OpenStax College Physics Urone Solution Manual, Exercises of Physics

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CONTENTS

15.3 Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency

• Contents
• Preface
• Chapter 1: Introduction: The Nature of Science and Physics
  • 1.2 Physical Quantities and Units
  • 1.3 Accuracy, Precision, and Significant Figures
• Chapter 2: Kinematics
  • 2.1 Displacement
  • 2.3 Time, Velocity, and Speed
  • 2.5 Motion Equations for Constant Acceleration in One Dimension........................................
  • 2.7 Falling Objects
  • 2.8 Graphical Analysis of One-Dimensional Motion
• Chapter 3: Two-Dimensional Kinematics
  • 3.2 Vector Addition and Subtraction: Graphical Methods
  • 3.3 Vector Addition and Subtraction: Analytical Methods
  • 3.4 Projectile Motion
  • 3.5 Addition of Velocities
• Chapter 4: Dynamics: Force and Newton’s Laws of Motion
  • 4.3 Newton’s Second Law of Motion: Concept of a System
  • 4.6 Problem-Solving Strategies
  • 4.7 Further Applications of Newton’s Laws of Motion
• Chapter 5: Further Application of Newton’s Laws: Friction, Drag, and Elasticity
  • 5.1 Friction.................................................................................................................................
  • 5.3 Elasticity: Stress and Strain
• Chapter 6: Uniform Circular Motion and Gravitation
  • 6.1 Rotation Angle and Angular Velocity
  • 6.2 Centripetal Acceleration
  • 6.3 Centripetal Force
  • 6.5 Newton’s Universal Law of Gravitation
  • 6.6 Satellites and Kepler’s Laws: An Argument for Simplicity
• Chapter 7: Work, Energy, and Energy Resources
  • 7.1 Work: The Scientific Definition
  • 7.2 Kinetic Energy and the Work-Energy Theorem
  • 7.3 Gravitational Potential Energy
  • 7.7 Power
  • 7.8 Work, Energy, and Power in Humans
• Chapter 8: Linear Momentum and Collisions
  • 8.1 Linear Momentum and Force..............................................................................................
  • 8.2 Impulse
  • 8.3 Conservation of Momentum
  • 8.5 Inelastic Collisions in One Dimension
  • 8.6 Collisions of Point Masses in Two Dimensions
  • 8.7 Introduction to Rocket Propulsion
• Chapter 9: Statics and Torque
  • 9.2 The Second Condition for Equilibrium
  • 9.3 Stability
  • 9.6 Forces and Torques in Muscles and Joints
• Chapter 10: Rotational Motion and Angular Momentum
  • 10.1 Angular Acceleration
  • 10.3 Dynamics of Rotational Motion: Rotational Inertia
  • 10.4 Rotational Kinetic Energy: Work and Energy Revisited
  • 10.5 Angular Momentum and Its Conservation........................................................................
  • 10.6 Collisions of Extended Bodies in Two Dimensions
• Chapter 11: Fluid Statics
  • 11.2 Density
  • 11.3 Pressure
  • 11.4 Variation of Pressure with Depth in a Fluid
  • 11.5 Pascal’s Principle
  • 11.7 Archimedes’ Principle........................................................................................................
  • 11.8 Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action
  • 11.9 Pressures in the Body
• Chapter 12: Fluid Dynamics and Its Biological and Medical Applications
  • 12.1 Flow Rate and Its Relation to Velocity
  • 12.2 Bernoulli’s Equation
  • 12.3 The Most General Applications of Bernoulli’s Equation
  • 12.4 Viscosity and Laminar Flow; Poiseuille’s Law....................................................................
  • 12.5 The Onset of Turbulence
  • 12.7 Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes
• Chapter 13: Temperature, Kinetic Theory, and the Gas Laws
  • 13.1 Temperature
  • 13.2 Thermal Expansion of Solids and Liquids
  • 13.3 The Ideal Gas Law
