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College Physics for AP® Courses

Chapter 11

College Physics for AP® CoursesChapter 11

Table of contents
  1. Preface
  2. 1 Introduction: The Nature of Science and Physics
    1. Connection for AP® Courses
    2. 1.1 Physics: An Introduction
    3. 1.2 Physical Quantities and Units
    4. 1.3 Accuracy, Precision, and Significant Figures
    5. 1.4 Approximation
    6. Glossary
    7. Section Summary
    8. Conceptual Questions
    9. Problems & Exercises
  3. 2 Kinematics
    1. Connection for AP® Courses
    2. 2.1 Displacement
    3. 2.2 Vectors, Scalars, and Coordinate Systems
    4. 2.3 Time, Velocity, and Speed
    5. 2.4 Acceleration
    6. 2.5 Motion Equations for Constant Acceleration in One Dimension
    7. 2.6 Problem-Solving Basics for One Dimensional Kinematics
    8. 2.7 Falling Objects
    9. 2.8 Graphical Analysis of One Dimensional Motion
    10. Glossary
    11. Section Summary
    12. Conceptual Questions
    13. Problems & Exercises
    14. Test Prep for AP® Courses
  4. 3 Two-Dimensional Kinematics
    1. Connection for AP® Courses
    2. 3.1 Kinematics in Two Dimensions: An Introduction
    3. 3.2 Vector Addition and Subtraction: Graphical Methods
    4. 3.3 Vector Addition and Subtraction: Analytical Methods
    5. 3.4 Projectile Motion
    6. 3.5 Addition of Velocities
    7. Glossary
    8. Section Summary
    9. Conceptual Questions
    10. Problems & Exercises
    11. Test Prep for AP® Courses
  5. 4 Dynamics: Force and Newton's Laws of Motion
    1. Connection for AP® Courses
    2. 4.1 Development of Force Concept
    3. 4.2 Newton's First Law of Motion: Inertia
    4. 4.3 Newton's Second Law of Motion: Concept of a System
    5. 4.4 Newton's Third Law of Motion: Symmetry in Forces
    6. 4.5 Normal, Tension, and Other Examples of Force
    7. 4.6 Problem-Solving Strategies
    8. 4.7 Further Applications of Newton's Laws of Motion
    9. 4.8 Extended Topic: The Four Basic Forces—An Introduction
    10. Glossary
    11. Section Summary
    12. Conceptual Questions
    13. Problems & Exercises
    14. Test Prep for AP® Courses
  6. 5 Further Applications of Newton's Laws: Friction, Drag, and Elasticity
    1. Connection for AP® Courses
    2. 5.1 Friction
    3. 5.2 Drag Forces
    4. 5.3 Elasticity: Stress and Strain
    5. Glossary
    6. Section Summary
    7. Conceptual Questions
    8. Problems & Exercises
    9. Test Prep for AP® Courses
  7. 6 Gravitation and Uniform Circular Motion
    1. Connection for AP® Courses
    2. 6.1 Rotation Angle and Angular Velocity
    3. 6.2 Centripetal Acceleration
    4. 6.3 Centripetal Force
    5. 6.4 Fictitious Forces and Non-inertial Frames: The Coriolis Force
    6. 6.5 Newton's Universal Law of Gravitation
    7. 6.6 Satellites and Kepler's Laws: An Argument for Simplicity
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  8. 7 Work, Energy, and Energy Resources
    1. Connection for AP® Courses
    2. 7.1 Work: The Scientific Definition
    3. 7.2 Kinetic Energy and the Work-Energy Theorem
    4. 7.3 Gravitational Potential Energy
    5. 7.4 Conservative Forces and Potential Energy
    6. 7.5 Nonconservative Forces
    7. 7.6 Conservation of Energy
    8. 7.7 Power
    9. 7.8 Work, Energy, and Power in Humans
    10. 7.9 World Energy Use
    11. Glossary
    12. Section Summary
    13. Conceptual Questions
