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  1. Preface
  2. Unit 1. Mechanics
    1. 1 Units and Measurement
      1. Introduction
      2. 1.1 The Scope and Scale of Physics
      3. 1.2 Units and Standards
      4. 1.3 Unit Conversion
      5. 1.4 Dimensional Analysis
      6. 1.5 Estimates and Fermi Calculations
      7. 1.6 Significant Figures
      8. 1.7 Solving Problems in Physics
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 2 Vectors
      1. Introduction
      2. 2.1 Scalars and Vectors
      3. 2.2 Coordinate Systems and Components of a Vector
      4. 2.3 Algebra of Vectors
      5. 2.4 Products of Vectors
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 3 Motion Along a Straight Line
      1. Introduction
      2. 3.1 Position, Displacement, and Average Velocity
      3. 3.2 Instantaneous Velocity and Speed
      4. 3.3 Average and Instantaneous Acceleration
      5. 3.4 Motion with Constant Acceleration
      6. 3.5 Free Fall
      7. 3.6 Finding Velocity and Displacement from Acceleration
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 4 Motion in Two and Three Dimensions
      1. Introduction
      2. 4.1 Displacement and Velocity Vectors
      3. 4.2 Acceleration Vector
      4. 4.3 Projectile Motion
      5. 4.4 Uniform Circular Motion
      6. 4.5 Relative Motion in One and Two Dimensions
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    5. 5 Newton's Laws of Motion
      1. Introduction
      2. 5.1 Forces
      3. 5.2 Newton's First Law
      4. 5.3 Newton's Second Law
      5. 5.4 Mass and Weight
      6. 5.5 Newton’s Third Law
      7. 5.6 Common Forces
      8. 5.7 Drawing Free-Body Diagrams
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    6. 6 Applications of Newton's Laws
      1. Introduction
      2. 6.1 Solving Problems with Newton’s Laws
      3. 6.2 Friction
      4. 6.3 Centripetal Force
      5. 6.4 Drag Force and Terminal Speed
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    7. 7 Work and Kinetic Energy
      1. Introduction
      2. 7.1 Work
      3. 7.2 Kinetic Energy
      4. 7.3 Work-Energy Theorem
      5. 7.4 Power
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    8. 8 Potential Energy and Conservation of Energy
      1. Introduction
      2. 8.1 Potential Energy of a System
      3. 8.2 Conservative and Non-Conservative Forces
      4. 8.3 Conservation of Energy
      5. 8.4 Potential Energy Diagrams and Stability
      6. 8.5 Sources of Energy
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    9. 9 Linear Momentum and Collisions
      1. Introduction
      2. 9.1 Linear Momentum
      3. 9.2 Impulse and Collisions
      4. 9.3 Conservation of Linear Momentum
      5. 9.4 Types of Collisions
      6. 9.5 Collisions in Multiple Dimensions
      7. 9.6 Center of Mass
      8. 9.7 Rocket Propulsion
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    10. 10 Fixed-Axis Rotation
      1. Introduction
      2. 10.1 Rotational Variables
      3. 10.2 Rotation with Constant Angular Acceleration
      4. 10.3 Relating Angular and Translational Quantities
      5. 10.4 Moment of Inertia and Rotational Kinetic Energy
      6. 10.5 Calculating Moments of Inertia
      7. 10.6 Torque
      8. 10.7 Newton’s Second Law for Rotation
      9. 10.8 Work and Power for Rotational Motion
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    11. 11 Angular Momentum
      1. Introduction
      2. 11.1 Rolling Motion
      3. 11.2 Angular Momentum
      4. 11.3 Conservation of Angular Momentum
      5. 11.4 Precession of a Gyroscope
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    12. 12 Static Equilibrium and Elasticity
      1. Introduction
      2. 12.1 Conditions for Static Equilibrium
      3. 12.2 Examples of Static Equilibrium
      4. 12.3 Stress, Strain, and Elastic Modulus
      5. 12.4 Elasticity and Plasticity
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    13. 13 Gravitation
      1. Introduction
      2. 13.1 Newton's Law of Universal Gravitation
      3. 13.2 Gravitation Near Earth's Surface
      4. 13.3 Gravitational Potential Energy and Total Energy
      5. 13.4 Satellite Orbits and Energy
      6. 13.5 Kepler's Laws of Planetary Motion
      7. 13.6 Tidal Forces
      8. 13.7 Einstein's Theory of Gravity
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    14. 14 Fluid Mechanics
      1. Introduction
      2. 14.1 Fluids, Density, and Pressure
      3. 14.2 Measuring Pressure
      4. 14.3 Pascal's Principle and Hydraulics
      5. 14.4 Archimedes’ Principle and Buoyancy
      6. 14.5 Fluid Dynamics
      7. 14.6 Bernoulli’s Equation
      8. 14.7 Viscosity and Turbulence
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  3. Unit 2. Waves and Acoustics
    1. 15 Oscillations
      1. Introduction
      2. 15.1 Simple Harmonic Motion
      3. 15.2 Energy in Simple Harmonic Motion
      4. 15.3 Comparing Simple Harmonic Motion and Circular Motion
      5. 15.4 Pendulums
      6. 15.5 Damped Oscillations
      7. 15.6 Forced Oscillations
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 16 Waves
      1. Introduction
      2. 16.1 Traveling Waves
      3. 16.2 Mathematics of Waves
      4. 16.3 Wave Speed on a Stretched String
      5. 16.4 Energy and Power of a Wave
      6. 16.5 Interference of Waves
      7. 16.6 Standing Waves and Resonance
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 17 Sound
      1. Introduction
      2. 17.1 Sound Waves
      3. 17.2 Speed of Sound
      4. 17.3 Sound Intensity
      5. 17.4 Normal Modes of a Standing Sound Wave
      6. 17.5 Sources of Musical Sound
      7. 17.6 Beats
      8. 17.7 The Doppler Effect
      9. 17.8 Shock Waves
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  4. A | Units
  5. B | Conversion Factors
  6. C | Fundamental Constants
  7. D | Astronomical Data
  8. E | Mathematical Formulas
  9. F | Chemistry
  10. G | The Greek Alphabet
  11. 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
  12. Index