  • 13.4 Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature
  • 13.6 Humidity, Evaporation, and Boiling
• Chapter 14: Heat and Heat Transfer Methods
  • 14.2 Temperature Change and Heat Capacity
  • 14.3 Phase Change and Latent Heat
  • 14.5 Conduction
  • 14.6 Convection.......................................................................................................................
  • 14.7 Radiation
• Chapter 15: Thermodynamics.....................................................................................................
  • 15.1 The First Law of Thermodynamics
  • 15.2 The First Law of Thermodynamics and Some Simple Processes.....................................
  • 15.5 Applications of Thermodynamics: Heat Pumps and Refrigerators
  • Energy 15.6 Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of
  • Underlying Explanation 15.7 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The
• Chapter 16: Oscillatory Motion and Waves
  • 16.1 Hooke’s Law: Stress and Strain Revisited........................................................................
  • 16.2 Period and Frequency in Oscillations
  • 16.3 Simple Harmonic Motion: A Special Periodic Motion
  • 16.4 The Simple Pendulum
  • 16.5 Energy and the Simple Harmonic Oscillator
  • 16.6 Uniform Circular Motion and Simple Harmonic Motion.................................................
  • 16.8 Forced Oscillations and Resonance.................................................................................
  • 16.9 Waves
  • 16.10 Superposition and Interference
  • 16.11 Energy in Waves: Intensity
• Chapter 17: Physics of Hearing
  • 17.2 Speed of Sound, Frequency, and Wavelength
  • 17.3 Sound Intensity and Sound Level
  • 17.4 Doppler Effect and Sonic Booms
  • 17.5 Sound Interference and Resonance: Standing Waves in Air Columns
  • 17.6 Hearing
  • 17.7 Ultrasound
• Chapter 18: Electric Charge and Electric Field
  • 18.1 Static Electricity and Charge: Conservation of Charge....................................................
  • 18.2 Conductors and Insulators
  • 18.3 Coulomb’s Law
  • 18.4 Electric Field: COncept of a Field Revisited
  • 18.5 Electric Field Lines: Multiple Charges..............................................................................
  • 18.7 Conductors and Electric Fields in Static Equilibrium
  • 18.8 Applications of Electrostatics
• Chapter 19: Electric Potential and Electric Field
  • 19.1 Electric Potential Energy: Potential Difference
  • 19.2 Electric Potential in a Uniform Electric Field
  • 19.3 Electric Potential Due to a Point Charge
  • 19.4 Equipotential Lines
  • 19.5 Capacitors and Dieletrics
  • 19.6 Capacitors in Series and Parallel
  • 19.7 Energy Stored in Capacitors
• Chapter 20: Electric Current, Resistance, and Ohm’s Law
  • 20.1 Current
  • 20.2 Ohm’s Law: Resistance and Simple Circuits
  • 20.3 Resistance and Resistivity
  • 20.4 Electric Power and Energy...............................................................................................
  • 20.5 Alternating Current versus Direct Current
  • 20.6 Electric Hazards and the Human Body
• Chapter 21: Circuits, Bioelectricity, and DC Instruments
  • 21.1 Resistors in Series and Parallel
  • 21.2 Electromotive Force: Terminal Voltage
  • 21.3 Kirchhoff’s Rules
  • 21.4 DC Voltmeters and Ammeters
  • 21.5 Null Measurements
  • 21.6 DC Circuits Containing Resistors and Capacitors
• Chapter 22: Magnetism
  • 22.4 Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field
  • 22.5 Force on a Moving Charge in a Magnetic Field: Examples and Applications
  • 22.6 The Hall Effect
  • 22.7 Magnetic Force on a Current-Carrying Conductor