    14. Problems & Exercises
    15. Test Prep for AP® Courses
  9. 8 Linear Momentum and Collisions
    1. Connection for AP® courses
    2. 8.1 Linear Momentum and Force
    3. 8.2 Impulse
    4. 8.3 Conservation of Momentum
    5. 8.4 Elastic Collisions in One Dimension
    6. 8.5 Inelastic Collisions in One Dimension
    7. 8.6 Collisions of Point Masses in Two Dimensions
    8. 8.7 Introduction to Rocket Propulsion
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  10. 9 Statics and Torque
    1. Connection for AP® Courses
    2. 9.1 The First Condition for Equilibrium
    3. 9.2 The Second Condition for Equilibrium
    4. 9.3 Stability
    5. 9.4 Applications of Statics, Including Problem-Solving Strategies
    6. 9.5 Simple Machines
    7. 9.6 Forces and Torques in Muscles and Joints
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  11. 10 Rotational Motion and Angular Momentum
    1. Connection for AP® Courses
    2. 10.1 Angular Acceleration
    3. 10.2 Kinematics of Rotational Motion
    4. 10.3 Dynamics of Rotational Motion: Rotational Inertia
    5. 10.4 Rotational Kinetic Energy: Work and Energy Revisited
    6. 10.5 Angular Momentum and Its Conservation
    7. 10.6 Collisions of Extended Bodies in Two Dimensions
    8. 10.7 Gyroscopic Effects: Vector Aspects of Angular Momentum
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  12. 11 Fluid Statics
    1. Connection for AP® Courses
    2. 11.1 What Is a Fluid?
    3. 11.2 Density
    4. 11.3 Pressure
    5. 11.4 Variation of Pressure with Depth in a Fluid
    6. 11.5 Pascal’s Principle
    7. 11.6 Gauge Pressure, Absolute Pressure, and Pressure Measurement
    8. 11.7 Archimedes’ Principle
    9. 11.8 Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action
    10. 11.9 Pressures in the Body
    11. Glossary
    12. Section Summary
    13. Conceptual Questions
    14. Problems & Exercises
    15. Test Prep for AP® Courses
  13. 12 Fluid Dynamics and Its Biological and Medical Applications
    1. Connection for AP® Courses
    2. 12.1 Flow Rate and Its Relation to Velocity
    3. 12.2 Bernoulli’s Equation
    4. 12.3 The Most General Applications of Bernoulli’s Equation
    5. 12.4 Viscosity and Laminar Flow; Poiseuille’s Law
    6. 12.5 The Onset of Turbulence
    7. 12.6 Motion of an Object in a Viscous Fluid
    8. 12.7 Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  14. 13 Temperature, Kinetic Theory, and the Gas Laws
    1. Connection for AP® Courses
    2. 13.1 Temperature
    3. 13.2 Thermal Expansion of Solids and Liquids
    4. 13.3 The Ideal Gas Law
    5. 13.4 Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature
    6. 13.5 Phase Changes
    7. 13.6 Humidity, Evaporation, and Boiling
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  15. 14 Heat and Heat Transfer Methods
    1. Connection for AP® Courses
    2. 14.1 Heat
    3. 14.2 Temperature Change and Heat Capacity
    4. 14.3 Phase Change and Latent Heat
    5. 14.4 Heat Transfer Methods
    6. 14.5 Conduction
    7. 14.6 Convection
    8. 14.7 Radiation
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  16. 15 Thermodynamics
    1. Connection for AP® Courses
    2. 15.1 The First Law of Thermodynamics
    3. 15.2 The First Law of Thermodynamics and Some Simple Processes
    4. 15.3 Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency
    5. 15.4 Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated
