Solutions Manual For Physics
For Scientists & Engineers
With Modern Physics
(Volume 3) 5e (Global Edition)
By Douglas C. Giancoli
,CHAPTER 36: The Special Theory Of Relativity
Responses To Questions
1. No. Since The Windowless Car In An Exceptionally Smooth Train Moving At A Constant
Velocity Is An
Inertial Reference Frame And The Basic Laws Of Physics Are The Same In All Inertial
Reference Frames, There Is No Way For You To Tell If You Are Moving Or Not. The First
Postulate Of The Special Theory Of Relativity Can Be Phrased As “No Experiment Can Tell
You If An Inertial Reference Frame Is At Rest Or Moving Uniformly At Constant Velocity.”
2. The Fact That You Instinctively Think You Are Moving Is Consistent With The Relativity
Principle Applied To Mechanics. Even Though You Are At Rest Relative To The Ground,
When The Car Next To You Creeps Forward, You Are Moving Backward Relative To That
Car.
3. Since The Railroad Car Is Traveling With A Constant Velocity, The Ball Will Land Back In
His Hand. Both The Ball And The Car Are Already Moving Forward (Relative To The
Ground), So When The Ball Is Thrown Straight Up Into The Air With Respect To The Car, It
Will Continue To Move Forward At The Same Rate As The Car And Fall Back Down To Land
In His Hand.
4. Whether You Say The Earth Goes Around The Sun Or The Sun Goes Around The Earth
Depends On Your Reference Frame. It Is Valid To Say Either One, Depending On Which
Frame You Choose. The Laws Of Physics, Though, Won’t Be The Same In Each Of These
Reference Frames, Since The Earth Is Accelerating As It Goes Around The Sun. The Sun Is
Nearly An Inertial Reference Frame, But The Earth Is Not.
5. The Starlight Would Pass At C, Regardless Of Your Spaceship’s Speed. This Is
Consistent With The Second Postulate Of Relativity, Which States That The Speed Of
Light Through Empty Space Is Independent Of The Speed Of The Source Or The
Observer.
6. The Clocks Are Not At Fault And They Are Functioning Properly. Time Itself Is Actually
Measured To Pass More Slowly In Moving Reference Frames When Compared To A Rest
Frame. Any Measurement Of Time (Heartbeats Or Decay Rates, For Instance) Would Be
Measured As Slower Than Normal When Viewed By An Observer Outside The Moving
Reference Frame.
7. Time Actually Passes More Slowly In The Moving Reference Frame, Including Aging And
Other Life Processes. It Is Not Just That It Seems This Way–Time Has Actually Been
Measured To Pass More Slowly In The Moving Reference Frame, As Predicted By Special
Relativity.
8. This Situation Is An Example Of The “Twin Paradox” Applied To Parent–Child Instead Of
To Twins. This Situation Would Be Possible If The Woman Was Traveling At High Enough
Speeds During Her Trip. Time Would Have Passed More Slowly For Her And She Would
Have Aged Less Than Her Son, Who Stayed On Earth. (Note That The Situations Of The
Woman And Son Are Not Symmetric; She Must Undergo Acceleration During Her Journey.)
9. You Would Not Notice A Change In Your Own Heartbeat, Mass, Height, Or Waistline. No
,Matter How Fast You Are Moving Relative To Earth, You Are At Rest In Your Own
Reference Frame. Thus, You Would Not Notice Any Changes In Your Own Characteristics.
To Observers On Earth, You Are Moving Away At 0.6c, Which Gives = 1.25. If We Assume
That You Are Standing Up, So That Your Body Is Perpendicular To The Direction Of Motion,
Then To The Observers On Earth, It Would Appear That Your Heartbeat Has Slowed By A
Factor Of 1/1.25 = 0.80 And That Your Waistline Has Decreased By A Factor Of 0.80 (Due To
Time Dilation And Length Contraction). Your Height Would Be Unchanged (Since There Is
No Relative Motion Between You And Earth In That Direction). Also Note The Comments In
Section 36–9 Of The Text On “Rest Mass
, Chapter 36 The Special Theory of Relativity
And Relativistic Mass” For Comments About Mass Change And Relativity. Your Actual Mass
Has Not Changed.
10. Yes, They Do Occur. However, At A Speed Of Only 90 C Is Extremely Small, And Therefore Γ
Km/Hr, V Is
Very Close To One, So The Effects Would Not Be
Noticeable.
11. Length Contraction And Time Dilation Would Not Occur. If The Speed Of Light Were
Infinite, V C Would Be 0 For All Finite Values Of V, And Therefore Γ Would Always Be 1,
Resulting In T T0 And L L 0.
