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University Physics Volume 1

Additional Problems

University Physics Volume 1Additional Problems
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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

Additional Problems

99.

The two barges shown here are coupled by a cable of negligible mass. The mass of the front barge is 2.00×103kg2.00×103kg and the mass of the rear barge is 3.00×103kg.3.00×103kg. A tugboat pulls the front barge with a horizontal force of magnitude 20.0×103N,20.0×103N, and the frictional forces of the water on the front and rear barges are 8.00×103N8.00×103N and 10.0×103N,10.0×103N, respectively. Find the horizontal acceleration of the barges and the tension in the connecting cable.

An illustration showing a tug boat pulling two barges. The barge directly attached to the tug boat has mass 2.00 times 10 to the third kilograms. The barge at the end,  behind the first barge, has mass 3.00 times 10 to the third kilograms.
100.

If the order of the barges of the preceding exercise is reversed so that the tugboat pulls the 3.00×103-kg3.00×103-kg barge with a force of 20.0×103N,20.0×103N, what are the acceleration of the barges and the tension in the coupling cable?

101.

An object with mass m moves along the x-axis. Its position at any time is given by x(t)=pt3+qt2x(t)=pt3+qt2 where p and q are constants. Find the net force on this object for any time t.

102.

A helicopter with mass 2.35×104kg2.35×104kg has a position given by r(t)=(0.020t3)i^+(2.2t)j^(0.060t2)k^.r(t)=(0.020t3)i^+(2.2t)j^(0.060t2)k^. Find the net force on the helicopter at t=3.0s.t=3.0s.

103.

Located at the origin, an electric car of mass m is at rest and in equilibrium. A time dependent force of F(t)F(t) is applied at time t=0t=0, and its components are Fx(t)=p+ntFx(t)=p+nt and Fy(t)=qtFy(t)=qt where p, q, and n are constants. Find the position r(t)r(t) and velocity v(t)v(t) as functions of time t.

104.

A particle of mass m is located at the origin. It is at rest and in equilibrium. A time-dependent force of F(t)F(t) is applied at time t=0t=0, and its components are Fx(t)=ptFx(t)=pt and Fy(t)=n+qtFy(t)=n+qt where p, q, and n are constants. Find the position r(t)r(t) and velocity v(t)v(t) as functions of time t.

105.

A 2.0-kg object has a velocity of 4.0i^m/s4.0i^m/s at t=0.t=0. A constant resultant force of (2.0i^+4.0j^)N(2.0i^+4.0j^)N then acts on the object for 3.0 s. What is the magnitude of the object’s velocity at the end of the 3.0-s interval?

106.

A 1.5-kg mass has an acceleration of (4.0i^3.0j^)m/s2.(4.0i^3.0j^)m/s2. Only two forces act on the mass. If one of the forces is (2.0i^1.4j^)N,(2.0i^1.4j^)N, what is the magnitude of the other force?

107.

A box is dropped onto a conveyor belt moving at 3.4 m/s. If the coefficient of friction between the box and the belt is 0.27, how long will it take before the box moves without slipping?

108.

Shown below is a 10.0-kg block being pushed by a horizontal force FF of magnitude 200.0 N. The coefficient of kinetic friction between the two surfaces is 0.50. Find the acceleration of the block.

An illustration of a 10.0 kilogram block being pushed into a slope by a horizontal force F. The slope angles up and to the right at an angle of 30 degrees to the horizontal and the force F points to the right.
109.

As shown below, the mass of block 1 is m1=4.0kg,m1=4.0kg, while the mass of block 2 is m2=8.0kg.m2=8.0kg. The coefficient of friction between m1m1 and the inclined surface is μk=0.40.μk=0.40. What is the acceleration of the system?

Block 1 is on a ramp inclined up and to the right at an angle of 37 degrees above the horizontal. It is connected to a string that passes over a pulley at the top of the ramp, then hangs straight down and connects to  block 2. Block 2 is not in contact with the ramp.
110.

A student is attempting to move a 30-kg mini-fridge into her dorm room. During a moment of inattention, the mini-fridge slides down a 35 degree incline at constant speed when she applies a force of 25 N acting up and parallel to the incline. What is the coefficient of kinetic friction between the fridge and the surface of the incline?

111.

A crate of mass 100.0 kg rests on a rough surface inclined at an angle of 37.0°37.0° with the horizontal. A massless rope to which a force can be applied parallel to the surface is attached to the crate and leads to the top of the incline. In its present state, the crate is just ready to slip and start to move down the plane. The coefficient of friction is 80%80% of that for the static case. (a) What is the coefficient of static friction? (b) What is the maximum force that can be applied upward along the plane on the rope and not move the block? (c) With a slightly greater applied force, the block will slide up the plane. Once it begins to move, what is its acceleration and what reduced force is necessary to keep it moving upward at constant speed? (d) If the block is given a slight nudge to get it started down the plane, what will be its acceleration in that direction? (e) Once the block begins to slide downward, what upward force on the rope is required to keep the block from accelerating downward?

112.

A car is moving at high speed along a highway when the driver makes an emergency braking. The wheels become locked (stop rolling), and the resulting skid marks are 32.0 meters long. If the coefficient of kinetic friction between tires and road is 0.550, and the acceleration was constant during braking, how fast was the car going when the wheels became locked?

113.

A crate having mass 50.0 kg falls horizontally off the back of the flatbed truck, which is traveling at 100 km/h. Find the value of the coefficient of kinetic friction between the road and crate if the crate slides 50 m on the road in coming to rest. The initial speed of the crate is the same as the truck, 100 km/h.

The figure shows a truck moving to the right at 100 kilometers per hour and a 50 kilogram crate on the ground behind the truck.
114.