    6. 15.5 Applications of Thermodynamics: Heat Pumps and Refrigerators
    7. 15.6 Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy
    8. 15.7 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  17. 16 Oscillatory Motion and Waves
    1. Connection for AP® Courses
    2. 16.1 Hooke’s Law: Stress and Strain Revisited
    3. 16.2 Period and Frequency in Oscillations
    4. 16.3 Simple Harmonic Motion: A Special Periodic Motion
    5. 16.4 The Simple Pendulum
    6. 16.5 Energy and the Simple Harmonic Oscillator
    7. 16.6 Uniform Circular Motion and Simple Harmonic Motion
    8. 16.7 Damped Harmonic Motion
    9. 16.8 Forced Oscillations and Resonance
    10. 16.9 Waves
    11. 16.10 Superposition and Interference
    12. 16.11 Energy in Waves: Intensity
    13. Glossary
    14. Section Summary
    15. Conceptual Questions
    16. Problems & Exercises
    17. Test Prep for AP® Courses
  18. 17 Physics of Hearing
    1. Connection for AP® Courses
    2. 17.1 Sound
    3. 17.2 Speed of Sound, Frequency, and Wavelength
    4. 17.3 Sound Intensity and Sound Level
    5. 17.4 Doppler Effect and Sonic Booms
    6. 17.5 Sound Interference and Resonance: Standing Waves in Air Columns
    7. 17.6 Hearing
    8. 17.7 Ultrasound
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  19. 18 Electric Charge and Electric Field
    1. Connection for AP® Courses
    2. 18.1 Static Electricity and Charge: Conservation of Charge
    3. 18.2 Conductors and Insulators
    4. 18.3 Conductors and Electric Fields in Static Equilibrium
    5. 18.4 Coulomb’s Law
    6. 18.5 Electric Field: Concept of a Field Revisited
    7. 18.6 Electric Field Lines: Multiple Charges
    8. 18.7 Electric Forces in Biology
    9. 18.8 Applications of Electrostatics
    10. Glossary
    11. Section Summary
    12. Conceptual Questions
    13. Problems & Exercises
    14. Test Prep for AP® Courses
  20. 19 Electric Potential and Electric Field
    1. Connection for AP® Courses
    2. 19.1 Electric Potential Energy: Potential Difference
    3. 19.2 Electric Potential in a Uniform Electric Field
    4. 19.3 Electrical Potential Due to a Point Charge
    5. 19.4 Equipotential Lines
    6. 19.5 Capacitors and Dielectrics
    7. 19.6 Capacitors in Series and Parallel
    8. 19.7 Energy Stored in Capacitors
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  21. 20 Electric Current, Resistance, and Ohm's Law
    1. Connection for AP® Courses
    2. 20.1 Current
    3. 20.2 Ohm’s Law: Resistance and Simple Circuits
    4. 20.3 Resistance and Resistivity
    5. 20.4 Electric Power and Energy
    6. 20.5 Alternating Current versus Direct Current
    7. 20.6 Electric Hazards and the Human Body
    8. 20.7 Nerve Conduction–Electrocardiograms
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  22. 21 Circuits, Bioelectricity, and DC Instruments
    1. Connection for AP® Courses
    2. 21.1 Resistors in Series and Parallel
    3. 21.2 Electromotive Force: Terminal Voltage
    4. 21.3 Kirchhoff’s Rules
    5. 21.4 DC Voltmeters and Ammeters
    6. 21.5 Null Measurements
    7. 21.6 DC Circuits Containing Resistors and Capacitors
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  23. 22 Magnetism
    1. Connection for AP® Courses
    2. 22.1 Magnets
    3. 22.2 Ferromagnets and Electromagnets
    4. 22.3 Magnetic Fields and Magnetic Field Lines
