Question 1

A proton, which has a mass of 1.67 × 10-27, is moving at 0.80c relative to the laboratory. What does a physicist in that lab measure for its momentum? (c = 3.0 × 108 m/s)

Accepted Answer

A)  4.0 × 10-19 kg ∙ m/s 
B)  4.4 × 10-19 kg ∙ m/s 
C)  5.0 × 10-19 kg ∙ m/s 
D)  5.8 × 10-19 kg ∙ m/s 
E)  6.7 × 10-19 kg ∙ m/s 
A)  4.0 × 10-19 kg ∙ m/s 
B)  4.4 × 10-19 kg ∙ m/s 
C)  5.0 × 10-19 kg ∙ m/s 
D)  5.8 × 10-19 kg ∙ m/s 
E)  6.7 × 10-19 kg ∙ m/s

Question 2

The figure shows a right-angled construction frame ABC. When measured at rest, it has dimensions as follows: AB = 18.9 m, AC = 10.0 m, and BC = 16.0 m. This frame is now given a new velocity of 0.420c, relative to Earth, in a direction parallel to AC. How long is part BC of this frame with the new velocity as measured by Earth-based engineers?

Accepted Answer

A)  16.0 m 
B)  14.0 m 
C)  12.0 m 
D)  10.0 m 
E)  18.0 m 
A)  16.0 m 
B)  14.0 m 
C)  12.0 m 
D)  10.0 m 
E)  18.0 m

Question 3

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 
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

Question 4

How fast must a meter stick move, relative to the frame of the observer making the measurement, so its length will be measured to be 0.60 m?

Accepted Answer

A)  0.40c 
B)  0.60c 
C)  0.70c 
D)  0.80c 
E)  0.90c 
A)  0.40c 
B)  0.60c 
C)  0.70c 
D)  0.80c 
E)  0.90c

Question 5

Astronaut Rachel leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth. Rachel's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year). According to Rachel, how long does the trip take?

Accepted Answer

A)  14 years 
B)  15 years 
C)  11 years 
D)  4.2 years 
E)  23 years 
A)  14 years 
B)  15 years 
C)  11 years 
D)  4.2 years 
E)  23 years

Question 6

When a proton is traveling at 0.80c, what is the ratio of its kinetic energy to its rest energy?

Accepted Answer

A)  0.60 
B)  0.67 
C)  0.80 
D)  1.2 
E)  1.7 
A)  0.60 
B)  0.67 
C)  0.80 
D)  1.2 
E)  1.7

Question 7

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 board the spaceship?

Accepted Answer

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

Question 8

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

Question 9

A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship that travels away from Earth at a speed of 0.60c for 10 years (as measured by Courtney). At the end of the trip, Courtney is 20 years old. How old is Andrea?

Accepted Answer

A)  10 years 
B)  12 years 
C)  18 years 
D)  20 years 
A)  10 years 
B)  12 years 
C)  18 years 
D)  20 years

Question 10

One of the first atomic bombs released energy equivalent to that of 20,000 tons of TNT explosive. How much mass was converted to energy by this explosion, given that 1000 tons of TNT produce 4.3 × 1012 J of energy. Incidentally, modern H-bombs have energy yields 1000 times as much! (c = 3.0 × 108 m/s)

Accepted Answer

Question 11

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

Question 12

An electron has a relativistic momentum of 1.1 × 10-21 kg ∙ m/s. What percent of its total energy is its kinetic energy? (melectron = 9.11 ×10-31 kg, c = 3.0 × 108 m/s)

Accepted Answer

Question 13

How much work must be done to accelerate a particle of mass $3.5 \times 10 ^{- 14 }\mathrm {~kg}$ from a speed of $1.2 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ to a speed of $1.9 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } ?$ (c = 3.0 × 108 m/s)

Accepted Answer

Question 14

Consider a student whose mass is 70 kg. If all his mass were converted to electrical energy, for how many years could he keep a 100-W light bulb burning? (c = 3.0 × 108 m/s)

Accepted Answer

6.3 × 10¹⁶ s

Question 15

Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space. One is traveling at 0.650c and the other at 0.850c. The satellites collide and somehow manage to stick together. What is the rest mass of the combined object after the collision?

Accepted Answer

A)  100 kg 
B)  200 kg 
C)  277 kg 
D)  378 kg 
E)  312 kg 
A)  100 kg 
B)  200 kg 
C)  277 kg 
D)  378 kg 
E)  312 kg

Question 16

An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took $4.26 \mathrm { y }$ How long does this journey appear to take to someone in the rest frame of the two stars?

Accepted Answer

A)  11.4 y 
B)  1.60 y 
C)  2.30 y 
D)  12.6 y 
A)  11.4 y 
B)  1.60 y 
C)  2.30 y 
D)  12.6 y

Question 17

A muon at rest decays in 2.2 μs. Moving at 99.00% the speed of light, it would be seen to "live" for how long?

