Question 1

A spaceship,traveling at 0.100c away from a stationary space platform,launches a secondary rocket towards the station,with a speed of 0.560c relative to the spaceship.What is the speed of the secondary rocket relative to the space platform?

Accepted Answer

A) 0.460c 
B) 0.487c 
C) 0.492c 
D) 0.660c

Question 2

Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space.They have identical speeds of 0.600c.The satellites collide and somehow manage to stick together.What is the rest mass of the combined object after the collision?

Accepted Answer

A) 200 kg 
B) 225 kg 
C) 250 kg 
D) 275 kg 
E) 300 kg

Question 3

A satellite,initially at rest in deep space,separates into two pieces,which move away from each other.One piece has a rest mass of 190 kg and moves away with a speed 0.500c,and the second piece has a rest mass of 250 kg and moves in the opposite direction.What is the speed of the second piece?

Accepted Answer

A) 0.212c 
B) 0.380c 
C) 0.402c 
D) 0.473c 
E) 0.500c

Question 4

Two spaceships,each 100 m long in its own rest frame,approach Earth from opposite directions,each with a speed 0.50c relative to Earth.As measured by a passenger in one of the spaceships,how long is the other spaceship?

Accepted Answer

A) 50 m 
B) 60 m 
C) 70 m 
D) 80 m 
E) 90 m

Question 5

According to the equation E = mc2,an object turns into energy when it reaches the speed of light.

Accepted Answer

A) True 
 B)False

Question 6

How much energy would be required to accelerate a 77-kg professor from rest to 90% the speed of light? (c = 3.0 × 108 m/s)

Accepted Answer

A) 1.6 × 1019 J 
B) 2.1 × 1019 J 
C) 9.0 × 1019 J 
D) 2.8 × 1019 J 
E) 3.5 × 1019 J

Question 7

One of the first atomic explosion released approximately 1.0 × 1014 J of energy.How much matter had to be changed into energy to produce this yield? (c = 3.0 × 108 m/s)

Accepted Answer

A) 1.1 g 
B) 23 g 
C) 13 g 
D) 0.45 kg 
E) 1.1 kg

Question 8

A satellite with a rest mass of 200 kg and a speed of 0.800c and a second satellite with a rest mass of 100 kg and a speed of 0.600c are traveling toward each other in deep space.The satellites collide and somehow manage to stick together.What is the speed of the combined object after the collision?

Accepted Answer

A) 0.333c 
B) 0.374c 
C) 0.397c 
D) 0.418c 
E) 0.432c

Question 9

What is the total energy of an electron moving with a speed of 0.950c? (c = 3.0 × 108 m/s,mel = 9.11 × 10-31 kg)

Accepted Answer

A) 2.6 × 10-13 J 
B) 8.2 × 10-14 J 
C) 1.1 × 10-13 J 
D) 1.2 × 10-14 J

Question 10

Observer A sees a pendulum oscillating back and forth in a relativistic rocket and measures its period to be TA.Observer B moves along with the rocket and measures the period of the pendulum to be TB.What is true about these two time measurements?

Accepted Answer

A) TA > TB 
B) TA = TB 
C) TA B 
D) TA could be greater or smaller than TB depending on the direction of the motion.

Question 11

Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y,while an astronaut on the space ship says that the trip took 
What is the speed of the spaceship,assuming the planets are at essentially at rest?

Accepted Answer

A) 0.816 c 
B) 0.735 c 
C) 0.975 c 
D) 0.384 c

Question 12

A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth.How much time for this trip would elapse on a clock on Earth?

Accepted Answer

A) 3.23 y 
B) 4.40 y 
C) 5.15 y 
D) 5.38 y

Question 13

What is the momentum of a proton when it is moving with a speed of 0.60c? (mproton = 1.67 × 10-27 kg)

Accepted Answer

A) 1.2 × 10-19 kg∙ m/s 
B) 1.5 × 10-19 kg ∙ m/s 
C) 3.0 × 10-19 kg ∙ m/s 
D) 3.8 × 10-19 kg ∙ m/s

Question 14

As measured in Earth's rest frame,a spaceship traveling at 0.9640c takes 
To travel between two planets that are not moving relative to each other.How long does the trip take as measured by someone on the spaceship?

Accepted Answer

A) 2.79 y 
B) 6.83 y 
C) 39.5 y 
D) 28.8 y

Question 15

The relativistic kinetic energy formula is valid

Accepted Answer

A) only for speeds near the speed of light. 
B) at all speeds. 
C) only for subatomic particles,such as electrons and protons.