    5. 22.4 Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field
    6. 22.5 Force on a Moving Charge in a Magnetic Field: Examples and Applications
    7. 22.6 The Hall Effect
    8. 22.7 Magnetic Force on a Current-Carrying Conductor
    9. 22.8 Torque on a Current Loop: Motors and Meters
    10. 22.9 Magnetic Fields Produced by Currents: Ampere’s Law
    11. 22.10 Magnetic Force between Two Parallel Conductors
    12. 22.11 More Applications of Magnetism
    13. Glossary
    14. Section Summary
    15. Conceptual Questions
    16. Problems & Exercises
    17. Test Prep for AP® Courses
  24. 23 Electromagnetic Induction, AC Circuits, and Electrical Technologies
    1. Connection for AP® Courses
    2. 23.1 Induced Emf and Magnetic Flux
    3. 23.2 Faraday’s Law of Induction: Lenz’s Law
    4. 23.3 Motional Emf
    5. 23.4 Eddy Currents and Magnetic Damping
    6. 23.5 Electric Generators
    7. 23.6 Back Emf
    8. 23.7 Transformers
    9. 23.8 Electrical Safety: Systems and Devices
    10. 23.9 Inductance
    11. 23.10 RL Circuits
    12. 23.11 Reactance, Inductive and Capacitive
    13. 23.12 RLC Series AC Circuits
    14. Glossary
    15. Section Summary
    16. Conceptual Questions
    17. Problems & Exercises
    18. Test Prep for AP® Courses
  25. 24 Electromagnetic Waves
    1. Connection for AP® Courses
    2. 24.1 Maxwell’s Equations: Electromagnetic Waves Predicted and Observed
    3. 24.2 Production of Electromagnetic Waves
    4. 24.3 The Electromagnetic Spectrum
    5. 24.4 Energy in Electromagnetic Waves
    6. Glossary
    7. Section Summary
    8. Conceptual Questions
    9. Problems & Exercises
    10. Test Prep for AP® Courses
  26. 25 Geometric Optics
    1. Connection for AP® Courses
    2. 25.1 The Ray Aspect of Light
    3. 25.2 The Law of Reflection
    4. 25.3 The Law of Refraction
    5. 25.4 Total Internal Reflection
    6. 25.5 Dispersion: The Rainbow and Prisms
    7. 25.6 Image Formation by Lenses
    8. 25.7 Image Formation by Mirrors
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  27. 26 Vision and Optical Instruments
    1. Connection for AP® Courses
    2. 26.1 Physics of the Eye
    3. 26.2 Vision Correction
    4. 26.3 Color and Color Vision
    5. 26.4 Microscopes
    6. 26.5 Telescopes
    7. 26.6 Aberrations
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  28. 27 Wave Optics
    1. Connection for AP® Courses
    2. 27.1 The Wave Aspect of Light: Interference
    3. 27.2 Huygens's Principle: Diffraction
    4. 27.3 Young’s Double Slit Experiment
    5. 27.4 Multiple Slit Diffraction
    6. 27.5 Single Slit Diffraction
    7. 27.6 Limits of Resolution: The Rayleigh Criterion
    8. 27.7 Thin Film Interference
    9. 27.8 Polarization
    10. 27.9 *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light
    11. Glossary
    12. Section Summary
    13. Conceptual Questions
    14. Problems & Exercises
    15. Test Prep for AP® Courses
  29. 28 Special Relativity
    1. Connection for AP® Courses
    2. 28.1 Einstein’s Postulates
    3. 28.2 Simultaneity And Time Dilation
    4. 28.3 Length Contraction
    5. 28.4 Relativistic Addition of Velocities
    6. 28.5 Relativistic Momentum
    7. 28.6 Relativistic Energy
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  30. 29 Introduction to Quantum Physics
    1. Connection for AP® Courses
    2. 29.1 Quantization of Energy
    3. 29.2 The Photoelectric Effect
