The mass of a sports car is 1 200 kg. The shape of the body is such that the aerodynamic drag coefficient is 0.250 and the frontal area is 2.20 \(m^2\). Ignoring all other sources of friction, calculate the initial acceleration the car has if it has been traveling at 100 km/h and is now shifted into neutral and allowed to coast.
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Table of Contents
1
Physics and Measurement
1.1
Standards of Length, Mass, and Time
1.2
Modeling and Alternative Representations
1.3
Dimensional Analysis
1.4
Conversion of Units
1.5
Estimates and Order-of-Magnitude Calculations
1.6
Significant Figures
2
Motion in One Dimension
2.1
Position, Velocity, and Speed of a Particle
2.2
Instantaneous Velocity and Speed
2.3
Analysis Model: Particle Under Constant Velocity
2.5
Acceleration
2.6
Motion Diagrams
2.7
Analysis Model: Particle Under Constant Acceleration
2.8
Freely Falling Objects
2.9
Kinematic Equations Derived from Calculus
3
Vectors
3.1
Coordinate Systems
3.2
Vector and Scalar Quantities
3.3
Basic Vector Arithmetic
3.4
Components of a Vector and Unit Vectors
4
Motion in Two Dimensions
4.1
The Position, Velocity, and Acceleration Vectors
4.2
Two-Dimensional Motion with Constant Acceleration
4.3
Projectile Motion
4.4
Analysis Model: Particle in Uniform Circular Motion
4.5
Tangential and Radial Acceleration
4.6
Relative Velocity and Relative Acceleration
5
The Laws of Motion
5.1
The Concept of Force
5.4
Newton’s Second Law
5.5
The Gravitational Force and Weight
5.6
Newton’s Third Law
5.7
Analysis Models Using Newton’s Second Law
5.8
Forces of Friction
6
Circular Motion and Other Applications of Newton’s Laws
6.1
Extending the Particle in Uniform Circular Motion Model
6.2
Nonuniform Circular Motion
6.3
Motion in Accelerated Frames
6.4
Motion in the Presence of Resistive Forces
7
Energy of a System
7.2
Work Done by a Constant Force
7.3
The Scalar Product of Two Vectors
7.4
Work Done by a Varying Force
7.5
Kinetic Energy and the Work–Kinetic Energy Theorem
7.6
Potential Energy of a System
7.7
Conservative and Nonconservative Forces
7.8
Relationship Between Conservative Forces and Potential Energy
7.9
Energy Diagrams and Equilibrium of a System
8
Conservation of Energy
8.1
Analysis Model: Nonisolated System (Energy)
8.2
Analysis Model: Isolated System (Energy)
8.3
Situations Involving Kinetic Friction
8.4
Changes in Mechanical Energy for Nonconservative Forces
8.5
Power
9
Linear Momentum and Collisions
9.1
Linear Momentum
9.2
Analysis Model: Isolated System (Momentum)
9.3
Analysis Model: Nonisolated System (Momentum)
9.4
Collisions in One Dimension
9.5
Collisions in Two Dimensions
9.6
The Center of Mass
9.7
Systems of Many Particles
9.8
Deformable Systems
9.9
Rocket Propulsion
10
Rotation of a Rigid Object About a Fixed Axis
10.1
Angular Position, Velocity, and Acceleration
10.2
Analysis Model: Rigid Object Under Constant Angular Acceleration
10.3
Angular and Translational Quantities
10.4
Torque
10.5
Analysis Model: Rigid Object Under a Net Torque
10.6
Calculation of Moments of Inertia
10.7
Rotational Kinetic Energy
10.8
Energy Considerations in Rotational Motion
10.9
Rolling Motion of a Rigid Object
11
Angular Momentum
11.1
The Vector Product and Torque
11.2
Analysis Model: Nonisolated System (Angular Momentum)
11.3
Angular Momentum of a Rotating Rigid Object
11.4
Analysis Model: Isolated System (Angular Momentum)
11.5
The Motion of Gyroscopes and Tops
12
Static Equilibrium and Elasticity
12.1
Analysis Model: Rigid Object in Equilibrium
12.2
More on the Center of Gravity
12.3
Examples of Rigid Objects in Static Equilibrium
12.4
Elastic Properties of Solids
13
Universal Gravitation
13.1
Newton’s Law of Universal Gravitation
13.2
Free-Fall Acceleration and the Gravitational Force
13.3
Analysis Model: Particle in a Field (Gravitational)
13.4
Kepler’s Laws and the Motion of Planets
13.5
Gravitational Potential Energy
13.6
Energy Considerations in Planetary and Satellite Motion
14
Fluid Mechanics
14.1
Pressure
14.2
Variation of Pressure with Depth
14.3
Pressure Measurements
14.4
Buoyant Forces and Archimedes’s Principle
14.5
Fluid Dynamics
14.6
Bernoulli’s Equation
14.7
Flow of Viscous Fluids in Pipes
14.8
