

The atomic bomb that was dropped on Nagasaki in 1945 killed 140,000 people, helping to end World War II on the next day. It released energy equivalent to that of 20,000 tons of TNT explosive. How much mass was converted to energy when this took place? (1000 tons of TNT = 4.3x10^12 J) Incidentally, modern H-bombs have energy yields 1000 times as much

1 g

In a nuclear plant, 10^17 J of energy is available from mass conversion. How much mass was lost?

1 kg

A fast spaceship is traveling with a speed of 0.80c. How fast would light travel from the headlights of the ship relative to a stationary observer?

1.0c

You are in a rocket traveling away from the Sun at 0.95c. You measure the speed of light from the Sun to be

1.0c

An electron is accelerated through 100 kV. By what factor has its mass increased with respect to its rest mass?

1.20

An electron is traveling at 0.85c. What is its mass? (The rest mass is 9.11x10^-31 kg.)

1.7x10^-30 kg

How much energy would be released if 2.0 kg of material was lost during a reaction?

1.8x10^17 J

During a reaction, 1.7 x10^-4 J of energy is released. What change of mass would cause this?

1.9x10^-21 kg

A spaceship takes a nonstop journey to a planet and returns in 10 hours according to a clock on the spaceship. If the speed of the spaceship is 0.80c, how much time has elapsed on the Earth?

17 h

A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship, which travels away from Earth at a speed of 0.6c for five years (as measured by Courtney), then turns around and comes back at 0.6c. When Andrea returns, Courtney is 20 years old. How old is Andrea upon her return?

18 y

A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a space ship which travels away from Earth at a speed of 0.6c for five years (as measured by Courtney), then turns around and comes back at 0.6c. When Andrea returns, Courtney is 20 years old. How old is Andrea upon her return?

18 years

The amount of energy equivalent to two kilogram of mass at rest is

18x10^16 J

If the velocity of your spaceship goes from 0.3 c to 0.6 c, then your mass will increase by

19%

Henry takes trip on a spaceship, traveling at a speed of 0.6c, while his 15-year-old twin, Albert, remains on Earth. According to Albert, Henry spends 3 year going to planet X. After reaching his destination, Henry turns around and comes back at the same speed. When Henry returns, Albert is 21 years old. How old is Henry?

19.8 y

A spaceship leaves Earth and travels at a speed of 0.6c for a period of 2.0 years as measured by its shipboard clock. How long was the flight as measured by a clock on Earth?

2.5 y

The closest star to our solar system is Alpha Centauri, which is 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the Earth travels toward the star. What distance does the space ship travel according to a passenger on the ship?

2.58 ly

The kinetic energy of a proton is 80% of its total energy. What is the momentum in kg.m/s of the proton?

2.5x10^-18 kg.m/s

What is the total energy of an electron moving with a speed of 0.95c?

2.6x10^-13 J

A boat can travel 4.0 m/s in still water. With what speed, relative to the shore, does it move in a river that is flowing at 1.0 m/s if the boat is heading upstream?

3.0 m/s

Suppose a proton and an anti-proton (a negative proton) come together and annihilate each other. How much energy is released? (The mass of each particle is 1.67x10^-27 kg)

3.0x10^-10 J

How much mass is lost during a reaction in which 1.7x10^8 MeV of energy is released?

3.0x10^-22 kg

The closest star to our solar system is Alpha Centauri, which is 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the Earth travels toward the star. How much time would elapse on a clock on board the spaceship?

3.23 y

What is the momentum in kg.m/s of a proton when it is moving with a speed of 0.60c?

3.8x10^-19 kg.m/s

A boat can travel 4.0 m/s in still water. With what speed, relative to the shore, does it move in a river that is flowing at 1.0 m/s if the boat is heading straight across the river?

4.1 m/s

During a reaction, an element loses 4.8x10^-28 kg of mass. How much energy (in joules) is released?

4.3x10^-11 J

A boat can travel 4.0 m/s in still water. With what speed, relative to the shore, does it move in a river that is flowing at 1.0 m/s if the boat is heading downstream?

5.0 m/s

The closest star to our solar system is Alpha Centauri, which is 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the Earth travels toward the star. How much time would elapse on a clock on the Earth?

5.38 y

One 20-year-old twin brother takes a space trip with a speed of 0.80c for 30 years according to a clock on the spaceship. Upon returning to the Earth, what is his own age and the age of the Earth-based twin brother?

50; 70

The length of a spaceship is 10 m when it is at rest. If the spaceship travels by you with a speed of 0.70c, what length does it appear to you?

7.1 m

How many joules of energy are required to accelerate one kilogram of mass from rest to a velocity of 0.866 c?

9.0x10^16 J

What energy is released (in MeV) during a reaction in which 1.67x10^-25 kg of material is converted to energy?

9.4x10^4 MeV

Two spaceships are traveling through space at 0.60 c relative to the Earth. If the ships are headed directly toward each other, what is their approach velocity, as measured by a person on either craft?

none of the answers given