    4. 29.3 Photon Energies and the Electromagnetic Spectrum
    5. 29.4 Photon Momentum
    6. 29.5 The Particle-Wave Duality
    7. 29.6 The Wave Nature of Matter
    8. 29.7 Probability: The Heisenberg Uncertainty Principle
    9. 29.8 The Particle-Wave Duality Reviewed
    10. Glossary
    11. Section Summary
    12. Conceptual Questions
    13. Problems & Exercises
    14. Test Prep for AP® Courses
  31. 30 Atomic Physics
    1. Connection for AP® Courses
    2. 30.1 Discovery of the Atom
    3. 30.2 Discovery of the Parts of the Atom: Electrons and Nuclei
    4. 30.3 Bohr’s Theory of the Hydrogen Atom
    5. 30.4 X Rays: Atomic Origins and Applications
    6. 30.5 Applications of Atomic Excitations and De-Excitations
    7. 30.6 The Wave Nature of Matter Causes Quantization
    8. 30.7 Patterns in Spectra Reveal More Quantization
    9. 30.8 Quantum Numbers and Rules
    10. 30.9 The Pauli Exclusion Principle
    11. Glossary
    12. Section Summary
    13. Conceptual Questions
    14. Problems & Exercises
    15. Test Prep for AP® Courses
  32. 31 Radioactivity and Nuclear Physics
    1. Connection for AP® Courses
    2. 31.1 Nuclear Radioactivity
    3. 31.2 Radiation Detection and Detectors
    4. 31.3 Substructure of the Nucleus
    5. 31.4 Nuclear Decay and Conservation Laws
    6. 31.5 Half-Life and Activity
    7. 31.6 Binding Energy
    8. 31.7 Tunneling
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  33. 32 Medical Applications of Nuclear Physics
    1. Connection for AP® Courses
    2. 32.1 Medical Imaging and Diagnostics
    3. 32.2 Biological Effects of Ionizing Radiation
    4. 32.3 Therapeutic Uses of Ionizing Radiation
    5. 32.4 Food Irradiation
    6. 32.5 Fusion
    7. 32.6 Fission
    8. 32.7 Nuclear Weapons
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
    13. Test Prep for AP® Courses
  34. 33 Particle Physics
    1. Connection for AP® Courses
    2. 33.1 The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited
    3. 33.2 The Four Basic Forces
    4. 33.3 Accelerators Create Matter from Energy
    5. 33.4 Particles, Patterns, and Conservation Laws
    6. 33.5 Quarks: Is That All There Is?
    7. 33.6 GUTs: The Unification of Forces
    8. Glossary
    9. Section Summary
    10. Conceptual Questions
    11. Problems & Exercises
    12. Test Prep for AP® Courses
  35. 34 Frontiers of Physics
    1. Connection for AP® Courses
    2. 34.1 Cosmology and Particle Physics
    3. 34.2 General Relativity and Quantum Gravity
    4. 34.3 Superstrings
    5. 34.4 Dark Matter and Closure
    6. 34.5 Complexity and Chaos
    7. 34.6 High-Temperature Superconductors
    8. 34.7 Some Questions We Know to Ask
    9. Glossary
    10. Section Summary
    11. Conceptual Questions
    12. Problems & Exercises
  36. A | Atomic Masses
  37. B | Selected Radioactive Isotopes
  38. C | Useful Information
  39. D | Glossary of Key Symbols and Notation
  40. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
    14. Chapter 14
    15. Chapter 15
    16. Chapter 16
    17. Chapter 17
    18. Chapter 18
    19. Chapter 19
    20. Chapter 20
    21. Chapter 21
    22. Chapter 22
    23. Chapter 23
    24. Chapter 24
    25. Chapter 25
    26. Chapter 26
    27. Chapter 27
    28. Chapter 28
    29. Chapter 29
    30. Chapter 30
    31. Chapter 31
    32. Chapter 32
    33. Chapter 33
    34. Chapter 34
  41. Index