Other Applications of Fluid Dynamics
15
Oscillatory Motion
15.1
Motion of an Object Attached to a Spring
15.2
Analysis Model: Particle in Simple Harmonic Motion
15.3
Energy of the Simple Harmonic Oscillator
15.4
Comparing Simple Harmonic Motion with Uniform Circular Motion
15.5
The Pendulum
15.6
Damped Oscillations
15.7
Forced Oscillations
16
Wave Motion
16.1
Propagation of a Disturbance
16.2
Analysis Model: Traveling Wave
16.3
The Speed of Waves on Strings
16.4
Rate of Energy Transfer by Sinusoidal Waves on Strings
16.5
The Linear Wave Equation
16.6
Sound Waves
16.7
Speed of Sound Waves
16.8
Intensity of Sound Waves
16.9
The Doppler Effect
17
Superposition and Standing Waves
17.1
Analysis Model: Waves in Interference
17.2
Standing Waves
17.4
Analysis Model: Waves Under Boundary Conditions
17.5
Resonance
17.6
Standing Waves in Air Columns
17.7
Beats: Interference in Time
17.8
Nonsinusoidal Waveforms
18
Temperature
18.2
Thermometers and the Celsius Temperature Scale
18.3
The Constant-Volume Gas Thermometer and the Absolute Temperature Scale
18.4
Thermal Expansion of Solids and Liquids
18.5
Macroscopic Description of an Ideal Gas
19
The First Law of Thermodynamics
19.1
Heat and Internal Energy
19.2
Specific Heat and Calorimetry
19.3
Latent Heat
19.4
Work in Thermodynamic Processes
19.5
The First Law of Thermodynamics
19.6
Energy Transfer Mechanisms in Thermal Processes
20
The Kinetic Theory of Gases
20.1
Molecular Model of an Ideal Gas
20.2
Molar Specific Heat of an Ideal Gas
20.3
The Equipartition of Energy
20.4
Adiabatic Processes for an Ideal Gas
20.5
Distribution of Molecular Speeds
21
Heat Engines, Entropy, and the Second Law of Thermodynamics
21.1
Heat Engines and the Second Law of Thermodynamics
21.2
Heat Pumps and Refrigerators
21.4
The Carnot Engine
21.5
Gasoline and Diesel Engines
21.6
Entropy
21.7
Entropy in Thermodynamic Systems
21.8
Entropy and the Second Law
22
Electric Fields
22.1
Properties of Electric Charges
22.3
Coulomb’s Law
22.4
Analysis Model: Particle in a Field (Electric)
22.5
Electric Field Lines
22.6
Motion of a Charged Particle in a Uniform Electric Field
23
Continuous Charge Distributions and Gauss’s Law
23.1
Electric Field of a Continuous Charge Distribution
23.2
Electric Flux
23.3
Gauss’s Law
23.4
Application of Gauss’s Law to Various Charge Distributions
24
Electric Potential
24.1
Electric Potential and Potential Difference
24.2
Potential Difference in a Uniform Electric Field
24.3
Electric Potential and Potential Energy Due to Point Charges
24.4
Obtaining the Value of the Electric Field from the Electric Potential
24.5
Electric Potential Due to Continuous Charge Distributions
24.6
Conductors in Electrostatic Equilibrium
25
Capacitance and Dielectrics
25.1
Definition of Capacitance
25.2
Calculating Capacitance
25.3
Combinations of Capacitors
25.4
Energy Stored in a Charged Capacitor
25.5
Capacitors with Dielectrics
25.6
Electric Dipole in an Electric Field
25.7
An Atomic Description of Dielectrics
26
Current and Resistance
26.1
Electric Current
26.2
Resistance
26.3
A Model for Electrical Conduction
26.4
Resistance and Temperature
26.6
Electrical Power
27
Direct-Current Circuits
27.1
Electromotive Force
27.2
Resistors in Series and Parallel
27.3
Kirchhoff’s Rules
27.4
RC Circuits
27.5
Household Wiring and Electrical Safety
28
Magnetic Fields
28.1
Analysis Model: Particle in a Field (Magnetic)
28.2
Motion of a Charged Particle in a Uniform Magnetic Field
28.3
Applications Involving Charged Particles Moving in a Magnetic Field
28.4
Magnetic Force Acting on a Current-Carrying Conductor
28.5
Torque on a Current Loop in a Uniform Magnetic Field
28.6
The Hall Effect
29
Sources of the Magnetic Field
29.1
The Biot–Savart Law
29.2
The Magnetic Force Between Two Parallel Conductors
29.3
Ampère’s Law
29.4
The Magnetic Field of a Solenoid
29.5
Gauss’s Law in Magnetism
29.6
Magnetism in Matter
30
Faraday’s Law
30.1
Faraday’s Law of Induction
30.2
Motional emf
30.4
The General Form of Faraday’s Law
30.5
Generators and Motors
30.6
Eddy Currents
31
Inductance
31.1
Self-Induction and Inductance
31.2
RL Circuits
31.3
Energy in a Magnetic Field
31.4
Mutual Inductance
31.5
Oscillations in an LC Circuit
31.6
The RLC Circuit