Question 16

Two stars are at rest relative to each other.In their common rest frame,these stars are 90.0 light-years apart.If they are measured to be 
Apart by the navigator of a spaceship traveling between them,how fast is the spaceship moving relative to these stars?

Accepted Answer

A) 0.646c 
B) 0.604c 
C) 0.558c 
D) 0.505c

Question 17

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

Accepted Answer

A) 0.94c 
B) 0.23c 
C) 2.2c 
D) 0.54c 
E) 1.3c

Question 18

If,instead of the correct formula for kinetic energy,we carelessly use the classical expression for kinetic energy for a particle moving at half the speed of light,by what magnitude percent will our calculation be in error? (c = 3.0 × 108 m/s)

Accepted Answer

A) 24% 
B) 19% 
C) 27% 
D) 7% 
E) 1%

Question 19

One 20-year-old twin brother takes a space trip with a speed of 0.80c for 30 years according to a clock on his spaceship.At the end of this trip,what are (a)his own age and (b)the age of his Earth-based twin brother?

Accepted Answer

A) (a)20 y (b)30 y 
B) (a)30 y (b)50 y 
C) (a)50 y (b)70 y 
D) (a)70 y (b)90 y

Question 20

A spaceship approaches Earth with a speed 0.50c.A passenger in the spaceship measures his heartbeat as 70 beats per minute.What is his heartbeat rate according to an observer that is at rest relative to Earth?

Accepted Answer

A) 61 beats per minute 
B) 65 beats per minute 
C) 69 beats per minute 
D) 73 beats per minute 
E) 75 beats per minute

Exam 29: Relativity

A spaceship,traveling at 0.100c away from a stationary space platform,launches a secondary rocket towards the station,with a speed of 0.560c relative to the spaceship.What is the speed of the secondary rocket relative to the space platform?

Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space.They have identical speeds of 0.600c.The satellites collide and somehow manage to stick together.What is the rest mass of the combined object after the collision?

A satellite,initially at rest in deep space,separates into two pieces,which move away from each other.One piece has a rest mass of 190 kg and moves away with a speed 0.500c,and the second piece has a rest mass of 250 kg and moves in the opposite direction.What is the speed of the second piece?

Two spaceships,each 100 m long in its own rest frame,approach Earth from opposite directions,each with a speed 0.50c relative to Earth.As measured by a passenger in one of the spaceships,how long is the other spaceship?

According to the equation E = mc²,an object turns into energy when it reaches the speed of light.

How much energy would be required to accelerate a 77-kg professor from rest to 90% the speed of light? (c = 3.0 × 10⁸ m/s)

One of the first atomic explosion released approximately 1.0 × 10¹⁴ J of energy.How much matter had to be changed into energy to produce this yield? (c = 3.0 × 10⁸ m/s)

A satellite with a rest mass of 200 kg and a speed of 0.800c and a second satellite with a rest mass of 100 kg and a speed of 0.600c are traveling toward each other in deep space.The satellites collide and somehow manage to stick together.What is the speed of the combined object after the collision?

What is the total energy of an electron moving with a speed of 0.950c? (c = 3.0 × 10⁸ m/s,m_el = 9.11 × 10^-31 kg)

Observer A sees a pendulum oscillating back and forth in a relativistic rocket and measures its period to be T_A.Observer B moves along with the rocket and measures the period of the pendulum to be T_B.What is true about these two time measurements?

Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y,while an astronaut on the space ship says that the trip took What is the speed of the spaceship,assuming the planets are at essentially at rest?

A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth.How much time for this trip would elapse on a clock on Earth?

What is the momentum of a proton when it is moving with a speed of 0.60c? (m_proton = 1.67 × 10^-27 kg)

As measured in Earth's rest frame,a spaceship traveling at 0.9640c takes To travel between two planets that are not moving relative to each other.How long does the trip take as measured by someone on the spaceship?

The relativistic kinetic energy formula is valid

Two stars are at rest relative to each other.In their common rest frame,these stars are 90.0 light-years apart.If they are measured to be Apart by the navigator of a spaceship traveling between them,how fast is the spaceship moving relative to these stars?

If,instead of the correct formula for kinetic energy,we carelessly use the classical expression for kinetic energy for a particle moving at half the speed of light,by what magnitude percent will our calculation be in error? (c = 3.0 × 10⁸ m/s)

One 20-year-old twin brother takes a space trip with a speed of 0.80c for 30 years according to a clock on his spaceship.At the end of this trip,what are (a) his own age and (b) the age of his Earth-based twin brother?

A spaceship approaches Earth with a speed 0.50c.A passenger in the spaceship measures his heartbeat as 70 beats per minute.What is his heartbeat rate according to an observer that is at rest relative to Earth?