Problems & Exercises

1.

1 . 610 cm 3 1 . 610 cm 3 size 12{1 "." "610"`"cm" rSup { size 8{3} } } {}

3.

(a) 2.58 g

(b) The volume of your body increases by the volume of air you inhale. The average density of your body decreases when you take a deep breath, because the density of air is substantially smaller than the average density of the body before you took the deep breath.

4.

2 . 70 g/cm 3 2 . 70 g/cm 3 size 12{2 "." "70"`"g/cm" rSup { size 8{3} } } {}

6.

(a) 0.163 m

(b) Equivalent to 19.4 gallons, which is reasonable

8.

7 . 9 × 10 2 kg/m 3 7 . 9 × 10 2 kg/m 3 size 12{7 "." 9 times "10" rSup { size 8{2} } `"kg/m" rSup { size 8{3} } } {}

9.

15.8 g/cm 3 15.8 g/cm 3 size 12{"15" "." 6`"g/cm" rSup { size 8{3} } } {}

10.

(a) 1018kg/m31018kg/m3 size 12{"10" rSup { size 8{"18"} } `"kg/m" rSup { size 8{3} } } {}

(b) 2×104m2×104m size 12{2 times "10" rSup { size 8{4} } `m} {}

11.

3.59×106Pa3.59×106Pa; or 521 lb/in 2 521 lb/in 2 size 12{"521"`"lb/in" rSup { size 8{2} } } {}

13.

2.36 × 10 3 N 2.36 × 10 3 N size 12{2 "." "36" times "10" rSup { size 8{3} } `N} {}

14.

0.760 m

16.

hρ g units = ( m ) kg/m 3 m/s 2 = kg m 2 / m 3 s 2 = kg m/s 2 1/m 2 = N/m 2 hρ g units = ( m ) kg/m 3 m/s 2 = kg m 2 / m 3 s 2 = kg m/s 2 1/m 2 = N/m 2

18.

(a) 20.5 mm Hg

(b) The range of pressures in the eye is 12–24 mm Hg, so the result in part (a) is within that range

20.

1 . 09 × 10 3 N/m 2 1 . 09 × 10 3 N/m 2 size 12{1 "." "09" times "10" rSup { size 8{3} } `"N/m" rSup { size 8{2} } } {}

22.

24.0 N

24.

2.55×107Pa2.55×107Pa; or 251 atm

26.

5.76×103N5.76×103N size 12{5 "." "76" times "10" rSup { size 8{3} } `N} {} extra force

28.

(a) V = d i A i = d o A o d o = d i A i A o . V = d i A i = d o A o d o = d i A i A o . size 12{ V=d rSub { size 8{i} } A rSub { size 8{i} } =d rSub { size 8{o} } A rSub { size 8{o} } drarrow d rSub { size 8{o} } =d rSub { size 8{i} } left ( { {A rSub { size 8{i} } } over {A rSub { size 8{o} } } } right ) "." } {}

Now, using equation:

F 1 A 1 = F 2 A 2 F o = F i A o A i . F 1 A 1 = F 2 A 2 F o = F i A o A i . size 12{ { {F rSub { size 8{1} } } over {A rSub { size 8{1} } } } = { {F rSub { size 8{2} } } over {A rSub { size 8{2} } } } drarrow F rSub { size 8{o} } =F rSub { size 8{i} } left ( { {A rSub { size 8{o} } } over {A rSub { size 8{i} } } } right ) "." } {}

Finally,

W o = F o d o = F i A o A i d i A i A o = F i d i = W i . W o = F o d o = F i A o A i d i A i A o = F i d i = W i . size 12{W rSub { size 8{o} } =F rSub { size 8{o} } d rSub { size 8{o} } = left ( { {F rSub { size 8{i} } A rSub { size 8{o} } } over {A rSub { size 8{i} } } } right ) left ( { {d rSub { size 8{i} } A rSub { size 8{i} } } over {A rSub { size 8{o} } } } right )=F rSub { size 8{i} } d rSub { size 8{i} } =W rSub { size 8{i} } } {}

In other words, the work output equals the work input.

(b) If the system is not moving, friction would not play a role. With friction, we know there are losses, so that Wout=WinWfWout=WinWf size 12{W rSub { size 8{"out"} } =W rSub { size 8{"in"} } - W rSub { size 8{f} } } {}; therefore, the work output is less than the work input. In other words, with friction, you need to push harder on the input piston than was calculated for the nonfriction case.

29.

Balloon:

P g = 5.00 cm H 2 O, P abs = 1.035 × 10 3 cm H 2 O. P g = 5.00 cm H 2 O, P abs = 1.035 × 10 3 cm H 2 O. alignl { stack { size 12{P rSub { size 8{g} } =5 "." "00"`"cm"`H rSub { size 8{2} } "O,"} {} # P rSub { size 8{"abs"} } =1 "." "035" times "10" rSup { size 8{3} } `"cm"`H rSub { size 8{2} } O "." {} } } {}

Jar:

P g = 50.0 mm Hg , P abs = 710 mm Hg. P g = 50.0 mm Hg , P abs = 710 mm Hg. alignl { stack { size 12{P rSub { size 8{g} } = - "50" "." 0`"mm"`"Hg,"} {} # P rSub { size 8{"abs"} } ="710"`"mm"`"Hg" "." {} } } {}

31.