32
Alternating-Current Circuits
32.2
Resistors in an AC Circuit
32.3
Inductors in an AC Circuit
32.4
Capacitors in an AC Circuit
32.5
The RLC Series Circuit
32.6
Power in an AC Circuit
32.7
Resonance in a Series RLC Circuit
32.8
The Transformer and Power Transmission
33
Electromagnetic Waves
33.1
Displacement Current and the General Form of Ampère’s Law
33.2
Maxwell’s Equations and Hertz’s Discoveries
33.3
Plane Electromagnetic Waves
33.4
Energy Carried by Electromagnetic Waves
33.5
Momentum and Radiation Pressure
33.6
Production of Electromagnetic Waves by an Antenna
33.7
The Spectrum of Electromagnetic Waves
34
The Nature of Light and the Principles of Ray Optics
34.1
The Nature of Light
34.3
Analysis Model: Wave Under Reflection
34.4
Analysis Model: Wave Under Refraction
34.6
Dispersion
34.7
Total Internal Reflection
35
Image Formation
35.1
Images Formed by Flat Mirrors
35.2
Images Formed by Spherical Mirrors
35.3
Images Formed by Refraction
35.4
Images Formed by Thin Lenses
35.5
Lens Aberrations
35.6
Optical Instruments
36
Wave Optics
36.2
Analysis Model: Waves in Interference
36.3
Intensity Distribution of the Double-Slit Interference Pattern
36.5
Interference in Thin Films
36.6
The Michelson Interferometer
37
Diffraction Patterns and Polarization
37.2
Diffraction Patterns from Narrow Slits
37.3
Resolution of Single-Slit and Circular Apertures
37.4
The Diffraction Grating
37.5
Diffraction of X-Rays by Crystals
37.6
Polarization of Light Waves
38
Relativity
38.1
The Principle of Galilean Relativity
38.4
Consequences of the Special Theory of Relativity
38.5
The Lorentz Transformation Equations
38.6
The Lorentz Velocity Transformation Equations
38.7
Relativistic Linear Momentum
38.8
Relativistic Energy
38.9
The General Theory of Relativity
39
Introduction to Quantum Physics
39.1
Blackbody Radiation and Planck’s Hypothesis
39.2
The Photoelectric Effect
39.3
The Compton Effect
39.4
The Nature of Electromagnetic Waves
39.5
The Wave Properties of Particles
39.6
A New Model: The Quantum Particle
39.7
The Double-Slit Experiment Revisited
39.8
The Uncertainty Principle
40
Quantum Mechanics
40.1
The Wave Function
40.2
Analysis Model: Quantum Particle Under Boundary Conditions
40.3
The Schrödinger Equation
40.4
A Particle in a Well of Finite Height
40.5
Tunneling Through a Potential Energy Barrier
40.6
Applications of Tunneling
40.7
The Simple Harmonic Oscillator
41
Atomic Physics
41.1
Atomic Spectra of Gases
41.10
Lasers
41.2
Early Models of the Atom
41.3
Bohr’s Model of the Hydrogen Atom
41.4
The Quantum Model of the Hydrogen Atom
41.5
The Wave Functions for Hydrogen
41.6
Physical Interpretation of the Quantum Numbers
41.7
The Exclusion Principle and the Periodic Table
41.8
More on Atomic Spectra: Visible and X-Ray
42
Molecules and Solids
42.1
Molecular Bonds
42.2
Energy States and Spectra of Molecules
42.3
Bonding in Solids
42.4
Free-Electron Theory of Metals
42.6
Electrical Conduction in Metals, Insulators, and Semiconductors
42.7
Semiconductor Devices
43
Nuclear Physics
43.1
Some Properties of Nuclei
43.10
Nuclear Fusion
43.11
Biological Radiation Damage
43.12
Uses of Radiation from the Nucleus
43.13
Nuclear Magnetic Resonance and Magnetic Resonance Imaging
43.2
Nuclear Binding Energy
43.3
Nuclear Models
43.4
Radioactivity
43.5
The Decay Processes
43.6
Natural Radioactivity
43.7
Nuclear Reactions
43.8
Nuclear Fission
43.9
Nuclear Reactors
44
Particle Physics and Cosmology
44.11
The Cosmic Connection
44.12
Problems and Perspectives
44.2
Positrons and Other Antiparticles
44.3
Mesons and the Beginning of Particle Physics
44.5
Conservation Laws
44.6
Strange Particles and Strangeness
44.8
Quarks
Textbook Solutions for Physics for Scientists and Engineer with Modern Physics
Chapter 6.4 Problem 22
Question
Assume the resistive force acting on a speed skater is proportional to the square of the skater's speed v and is given by f = \(-k m v^2\), where k is a constant and m is the skater's mass. The skater crosses the finish line of a straight-line race with speed \(v_i\) and then slows down by coasting on his skates. Show that the skater's speed at any time t after crossing the finish line is v(t) = \(v_i /\left(1+k t v_i\right)\).