2 2
12. Both The Length Contraction And Time Dilation Formulas Include The Term 1 V C . If C
Were Not
The Limiting Speed In The Universe, Then It Would Be Possible To Have A Situation With
V C. However, This Would Result In A Negative Number Under The Square Root, Which
Gives An Imaginary Number As A Result, Indicating That C Must Be The Limiting Speed.
Also, Assuming The Relativistic Formulas Were Still Correct, As V Gets Very Close To C,
An Outside Observer Should Be Able To Show That
L L 0 1 − v2 c2 Is Getting Smaller And Smaller And That The Limit As V C Is L 0.
This Would Show That C Is A Limiting Speed, Since Nothing Can Get
Smaller Than Having A Length Of 0. A Similar Analysis For Time Dilation Should Show
To
That T 1−Isv2Getting
c2 Longer And Longer And That The
Limit As V C Is T . This Would Show That C Is A Limiting Speed, Since The Slowest
That Time Can Pass Is That It Comes To A Stop.
13. If The Speed Of Light Was 25 M/S, Then We Would See Relativistic Effects All The Time,
Something Like The Chapter Opening Figure Or Figure 36–16 With Question 21. Everything
Moving Relative To Us Would Be Length Contracted And Time Dilation Would Have To Be
Taken Into Account For Many Events. There Would Be No “Absolute Time” On Which We
Would All Agree, So It Would Be More Difficult, For Instance, To Plan To Meet Friends For
Lunch At A Certain Time. Many “Twin Paradox” Kind Of Events Would Occur, And The
Momentum Of Moving Objects Would Become Very Large, Making It Very Difficult To
Change Their Motion. One Of The Most Unusual Changes For Today’s Modern Inhabitants Of
Earth Would Be That Nothing Would Be Able To Move Faster Than 25 M/S, Which Is Only
About 56 Mi/H.
Mv
14. No. The Relativistic Momentum Of The Electron Is Given By P Mv . At Low
Speeds 1 − v2 c2
(Compared To C) This Reduces To The Classical Momentum, P Mv. As V Approaches C, Γ
Approaches Infinity So There Is No Upper Limit To The Electron’s Momentum.
15. No. To Accelerate A Particle With Nonzero Rest Mass Up To The Speed Of Light Would
For Scientists & Engineers
With Modern Physics
(Volume 3) 5e (Global Edition)
By Douglas C. Giancoli
,CHAPTER 36: The Special Theory Of Relativity
Responses To Questions
1. No. Since The Windowless Car In An Exceptionally Smooth Train Moving At A Constant
Velocity Is An
Inertial Reference Frame And The Basic Laws Of Physics Are The Same In All Inertial
Reference Frames, There Is No Way For You To Tell If You Are Moving Or Not. The First
Postulate Of The Special Theory Of Relativity Can Be Phrased As “No Experiment Can Tell
You If An Inertial Reference Frame Is At Rest Or Moving Uniformly At Constant Velocity.”
2. The Fact That You Instinctively Think You Are Moving Is Consistent With The Relativity
Principle Applied To Mechanics. Even Though You Are At Rest Relative To The Ground,
When The Car Next To You Creeps Forward, You Are Moving Backward Relative To That
Car.
3. Since The Railroad Car Is Traveling With A Constant Velocity, The Ball Will Land Back In
His Hand. Both The Ball And The Car Are Already Moving Forward (Relative To The
Ground), So When The Ball Is Thrown Straight Up Into The Air With Respect To The Car, It
Will Continue To Move Forward At The Same Rate As The Car And Fall Back Down To Land
In His Hand.
4. Whether You Say The Earth Goes Around The Sun Or The Sun Goes Around The Earth
Depends On Your Reference Frame. It Is Valid To Say Either One, Depending On Which
Frame You Choose. The Laws Of Physics, Though, Won’t Be The Same In Each Of These
Reference Frames, Since The Earth Is Accelerating As It Goes Around The Sun. The Sun Is
Nearly An Inertial Reference Frame, But The Earth Is Not.
5. The Starlight Would Pass At C, Regardless Of Your Spaceship’s Speed. This Is
Consistent With The Second Postulate Of Relativity, Which States That The Speed Of
Light Through Empty Space Is Independent Of The Speed Of The Source Or The
Observer.
6. The Clocks Are Not At Fault And They Are Functioning Properly. Time Itself Is Actually
Measured To Pass More Slowly In Moving Reference Frames When Compared To A Rest
Frame. Any Measurement Of Time (Heartbeats Or Decay Rates, For Instance) Would Be
Measured As Slower Than Normal When Viewed By An Observer Outside The Moving
Reference Frame.