A 15-kg sled is pulled across a horizontal, snow-covered surface by a force applied to a rope at 30 degrees with the horizontal. The coefficient of kinetic friction between the sled and the snow is 0.20. (a) If the force is 33 N, what is the horizontal acceleration of the sled? (b) What must the force be in order to pull the sled at constant velocity?

115.

A 30.0-g ball at the end of a string is swung in a vertical circle with a radius of 25.0 cm. The tangential velocity is 200.0 cm/s. Find the tension in the string: (a) at the top of the circle, (b) at the bottom of the circle, and (c) at a distance of 12.5 cm from the center of the circle (r=12.5cm).(r=12.5cm).

116.

A particle of mass 0.50 kg starts moves through a circular path in the xy-plane with a position given by r(t)=(4.0cos3t)i^+(4.0sin3t)j^r(t)=(4.0cos3t)i^+(4.0sin3t)j^ where r is in meters and t is in seconds. (a) Find the velocity and acceleration vectors as functions of time. (b) Show that the acceleration vector always points toward the center of the circle (and thus represents centripetal acceleration). (c) Find the centripetal force vector as a function of time.

117.

A stunt cyclist rides on the interior of a cylinder 12 m in radius. The coefficient of static friction between the tires and the wall is 0.68. Find the value of the minimum speed for the cyclist to perform the stunt.

118.

When a body of mass 0.25 kg is attached to a vertical massless spring, it is extended 5.0 cm from its unstretched length of 4.0 cm. The body and spring are placed on a horizontal frictionless surface and rotated about the held end of the spring at 2.0 rev/s. How far is the spring stretched?

119.

A piece of bacon starts to slide down the pan when one side of a pan is raised up 5.0 cm. If the length of the pan from pivot to the raising point is 23.5 cm, what is the coefficient of static friction between the pan and the bacon?

120.

A plumb bob hangs from the roof of a railroad car. The car rounds a circular track of radius 300.0 m at a speed of 90.0 km/h. At what angle relative to the vertical does the plumb bob hang?

121.

An airplane flies at 120.0 m/s and banks at a 30°30° angle. If its mass is 2.50×103kg,2.50×103kg, (a) what is the magnitude of the lift force? (b) what is the radius of the turn?

122.

The position of a particle is given by r(t)=A(cosωti^+sinωtj^),r(t)=A(cosωti^+sinωtj^), where ωω is a constant. (a) Show that the particle moves in a circle of radius A. (b) Calculate dr/dtdr/dt and then show that the speed of the particle is a constant Aω.Aω. (c) Determine d2r/dt2d2r/dt2 and show that a is given byac=rω2.ac=rω2. (d) Calculate the centripetal force on the particle. [Hint: For (b) and (c), you will need to use (d/dt)(cosωt)=ωsinωt(d/dt)(cosωt)=ωsinωt and (d/dt)(sinωt)=ωcosωt.(d/dt)(sinωt)=ωcosωt.

123.

Two blocks connected by a string are pulled across a horizontal surface by a force applied to one of the blocks, as shown below. The coefficient of kinetic friction between the blocks and the surface is 0.25. If each block has an acceleration of 2.0m/s22.0m/s2 to the right, what is the magnitude F of the applied force?

Two blocks, 1.0 kilograms on the left and 3.0 kilograms on the right, are connected by a string and are on a horizontal surface. Force F acts on the 3.0 kilogram mass and points up and to the right at a angle of 60 degrees above the horizontal.
124.

As shown below, the coefficient of kinetic friction between the surface and the larger block is 0.20, and the coefficient of kinetic friction between the surface and the smaller block is 0.30. If F=10NF=10N and M=1.0kgM=1.0kg, what is the tension in the connecting string?

Two blocks, 2 M on the left and M on the right, are connected by a string and are on a horizontal surface. Force F acts on M and points to the right.
125.

In the figure, the coefficient of kinetic friction between the surface and the blocks is μk.μk. If M=1.0kg,M=1.0kg, find an expression for the magnitude of the acceleration of either block (in terms of F, μk,μk, and g).

Two blocks, M on the left and 3 M on the right, are connected by a string and are on a horizontal surface. The following forces are indicated: f sub k 2 acting on M and pointing to the right, f sub k 1 acting on 3 M and pointing to the right, F acting on 3 M and pointing to the left, N sub 2 acting on M and pointing up, N sub 1 acting on 3 M and pointing up, M g acting on M and pointing down, , 3 M g acting on 3 M and pointing down.
126.

Two blocks are stacked as shown below, and rest on a frictionless surface. There is friction between the two blocks (coefficient of friction μμ). An external force is applied to the top block at an angle θθ with the horizontal. What is the maximum force F that can be applied for the two blocks to move together?

Rectangular block M sub 2 is on a horizontal surface. Rectangular block M sub 1 is on top of block M sub 2. A force F pushes on block M sub 1. Force F is directed down and to the right, at a angle theta to the horizontal.
127.

A box rests on the (horizontal) back of a truck. The coefficient of static friction between the box and the surface on which it rests is 0.24. What maximum distance can the truck travel (starting from rest and moving horizontally with constant acceleration) in 3.0 s without having the box slide?

128.

A double-incline plane is shown below. The coefficient of friction on the left surface is 0.30, and on the right surface 0.16. Calculate the acceleration of the system.

Two carts connected by a string passing over a pulley are on either side of a double inclined plane. The string passes over a pulley attached to the top of the double incline. On the left, the incline makes an angle of 37 degrees with the horizontal and the cart on that side has mass 10 kilograms. On the right, the incline makes an angle of 53 degrees with the horizontal and the cart on that side has mass 15 kilograms.
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