Check Your Understanding

5.1

14 N, 56°56° measured from the positive x-axis

5.2

a. His weight acts downward, and the force of air resistance with the parachute acts upward. b. neither; the forces are equal in magnitude

5.3

0.1m/s20.1m/s2

5.4

40m/s240m/s2

5.5

a. 159.0i^+770.0j^N159.0i^+770.0j^N; b. 0.1590i^+0.7700j^N0.1590i^+0.7700j^N

5.6

a=2.78m/s2a=2.78m/s2

5.7

a. 3.0m/s23.0m/s2; b. 18 N

5.8

a. 1.7m/s2;1.7m/s2; b. 1.3m/s21.3m/s2

5.9

6.0×1026.0×102 N

5.10
Figure a shows a free body diagram of an object on a line that slopes down to the right. Arrow T from the object points right and up, parallel to the slope. Arrow N1 points left and up, perpendicular to the slope. Arrow w1 points vertically down. Figure b shows a free body diagram of an object on a line that slopes down to the left. Arrow N2 from the object points right and up, perpendicular to the slope. Arrow T points left and up, parallel to the slope. Arrow w2 points vertically down.

;

Figure a shows a free body diagram of an object on a line that slopes down to the right. Arrow T from the object points right and up, parallel to the slope. Arrow N1 points left and up, perpendicular to the slope. Arrow w1 points vertically down. Arrow w1x points left and down, parallel to the slope. Arrow w1y points right and down, perpendicular to the slope. Figure b shows a free body diagram of an object on a line that slopes down to the left. Arrow N2 from the object points right and up, perpendicular to the slope. Arrow T points left and up, parallel to the slope. Arrow w2 points vertically down. Arrow w2y points left and down, perpendicular to the slope. Arrow w2x points right and down, parallel to the slope.