  • 22.8 Torque on a Current Loop: Motors and Meters
  • 22.10 Magnetic Force between Two Parallel Conductors
  • 22.11 More Applications of Magnetism..................................................................................
• Chapter 23: Electromagnetic Induction, AC Circuits, and Electrical Technologies.....................
  • 23.1 Induced Emf and Magnetic Flux
  • 23.2 Faraday’s Law of Induction: Lenz’s Law
  • 23.3 Motional Emf
  • 23.4 Eddy Currents and Magnetic Damping
  • 23.5 Electric Generators
  • 23.6 Back Emf
  • 23.7 Transformers
  • 23.9 Inductance
  • 23.10 RL Circuits
  • 23.11 Reactance, Inductive and Capacitive
  • 23.12 RLC Series AC Circuits
• Chapter 24: Electromagnetic Waves
  • 24.1 Maxwell’s Equations: Electromagnetic Waves Predicted and Observed
  • 24.3 The Electromagnetic Spectrum
  • 24.4 Energy in Electromagnetic Waves
• Chapter 25: Geometric Optics
  • 25.1 The Ray Aspect of Light
  • 25.3 The Law of Refraction
  • 25.4 Total Internal Reflection..................................................................................................
  • 25.5 Dispersion: The Rainbow and Prisms
  • 25.6 Image Formation by Lenses
  • 25.7 Image Formation by Mirrors
• Chapter 26: Vision and Optical Instruments
  • 26.1 Physics of the Eye
  • 26.2 Vision Correction
  • 26.5 Telescopes
  • 26.6 Aberrations
• Chapter 27: Wave Optics
  • 27.1 The Wave Aspect of Light: Interference
  • 27.3 Young’s Double Slit Experiment
  • 27.4 Multiple Slit Diffraction
  • 27.5 Single Slit Diffraction
  • 27.6 Limits of Resolution: The Rayleigh Criterion
  • 27.7 Thin Film Interference
  • 27.8 Polarization......................................................................................................................
• Chapter 28: Special Relativity
  • 28.2 Simultaneity and Time Dilation
  • 28.3 Length Contraction
  • 28.4 Relativistic Addition of Velocities
  • 28.5 Relativistic Momentum
  • 28.6 Relativistic Energy
• Chapter 29: Introduction to Quantum Physics
  • 29.1 Quantization of Energy....................................................................................................
  • 29.2 The Photoelectric Effect
  • 29.3 Photon Energies and the Electromagnetic Spectrum
  • 29.4 Photon Momentum
  • 29.6 The Wave Nature of Matter
  • 29.7 Probability: The Heisenberg Uncertainty Principle
  • 29.8 The Particle-Wave Duality Reviewed
• Chapter 30: Atomic Physics
  • 30.1 Discovery of the Atom
  • 30.3 Bohr’s Theory of the Hydrogen Atom
  • 30.4 X Rays: Atomic Origins and Applications.........................................................................
  • 30.5 Applications of Atomic Excitations and De-Excitations
  • 30.8 Quantum Numbers and Rules
  • 30.9 The Pauli Exclusion Principle
• Chapter 31: Radioactivity and Nuclear Physics
  • 31.2 Radiation Detection and Detectors
  • 31.3 Substructure of the Nucleus
  • 31.4 Nuclear Decay and Conservation Laws
  • 31.5 Half-Life and Activity
  • 31.6 Binding Energy
  • 31.7 Tunneling
• Chapter 32: Medical Applications of Nuclear Physics
  • 32.1 Medical Imaging and Diagnostics
  • 32.2 Biological Effects of Ionizing Radiation
  • 32.3 Therapeutic Uses of Ionizing Radiation
  • 32.5 Fusion
  • 32.6 Fission
  • 32.7 Nuclear Weapons
• Chapter 33: Particle Physics
  • 33.2 The Four Basic Forces
  • 33.3 Accelerators Create Matter from Energy
  • 33.4 Particles, Patterns, and Conservation Laws
  • 33.5 Quarks: Is That All There Is?
  • 33.6 GUTS: The Unification of Forces......................................................................................
• Chapter 34: Frontiers of Physics
  • 34.1 Cosmology and Particle Physics