Accepted Answer

The answer of A muon at rest decays in 2.2...

Question 18

The figure shows a right-angled construction frame ABC. When measured at rest, it has dimensions as follows: AB = 26.0 m, AC = 10.0 m, and BC = 24.0 m. This frame is now given a new velocity of 0.760c, relative to Earth, in a direction parallel to AC. How long is part AC of this frame with the new velocity as measured by Earth-based engineers?

Accepted Answer

A)  6.50 m 
B)  25.4 m 
C)  24.3 m 
D)  23.7 m 
E)  24.9 m 
A)  6.50 m 
B)  25.4 m 
C)  24.3 m 
D)  23.7 m 
E)  24.9 m

Question 19

As an electron slows down from 0.9980c to 0.5000c, how much momentum does it lose? (c = 3.0 × 108 m/s, melectron = 9.11 × 10-31 kg)

Accepted Answer

Question 20

How much energy would be released if 2.0 kg of material was lost during a reaction? (c = 3.0 × 108 m/s)

Accepted Answer

A)  1.8 × 1017 J 
B)  1.5 × 1016 J 
C)  6.0 × 108 J 
D)  4.7 × 10-8 J 
A)  1.8 × 1017 J 
B)  1.5 × 1016 J 
C)  6.0 × 108 J 
D)  4.7 × 10-8 J

Exam 27: Relativity

A proton, which has a mass of 1.67 × 10-27, is moving at 0.80c relative to the laboratory. What does a physicist in that lab measure for its momentum? (c = 3.0 × 108 m/s)

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?

How fast must a meter stick move, relative to the frame of the observer making the measurement, so its length will be measured to be 0.60 m?

Astronaut Rachel leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth. Rachel's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year). According to Rachel, how long does the trip take?

When a proton is traveling at 0.80c, what is the ratio of its kinetic energy to its rest energy?

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 board the spaceship?

The relativistic kinetic energy formula is valid

A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship that travels away from Earth at a speed of 0.60c for 10 years (as measured by Courtney). At the end of the trip, Courtney is 20 years old. How old is Andrea?

An electron has a relativistic momentum of 1.1 × 10-21 kg ∙ m/s. What percent of its total energy is its kinetic energy? (melectron = 9.11 ×10-31 kg, c = 3.0 × 108 m/s)

Consider a student whose mass is 70 kg. If all his mass were converted to electrical energy, for how many years could he keep a 100-W light bulb burning? (c = 3.0 × 108 m/s)

Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space. One is traveling at 0.650c and the other at 0.850c. The satellites collide and somehow manage to stick together. What is the rest mass of the combined object after the collision?

An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took 4.26y4.26 \mathrm { y }4.26y How long does this journey appear to take to someone in the rest frame of the two stars?

A muon at rest decays in 2.2 μs. Moving at 99.00% the speed of light, it would be seen to "live" for how long?

As an electron slows down from 0.9980c to 0.5000c, how much momentum does it lose? (c = 3.0 × 108 m/s, melectron = 9.11 × 10-31 kg)

How much energy would be released if 2.0 kg of material was lost during a reaction? (c = 3.0 × 108 m/s)

Representing Motion

Motion in One Dimension

Vectors and Motion in Two Dimensions

Forces and Newtons Laws of Motion

Applying Newtons Laws

Gravity

Rotational Motion

Equilibrium Ad Elasticity

Momentum

Energy and Work

Using Energy

Thermal Properties of Matter

Fluids

Oscillations

Traveling Waves and Sound

Superposition and Standing Waves

Wave Optics

Ray Optics

Optical Instruments

Electric Fields and Forces

Electric Potential

Current and Resistance

Circuits

Magnetic Fields and Forces

EM Induction and Em Waves

AC Electricity

Quantum Physics

Atoms and Molecules

Nuclear Physics

Filters

A proton, which has a mass of 1.67 × 10^-27, is moving at 0.80c relative to the laboratory. What does a physicist in that lab measure for its momentum? (c = 3.0 × 10⁸ m/s)

An electron has a relativistic momentum of 1.1 × 10^-21 kg ∙ m/s. What percent of its total energy is its kinetic energy? (m_electron = 9.11 ×10^-31 kg, c = 3.0 × 10⁸ m/s)

Consider a student whose mass is 70 kg. If all his mass were converted to electrical energy, for how many years could he keep a 100-W light bulb burning? (c = 3.0 × 10⁸ m/s)

An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took $4.26 \mathrm { y }$ How long does this journey appear to take to someone in the rest frame of the two stars?

As an electron slows down from 0.9980c to 0.5000c, how much momentum does it lose? (c = 3.0 × 10⁸ m/s, m_electron = 9.11 × 10^-31 kg)

How much energy would be released if 2.0 kg of material was lost during a reaction? (c = 3.0 × 10⁸ m/s)