4.08 m

33.

ΔP = 38.7 mm Hg, Leg blood pressure = 159 119 . ΔP = 38.7 mm Hg, Leg blood pressure = 159 119 . alignl { stack { size 12{ΔP="38" "." 7`"mm"`"Hg,"} {} # size 12{"Leg"`"blood"`"pressure"= { {"159"} over {"119"} } "." } {} } } {}

35.

22 . 4 cm 2 22 . 4 cm 2 size 12{"22" "." 4`"cm" rSup { size 8{2} } } {}

36.

91 . 7% 91 . 7% size 12{"91" "." 7%} {}

38.

815 kg /m 3 815 kg /m 3 size 12{"815"`"kg/m" rSup { size 8{3} } } {}

40.

(a) 41.4 g

(b) 41.4cm341.4cm3 size 12{"41" "." 4`"cm" rSup { size 8{3} } } {}

(c) 1.09 g/cm31.09 g/cm3 size 12{1 "." "09"`"g/cm" rSup { size 8{3} } } {}

42.

(a) 39.5 g

(b) 50cm350cm3 size 12{"50"`"cm" rSup { size 8{3} } } {}

(c) 0.79g/cm30.79g/cm3 size 12{0 "." "79"`"g/cm" rSup { size 8{3} } } {}

It is ethyl alcohol.

44.

8.21 N

46.

(a) 960kg/m3960kg/m3 size 12{"960" `"kg/m" rSup { size 8{3} } } {}

(b) 6.34%6.34%

She indeed floats more in seawater.

48.

(a) 0.240.24 size 12{0 "." "24"} {}

(b) 0.680.68 size 12{0 "." "68"} {}

(c) Yes, the cork will float because ρobj<ρethyl alcohol(0.678g/cm3<0.79g/cm3)ρobj<ρethyl alcohol(0.678g/cm3<0.79g/cm3) size 12{ρ rSub { size 8{"obj"} } <ρ rSub { size 8{"ethyl"`"alcohol"} } \( 0 "." "678"`"g/cm" rSup { size 8{3} } <0 "." "79"`"g/cm" rSup { size 8{3} } \) } {}

50.

The difference is 0.006%.0.006%.

52.

F net = F 2 F 1 = P 2 A P 1 A = P 2 P 1 A F net = F 2 F 1 = P 2 A P 1 A = P 2 P 1 A size 12{F rSub { size 8{"net"} } =F rSub { size 8{2} } - F rSub { size 8{1} } =P rSub { size 8{2} } A - P rSub { size 8{1} } A= left (P rSub { size 8{2} } - P rSub { size 8{1} } right )A} {}

= h 2 ρ fl g h 1 ρ fl g A = h 2 ρ fl g h 1 ρ fl g A size 12{ {}= left (h rSub { size 8{2} } ρ rSub { size 8{"fl"} } g - h rSub { size 8{1} } ρ rSub { size 8{"fl"} } g right )A} {}

= h 2 h 1 ρ fl gA = h 2 h 1 ρ fl gA size 12{ {}= left (h rSub { size 8{2} } - h rSub { size 8{1} } right )ρ rSub { size 8{"fl"} } ital "gA"} {}

where ρflρfl size 12{ρ rSub { size 8{"fl"} } } {} = density of fluid. Therefore,

F net = ( h 2 h 1 ) fl g = V fl ρ fl g = m fl g = w fl F net = ( h 2 h 1 ) fl g = V fl ρ fl g = m fl g = w fl size 12{F rSub { size 8{"net"} } = \( h rSub { size 8{2} } - h rSub { size 8{1} } \) Aρ rSub { size 8{"fl"} } g=V rSub { size 8{"fl"} } ρ rSub { size 8{"fl"} } g=m rSub { size 8{"fl"} } g=w rSub { size 8{"fl"} } } {}

where is wflwfl size 12{w rSub { size 8{"fl"} } } {} the weight of the fluid displaced.

54.