Solution
The first step in solving 6.4 problem number trying to solve the problem we have to refer to the textbook question: Assume the resistive force acting on a speed skater is proportional to the square of the skater's speed v and is given by f = \(-k m v^2\), where k is a constant and m is the skater's mass. The skater crosses the finish line of a straight-line race with speed \(v_i\) and then slows down by coasting on his skates. Show that the skater's speed at any time t after crossing the finish line is v(t) = \(v_i /\left(1+k t v_i\right)\).
From the textbook chapter Motion in the Presence of Resistive Forces you will find a few key concepts needed to solve this.
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full solution
full solution
Title
Physics for Scientists and Engineer with Modern Physics 10
Author
Raymond A. Serway; John W. Jewett
ISBN
9781337553292
Assume the resistive force acting on a speed skater is proportional to the square of the skater's speed v and is given by f = \(-k m v^2\), where k is a constant and m is the skater's mass. The skater crosses the finish line of a straight-line race with speed \(v_i\) and then slows down by coasting on his skates. Show that the skater's speed at any time t after crossing the finish line is v(t) = \(v_i /\left(1+k t v_i\right)\).
Chapter 6.4 textbook questions
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Chapter 6: Problem 18 Physics for Scientists and Engineer with Modern Physics 10
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Chapter 6: Problem 19 Physics for Scientists and Engineer with Modern Physics 10
Review. A window washer pulls a rubber squeegee down a very tall vertical window. The squeegee has mass 160 g and is mounted on the end of a light rod. The coefficient of kinetic friction between the squeegee and the dry glass is 0.900. The window washer presses it against the window with a force having a horizontal component of 4.00 N. (a) If she pulls the squeegee down the window at constant velocity, what vertical force component must she exert? (b) The window washer increases the downward force component by 25.0%, while all other forces remain the same. Find the squeegee’s acceleration in this situation. (c) The squeegee is moved into a wet portion of the window, where its motion is resisted by a fluid drag force R proportional to its velocity according to R = -20.0v, where R is in newtons and v is in meters per second. Find the terminal velocity that the squeegee approaches, assuming the window washer exerts the same force described in part (b).
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Chapter 6: Problem 20 Physics for Scientists and Engineer with Modern Physics 10
A small piece of Styrofoam packing material is dropped from a height of 2.00 m above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by a = g - Bv. After falling 0.500 m, the Styrofoam effectively reaches terminal speed and then takes 5.00 s more to reach the ground. (a) What is the value of the constant B? (b) What is the acceleration at t = 0? (c) What is the acceleration when the speed is 0.150 m/s?
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Chapter 6: Problem 21 Physics for Scientists and Engineer with Modern Physics 10
A small, spherical bead of mass 3.00 g is released from rest at t = 0 from a point under the surface of a viscous liquid. The terminal speed is observed to be \(v_T\) = 2.00 cm/s. Find (a) the value of the constant b that appears in Equation 6.2, (b) the time t at which the bead reaches 0.632\(v_T\), and (c) the value of the resistive force when the bead reaches terminal speed.
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Chapter 6: Problem 22 Physics for Scientists and Engineer with Modern Physics 10
Assume the resistive force acting on a speed skater is proportional to the square of the skater's speed v and is given by f = \(-k m v^2\), where k is a constant and m is the skater's mass. The skater crosses the finish line of a straight-line race with speed \(v_i\) and then slows down by coasting on his skates. Show that the skater's speed at any time t after crossing the finish line is v(t) = \(v_i /\left(1+k t v_i\right)\).
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Chapter 6: Problem 23 Physics for Scientists and Engineer with Modern Physics 10
You can feel a force of air drag on your hand if you stretch your arm out of the open window of a speeding car. Note: Do not endanger yourself. What is the order of magnitude of this force? In your solution, state the quantities you measure or estimate and their values.
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