Conceptual Questions

1.

Forces are directional and have magnitude.

3.

The cupcake velocity before the braking action was the same as that of the car. Therefore, the cupcakes were unrestricted bodies in motion, and when the car suddenly stopped, the cupcakes kept moving forward according to Newton’s first law.

5.

No. If the force were zero at this point, then there would be nothing to change the object’s momentary zero velocity. Since we do not observe the object hanging motionless in the air, the force could not be zero.

7.

The astronaut is truly weightless in the location described, because there is no large body (planet or star) nearby to exert a gravitational force. Her mass is 70 kg regardless of where she is located.

9.

The force you exert (a contact force equal in magnitude to your weight) is small. Earth is extremely massive by comparison. Thus, the acceleration of Earth would be incredibly small. To see this, use Newton’s second law to calculate the acceleration you would cause if your weight is 600.0 N and the mass of Earth is 6.00×1024kg6.00×1024kg.

11.

a. action: Earth pulls on the Moon, reaction: Moon pulls on Earth; b. action: foot applies force to ball, reaction: ball applies force to foot; c. action: rocket pushes on gas, reaction: gas pushes back on rocket; d. action: car tires push backward on road, reaction: road pushes forward on tires; e. action: jumper pushes down on ground, reaction: ground pushes up on jumper; f. action: gun pushes forward on bullet, reaction: bullet pushes backward on gun.

13.

a. The rifle (the shell supported by the rifle) exerts a force to expel the bullet; the reaction to this force is the force that the bullet exerts on the rifle (shell) in opposite direction. b. In a recoilless rifle, the shell is not secured in the rifle; hence, as the bullet is pushed to move forward, the shell is pushed to eject from the opposite end of the barrel. c. It is not safe to stand behind a recoilless rifle.

15.

a. Yes, the force can be acting to the left; the particle would experience deceleration and lose speed. B. Yes, the force can be acting downward because its weight acts downward even as it moves to the right.

17.

two forces of different types: weight acting downward and normal force acting upward

Problems

19.

a. Fnet=5.0i^+10.0j^NFnet=5.0i^+10.0j^N; b. the magnitude is Fnet=11NFnet=11N, and the direction is θ=63°θ=63°

21.

a. Fnet=660.0i^+150.0j^NFnet=660.0i^+150.0j^N; b. Fnet=676.6NFnet=676.6N at θ=12.8°θ=12.8° from David’s rope

23.

a. Fnet=95.0i^+283j^NFnet=95.0i^+283j^N; b. 299 N at 71°71° north of east; c. FDS=(95.0i^+283j^)NFDS=(95.0i^+283j^)N

25.

Running from rest, the sprinter attains a velocity of v=12.96m/sv=12.96m/s, at end of acceleration. We find the time for acceleration using x=20.00m=0+0.5at12x=20.00m=0+0.5at12, or t1=3.086s.t1=3.086s. For maintained velocity, x2=vt2x2=vt2, or t2=x2/v=80.00m/12.96m/s=6.173st2=x2/v=80.00m/12.96m/s=6.173s. Total time=9.259sTotal time=9.259s.

27.

a. m=56.0kgm=56.0kg; b. ameas=aastro+aship,whereaship=mastroaastromshipameas=aastro+aship,whereaship=mastroaastromship; c. If the force could be exerted on the astronaut by another source (other than the spaceship), then the spaceship would not experience a recoil.

29.

Fnet=4.12×105NFnet=4.12×105N

31.

a=253m/s2a=253m/s2

33.

Fnet=Ff=maF=1.26×103NFnet=Ff=maF=1.26×103N

35.

v2=v02+2axa=7.80m/s2Fnet=−7.80×103Nv2=v02+2axa=7.80m/s2Fnet=−7.80×103N

37.

a. Fnet=maa=9.0i^m/s2Fnet=maa=9.0i^m/s2; b. The acceleration has magnitude 9.0m/s29.0m/s2, so x=110mx=110m.