College Physics Student Solutions Manual Chapter 1

CHAPTER 1: INTRODUCTION: THE NATURE

OF SCIENCE AND PHYSICS

1.2 PHYSICAL QUANTITIES AND UNITS

4. American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)

Solution Since 3 feet = 1 yard and 3.281 feet = 1 meter, multiply 100 yards by these conversion factors to cancel the units of yards, leaving the units of meters:

91. 4 m 3.281ft

1 m 1 yd

100 yd= 100 yd×^3 ft× =

A football field is 91.4 m long.

10. (a) Refer to Table 1.3 to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?

Solution (a) The average speed of the earth’s orbit around the sun is calculated by dividing the distance traveled by the time it takes to go one revolution:

20 km/s 3600 s

1 h 24 h

1 d 365.25d

2 ( 10 km)

1 year

averagespeed^2 (averagedistofEarth tosun) 8 = × × =

=

π

π

The earth travels at an average speed of 20 km/s around the sun.

(b) To convert the average speed into units of m/s, use the conversion factor: 1000 m

College Physics Student Solutions Manual Chapter 1

= 1 km:

20 10 m/s 1 km

1000 m s

20 km average speed= × = ×^3

1.3 ACCURACY, PRECISION, AND SIGNIFICANT FIGURES

15. (a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?

Solution (a) To calculate the number of beats she has in 2.0 years, we need to multiply 72. beats/minute by 2.0 years and use conversion factors to cancel the units of time:

× × ×

1.00d

24.0 h 1.00 h

60.0 min 1 min

72.0 beats 2.0y 7.5738 10 beats 1.00y

365.25 d× = × 7

Since there are only 2 significant figures in 2.0 years, we must report the answer with 2 significant figures: 7.6 × 107 beats.

(b) Since we now have 3 significant figures in 2.00 years, we now report the answer with 3 significant figures: 7.57 × 107 beats.

(c) Even though we now have 4 significant figures in 2.000 years, the 72. beats/minute only has 3 significant figures, so we must report the answer with 3 significant figures: 7.57 × 107 beats.

21. A person measures his or her heart rate by counting the number of beats in 30 s_._ If 40 ± 1 beats are counted in 30. 0 ± 0. 5 s , what is the heart rate and its uncertainty in beats per minute?

Solution To calculate the heart rate, we need to divide the number of beats by the time and convert to beats per minute.

College Physics Student Solutions Manual Chapter 2

CHAPTER 2: KINEMATICS

2.1 DISPLACEMENT

1. Find the following for path A in Figure 2.59: (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.

Solution (a) The total distance traveled is the length of the line from the dot to the arrow in path A, or 7 m. (b) The distance from start to finish is the magnitude of the difference between the position of the arrows and the position of the dot in path A: ∆ x = x 2 − x 1 = 7 m− 0 m= 7 m

(c) The displacement is the difference between the value of the position of the arrow and the value of the position of the dot in path A: The displacement can be either positive or negative: ∆ x = x 2 − x 1 = 7 m− 0 m=+ 7 m

2.3 TIME, VELOCITY, AND SPEED

14. A football quarterback runs 15.0 m straight down the playing field in 2.50 s. He is then hit and pushed 3.00 m straight backward in 1.75 s. He breaks the tackle and runs straight forward another 21.0 m in 5.20 s. Calculate his average velocity (a) for each of the three intervals and (b) for the entire motion.

Solution (a) The average velocity for the first segment is the distance traveled downfield (the positive direction) divided by the time he traveled:

6.00m/s (forward) 2.50 s

15.0 m time

displaceme nt 1

_ = +

v = =

The average velocity for the second segment is the distance traveled (this time in the negative direction because he is traveling backward) divided by the time he

College Physics Student Solutions Manual Chapter 2

traveled: 1. 71 m/s(backward) 1.75 s

3.00 m 2

_ v =^ − = −

Finally, the average velocity for the third segment is the distance traveled (positive again because he is again traveling downfield) divided by the time he

traveled: 4. 04 m/s(forward) 5.20 s

21.0 m 3

_ = +

v =

(b) To calculate the average velocity for the entire motion, we add the displacement from each of the three segments (remembering the sign of the numbers), and divide by the total time for the motion:

3.49 m/s 2.50s 1.75s 5.20 s

15.0m 3.00m 21.0 m total

_ = +

v =

Notice that the average velocity for the entire motion is not just the addition of the average velocities for the segments.