592 N/m 2 592 N/m 2 size 12{"592"`"N/m" rSup { size 8{2} } } {}

56.

2 . 23 × 10 2 mm Hg 2 . 23 × 10 2 mm Hg size 12{2 "." "23" times "10" rSup { size 8{ - 2} } `"mm"`"Hg"} {}

58.

(a) 1.65×103m1.65×103m size 12{1 "." "65" times "10" rSup { size 8{ - 3} } `m} {}

(b) 3.71×10–4m3.71×10–4m size 12{3 "." "71" times "10" rSup { size 8{4} } `m} {}

60.

6 . 32 × 10 2 N/m 6 . 32 × 10 2 N/m size 12{6 "." "32" times "10" rSup { size 8{ - 2} } `"N/m"} {}

Based on the values in table, the fluid is probably glycerin.

62.

P w = 14 . 6 N/m 2 , P a = 4.46 N/m 2 , P sw = 7.40 N/m 2 . P w = 14 . 6 N/m 2 , P a = 4.46 N/m 2 , P sw = 7.40 N/m 2 . alignl { stack { size 12{P rSub { size 8{w} } ="14" "." 6`"N/m" rSup { size 8{2} } , } {} # p rSub { size 8{a} } =4 "." "46"`"N/m" rSup { size 8{2} } , {} # P rSub { size 8{"sw"} } =7 "." "40"`"N/m" rSup { size 8{2} } "." {} } } {}

Alcohol forms the most stable bubble, since the absolute pressure inside is closest to atmospheric pressure.

64.

5.1º 5.1º size 12{5 "." 1°} {}

This is near the value of θ=θ= size 12{θ=0°} {} for most organic liquids.

66.

2 . 78 2 . 78 size 12{ - 2 "." "78"} {}

The ratio is negative because water is raised whereas mercury is lowered.

68.

479 N

70.

1.96 N

71.

63.0 cm H 2 O 63.0 cm H 2 O size 12{ - "63" "." 0`"cm"`H rSub { size 8{2} } O} {}

73.

(a) 3.81×103N/m23.81×103N/m2 size 12{3 "." "81" times "10" rSup { size 8{3} } `"N/m" rSup { size 8{2} } } {}

(b) 28.7 mm Hg28.7 mm Hg size 12{"28" "." 7`"mm"`"Hg"} {}, which is sufficient to trigger micturition reflex

75.

(a) 13.6 m water

(b) 76.5 cm water

77.

(a) 3.98×106Pa3.98×106Pa size 12{3 "." "98" times "10" rSup { size 8{6} } `"Pa"} {}

(b) 2.1×103cm2.1×103cm size 12{2 "." 1 times "10" rSup { size 8{ - 3} } `"cm"} {}

79.

(a) 2.97 cm

(b) 3.39×106J3.39×106J size 12{3 "." "39" times "10" rSup { size 8{ - 6} } `J} {}

(c) Work is done by the surface tension force through an effective distance h/2h/2 size 12{h/2} {} to raise the column of water.

81.

(a) 2.01×104N2.01×104N size 12{2 "." "01" times "10" rSup { size 8{4} } `N} {}

(b) 1.17×103m1.17×103m size 12{1 "." "17" times "10" rSup { size 8{ - 3} } `m} {}

(c) 2.56×1010N/m22.56×1010N/m2 size 12{2 "." "56" times "10" rSup { size 8{8} } `"N/m" rSup { size 8{2} } } {}

83.

(a) 1.38×104N1.38×104N size 12{1 "." "38" times "10" rSup { size 8{4} } `N} {}

(b) 2.81×107N/m22.81×107N/m2 size 12{2 "." "81" times "10" rSup { size 8{7} } `N} {}

(c) 283 N

85.

(a) 867 N

(b) This is too much force to exert with a hand pump.

(c) The assumed radius of the pump is too large; it would be nearly two inches in diameter—too large for a pump or even a primary cylinder. The pressure is reasonable for bicycle tires.

Test Prep for AP® Courses

1.

(e)

3.

(a) 100 kg/m3 (b) 60% (c) yes; yes (76% will be submerged) (d) answers vary

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