39.

1.6i^0.8j^m/s21.6i^0.8j^m/s2

41.

a. wMoon=mgMoonm=150kgwEarth=1.5×103NwMoon=mgMoonm=150kgwEarth=1.5×103N; b. Mass does not change, so the suited astronaut’s mass on both Earth and the Moon is 150kg.150kg.

43.

a. Fh=3.68×103N andw=7.35×102NFhw=5.00times greater than weightFh=3.68×103N andw=7.35×102NFhw=5.00times greater than weight;
b. Fnet=3750Nθ=11.3°from horizontalFnet=3750Nθ=11.3°from horizontal

45.

w=19.6NFnet=5.40NFnet=maa=2.70m/s2w=19.6NFnet=5.40NFnet=maa=2.70m/s2

47.

98 N

49.

497 N

51.

a. Fnet=2.64×107N;Fnet=2.64×107N; b. The force exerted on the ship is also 2.64×107N2.64×107N because it is opposite the shell’s direction of motion.

53.

Because the weight of the history book is the force exerted by Earth on the history book, we represent it as FEH=−14j^N.FEH=−14j^N. Aside from this, the history book interacts only with the physics book. Because the acceleration of the history book is zero, the net force on it is zero by Newton’s second law: FPH+FEH=0,FPH+FEH=0, where FPHFPH is the force exerted by the physics book on the history book. Thus, FPH=FEH=(−14j^)N=14j^N.FPH=FEH=(−14j^)N=14j^N. We find that the physics book exerts an upward force of magnitude 14 N on the history book. The physics book has three forces exerted on it: FEPFEP due to Earth, FHPFHP due to the history book, and FDPFDP due to the desktop. Since the physics book weighs 18 N, FEP=−18j^N.FEP=−18j^N. From Newton’s third law, FHP=FPH,FHP=FPH, so FHP=−14j^N.FHP=−14j^N. Newton’s second law applied to the physics book gives F=0,F=0, or FDP+FEP+FHP=0,FDP+FEP+FHP=0, so FDP=(−18j^)(−14j^)=32j^N.FDP=(−18j^)(−14j^)=32j^N. The desk exerts an upward force of 32 N on the physics book. To arrive at this solution, we apply Newton’s second law twice and Newton’s third law once.

55.

a. The free-body diagram of pulley 4:

A free body diagram shows vector F pointing left, a vector T pointing right and up, forming an angle theta with the horizontal and another vector T pointing right and down, forming an angle theta with the horizontal.


b. T=mg,F=2Tcosθ=2mgcosθT=mg,F=2Tcosθ=2mgcosθ

57.

a.

Figure shows two teams of nine members each pulling on a rope form either side. Each member of the team on the left has mass m1 and applies force F1. Each member of the team on the right has mass m2 and applies force F2.


Fnet=Ma;F1=1350N;F2=1365 N9(F2F1)=9(m1+m2)a;m1=68kg;m2=73 kga=0.11m/s2;Fnet=Ma;F1=1350N;F2=1365 N9(F2F1)=9(m1+m2)a;m1=68kg;m2=73 kga=0.11m/s2;
Thus, the heavy team wins.
b.

Figure shows a team of people each with mass m1 pulling on a rope towards the left with force F1. An arrow parallel to the rope, pointing right is labeled T. Net F prime is equal to M prime a.


T9F1=9m1aT=9m1a+9F1=1.2×104NT9F1=9m1aT=9m1a+9F1=1.2×104N

59.

a. T=1.96×10−4N;T=1.96×10−4N;
b. T=4.71×10−4NTT=2.40times the tension in the vertical strandT=4.71×10−4NTT=2.40times the tension in the vertical strand

61.
Figure shows a horizontal line parallel to x axis. An arrow F pointing downwards originates from the center of the line, with its tip intersecting x-axis. Two arrows originate from this point of intersection and their tips touch the line on either side. They form the same angle with the x-axis and the line.