7. Time Actually Passes More Slowly In The Moving Reference Frame, Including Aging And
Other Life Processes. It Is Not Just That It Seems This Way–Time Has Actually Been
Measured To Pass More Slowly In The Moving Reference Frame, As Predicted By Special
Relativity.
8. This Situation Is An Example Of The “Twin Paradox” Applied To Parent–Child Instead Of
To Twins. This Situation Would Be Possible If The Woman Was Traveling At High Enough
Speeds During Her Trip. Time Would Have Passed More Slowly For Her And She Would
Have Aged Less Than Her Son, Who Stayed On Earth. (Note That The Situations Of The
Woman And Son Are Not Symmetric; She Must Undergo Acceleration During Her Journey.)
9. You Would Not Notice A Change In Your Own Heartbeat, Mass, Height, Or Waistline. No
,Matter How Fast You Are Moving Relative To Earth, You Are At Rest In Your Own
Reference Frame. Thus, You Would Not Notice Any Changes In Your Own Characteristics.
To Observers On Earth, You Are Moving Away At 0.6c, Which Gives = 1.25. If We Assume
That You Are Standing Up, So That Your Body Is Perpendicular To The Direction Of Motion,
Then To The Observers On Earth, It Would Appear That Your Heartbeat Has Slowed By A
Factor Of 1/1.25 = 0.80 And That Your Waistline Has Decreased By A Factor Of 0.80 (Due To
Time Dilation And Length Contraction). Your Height Would Be Unchanged (Since There Is
No Relative Motion Between You And Earth In That Direction). Also Note The Comments In
Section 36–9 Of The Text On “Rest Mass
, Chapter 36 The Special Theory of Relativity
And Relativistic Mass” For Comments About Mass Change And Relativity. Your Actual Mass
Has Not Changed.
10. Yes, They Do Occur. However, At A Speed Of Only 90 C Is Extremely Small, And Therefore Γ
Km/Hr, V Is
Very Close To One, So The Effects Would Not Be
Noticeable.
11. Length Contraction And Time Dilation Would Not Occur. If The Speed Of Light Were
Infinite, V C Would Be 0 For All Finite Values Of V, And Therefore Γ Would Always Be 1,
Resulting In T T0 And L L 0.
2 2
12. Both The Length Contraction And Time Dilation Formulas Include The Term 1 V C . If C
Were Not
The Limiting Speed In The Universe, Then It Would Be Possible To Have A Situation With
V C. However, This Would Result In A Negative Number Under The Square Root, Which
Gives An Imaginary Number As A Result, Indicating That C Must Be The Limiting Speed.
Also, Assuming The Relativistic Formulas Were Still Correct, As V Gets Very Close To C,
An Outside Observer Should Be Able To Show That
L L 0 1 − v2 c2 Is Getting Smaller And Smaller And That The Limit As V C Is L 0.
This Would Show That C Is A Limiting Speed, Since Nothing Can Get
Smaller Than Having A Length Of 0. A Similar Analysis For Time Dilation Should Show
To
That T 1−Isv2Getting
c2 Longer And Longer And That The
Limit As V C Is T . This Would Show That C Is A Limiting Speed, Since The Slowest
That Time Can Pass Is That It Comes To A Stop.
13. If The Speed Of Light Was 25 M/S, Then We Would See Relativistic Effects All The Time,
Something Like The Chapter Opening Figure Or Figure 36–16 With Question 21. Everything
Moving Relative To Us Would Be Length Contracted And Time Dilation Would Have To Be
Taken Into Account For Many Events. There Would Be No “Absolute Time” On Which We
Would All Agree, So It Would Be More Difficult, For Instance, To Plan To Meet Friends For
Lunch At A Certain Time. Many “Twin Paradox” Kind Of Events Would Occur, And The
Momentum Of Moving Objects Would Become Very Large, Making It Very Difficult To
Change Their Motion. One Of The Most Unusual Changes For Today’s Modern Inhabitants Of
Earth Would Be That Nothing Would Be Able To Move Faster Than 25 M/S, Which Is Only
About 56 Mi/H.
Mv
14. No. The Relativistic Momentum Of The Electron Is Given By P Mv . At Low
Speeds 1 − v2 c2
(Compared To C) This Reduces To The Classical Momentum, P Mv. As V Approaches C, Γ
Approaches Infinity So There Is No Upper Limit To The Electron’s Momentum.
15. No. To Accelerate A Particle With Nonzero Rest Mass Up To The Speed Of Light Would