15. The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit 1. 06 × 10 −^10 m in diameter. (a) If the average speed of the electron in this orbit is known to be 2. 20 × 106 m/s , calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron’s average velocity?

Solution (a) The average speed is defined as the total distance traveled divided by the elapsed

time, so that: 2. 20 10 m/s timeelapsed

average speed=distancetraveled= ×^6

If we want to find the number of revolutions per second, we need to know how far the electron travels in one revolution.

1 rev

3.33 10 m 1 rev

2 [(0.5)(1.06 10 m)] 1 rev

2 r revolution

distance traveled= π = π ×^ −^10 = × -

So to calculate the number of revolutions per second, we need to divide the average speed by the distance traveled per revolution, thus canceling the units of

College Physics Student Solutions Manual Chapter 2

Solution (a)

(b) Knowns: “Accelerated from rest”  v 0 = 0 m/s

“to 30.0 cm/s”  v =0.300m/s “in a distance of 1.80 cm”  x − x 0 = 0.0180m. (c) “How long” tells us to find t. To determine which equation to use, we look for an equation that has (^) v 0 (^) , v , x − x 0 and (^) t , since those are parameters that we know or

want to know. Using the equations x x vt

_ = 0 + and (^2) v^ ___^ = v^0 + v gives

x x v v  t 

− =^ +

0

Solving for t gives: (^) 0.120s (0m/s) (0.300m/s)

2 ( ) 2(0.0180m) 0

v v

x x t

It takes 120 ms to accelerate the blood from rest to 30.0 cm/s. Converting everything to standard units first makes it easy to see that the units of meters cancel, leaving only the units of seconds.

(d) Yes, the answer is reasonable. An entire heartbeat cycle takes about one second. The time for acceleration of blood out of the ventricle is only a fraction of the entire cycle.

College Physics Student Solutions Manual Chapter 2

32. Professional Application A woodpecker’s brain is specially protected from large decelerations by tendon-like attachments inside the skull. While pecking on a tree, the woodpecker’s head comes to a stop from an initial velocity of 0.600 m/s in a distance of only 2.00 mm. (a) Find the acceleration in m/s^2 and in multiples of g ( g = 9. 80 m/s^2 ). (b) Calculate the stopping time. (c) The tendons cradling the brain stretch, making its stopping distance 4.50 mm (greater than the head and, hence, less deceleration of the brain). What is the brain’s deceleration, expressed in multiples of g?

Solution (a) Find^ a^ (which should be negative).

Given: “comes to a stop”  v = 0 m/s.

“from an initial velocity of”  v 0 = 0. 600 m/s.

“in a distance of 2.00 m”  x − x 0 =2.00 × 10 -3m.

So, we need an equation that involves a , v , v 0 ,and x − x 0 ,or the equation

v^2 = v 02 + 2 a ( x − x 0 ), so that

2 3

2 2

0

2 0

2 90.0 m/s 2(2.00 10 m)

(0m/s) (0.600m/s) 2 ( )

×

x x

v v a

So the deceleration is 90. 0 m/s^2. To get the deceleration in multiples of g , we

divide a by g : 9.^18 9.. 9.80m/s

90.0 m/s 2

2 a g g

a = =  =

(b) The words “Calculate the stopping time” mean find t. Using (^) x x ( v v ) t 2

gives x x ( v v ) t 2

− 0 = 0 + , so that

6.67 10 s (0.600m/s) (0m/s)

2 ( ) 2(2.00 103 m) 3 0

0 − − = ×

= ×

v v

x x t

(c) To calculate the deceleration of the brain, use (^) x − x 0 = 4. 50 mm= 4. 50 × 10 −^3 m