Fynet=F2Tsinθ=0F=2TsinθT=F2sinθFynet=F2Tsinθ=0F=2TsinθT=F2sinθ

63.

a. see Example 5.13; b. 1.5 N; c. 15 N

65.

a. 5.6 kg; b. 55 N; c. T2=60NT2=60N;
d.

Figure a shows a baby in a basket, with arrow T1 pointing up and arrow w pointing down. Figure b shows a free body diagram of arrow T1 pointing down. Figure c shows a free body diagram of T1 pointing down, T2 pointing up and mg pointing down.
67.

a. 4.9m/s24.9m/s2, 17 N; b. 9.8 N

69.
A free body diagram shows a vector F subscript e pointing right, vector N pointing up, vector f pointing left and arrow w pointing down.
71.
Figure shows coordinate axes. Three arrows radiate out from the origin. T1, labeled 41 degrees points up and left. T2, labeled 63 degrees points up and right. T3 equal to w equal to 200 N is along the negative y axis.

Additional Problems

73.

5.90 kg

75.
A free body diagram with arrow F pointing up and arrow w pointing down.
77.

a. Fnet=m(v2v02)2xFnet=m(v2v02)2x; b. 2590 N

79.

Fnet=F1+F2+F3=(6.02i^+14.0j^)N Fnet=maa=Fnetm=6.02i^+14.0j^N10.0kg= (0.602i^+1.40j^)m/s2 Fnet=F1+F2+F3=(6.02i^+14.0j^)N Fnet=maa=Fnetm=6.02i^+14.0j^N10.0kg= (0.602i^+1.40j^)m/s2

81.

Fnet=FA+FBFnet=Ai^+(−1.41Ai^1.41Aj^)Fnet=A(−0.41i^1.41j^)θ=254°Fnet=FA+FBFnet=Ai^+(−1.41Ai^1.41Aj^)Fnet=A(−0.41i^1.41j^)θ=254°
(We add 180°180°, because the angle is in quadrant IV.)

83.

F=2mk2x2F=2mk2x2; First, take the derivative of the velocity function to obtain a=2kxv=2kx(kx2)=2k2x3a=2kxv=2kx(kx2)=2k2x3. Then apply Newton’s second law F=ma=2mk2x2F=ma=2mk2x2.

85.

a. For box A, NA=mgNA=mg and NB=mgcosθNB=mgcosθ; b. NA>NBNA>NB because for θ<90°θ<90°, cosθ<1cosθ<1; c. NA>NBNA>NB when θ=10°θ=10°

87.

a. 8.66 N; b. 0.433 m

89.

0.40 or 40%

91.

16 N

Challenge Problems

93.

a.

Figure shows a free body diagram with F1 pointing up and left and F2 pointing down and left.

; b. No; FRFR is not shown, because it would replace F1F1 and F2F2. (If we want to show it, we could draw it and then place squiggly lines on F1F1 and F2F2 to show that they are no longer considered.

95.

a. 14.1 m/s; b. 601 N

97.

Fmt2Fmt2

99.

936 N

101.

a=−248i^433j^m/s2a=−248i^433j^m/s2

103.

0.548m/s20.548m/s2

105.

a. T1=2mgsinθT1=2mgsinθ, T2=mgsin(arctan(12tanθ))T2=mgsin(arctan(12tanθ)), T3=2mgtanθ;T3=2mgtanθ; b. ϕ=arctan(12tanθ)ϕ=arctan(12tanθ); c. 2.56°2.56°; (d) x=d(2cosθ+2cos(arctan(12tanθ))+1)x=d(2cosθ+2cos(arctan(12tanθ))+1)

107.

a. a=(5.00mi^+3.00mj^)m/s2;a=(5.00mi^+3.00mj^)m/s2; b. 1.38 kg; c. 21.2 m/s; d. v=(18.1i^+10.9j^)m/s2v=(18.1i^+10.9j^)m/s2

109.

a. 0.900i^+0.600j^N0.900i^+0.600j^N; b. 1.08 N

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