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HomeStudy GuidesPhysics

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The Nature of Science and Physics

Kinematics

Introduction to One-Dimensional KinematicsDisplacementVectors, Scalars, and Coordinate SystemsTime, Velocity, and SpeedVideo: One-Dimensional KinematicsAccelerationMotion Equations for Constant Acceleration in One DimensionProblem-Solving Basics for One-Dimensional KinematicsFalling ObjectsGraphical Analysis of One-Dimensional Motion

Two-Dimensional Kinematics

Dynamics: Force and Newton's Laws of Motion

Introduction to Dynamics: Newton's Laws of MotionDevelopment of Force ConceptNewton's First Law of Motion: InertiaNewton's Second Law of Motion: Concept of a SystemNewton's Third Law of Motion: Symmetry in ForcesVideo: Newton's LawsNormal, Tension, and Other Examples of ForcesProblem-Solving StrategiesFurther Applications of Newton's Laws of MotionExtended Topic: The Four Basic Forces—An Introduction

Further Applications of Newton's Laws: Friction, Drag, and Elasticity

Uniform Circular Motion and Gravitation

Introduction to Uniform Circular Motion and GravitationRotation Angle and Angular VelocityCentripetal AccelerationCentripetal ForceFictitious Forces and Non-inertial Frames: The Coriolis ForceNewton's Universal Law of GravitationVideo: GravitationSatellites and Kepler's Laws: An Argument for Simplicity

Work, Energy, and Energy Resources

Introduction to Work, Energy, and Energy ResourcesWork: The Scientific DefinitionKinetic Energy and the Work-Energy TheoremGravitational Potential EnergyVideo: Potential and Kinetic EnergyConservative Forces and Potential EnergyNonconservative ForcesConservation of EnergyPowerWork, Energy, and Power in HumansWorld Energy Use

Linear Momentum and Collisions

Rotational Motion and Angular Momentum

Introduction to Rotational Motion and Angular MomentumAngular AccelerationKinematics of Rotational MotionVideo: Rotational MotionDynamics of Rotational Motion: Rotational InertiaRotational Kinetic Energy: Work and Energy RevisitedAngular Momentum and Its ConservationVideo: Angular MomentumCollisions of Extended Bodies in Two DimensionsGyroscopic Effects: Vector Aspects of Angular Momentum

Statics and Torque

Fluid Statics

Introduction to Fluid StaticsWhat Is a Fluid?DensityPressureVariation of Pressure with Depth in a FluidPascal's PrincipleGauge Pressure, Absolute Pressure, and Pressure MeasurementArchimedes' PrincipleVideo: BuoyancyCohesion and Adhesion in Liquids: Surface Tension and Capillary ActionPressures in the Body

Fluid Dynamics and Its Biological and Medical Applications

Introduction to Fluid Dynamics and Biological and Medical ApplicationsFlow Rate and Its Relation to VelocityBernoulli's EquationVideo: Fluid FlowThe Most General Applications of Bernoulli's EquationViscosity and Laminar Flow; Poiseuille's LawThe Onset of TurbulenceMotion of an Object in a Viscous FluidMolecular Transport Phenomena: Diffusion, Osmosis, and Related Processes

Temperature, Kinetic Theory, and the Gas Laws

Heat and Heat Transfer Methods

Thermodynamics

Introduction to ThermodynamicsThe First Law of ThermodynamicsThe First Law of Thermodynamics and Some Simple ProcessesIntroduction to the Second Law of Thermodynamics: Heat Engines and Their EfficiencyCarnot's Perfect Heat Engine: The Second Law of Thermodynamics RestatedApplications of Thermodynamics: Heat Pumps and RefrigeratorsEntropy and the Second Law of Thermodynamics: Disorder and the Unavailability of EnergyStatistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation

Oscillatory Motion and Waves

Introduction to Oscillatory Motion and WavesHooke's Law: Stress and Strain RevisitedPeriod and Frequency in OscillationsSimple Harmonic Motion: A Special Periodic MotionVideo: Harmonic MotionThe Simple PendulumEnergy and the Simple Harmonic OscillatorUniform Circular Motion and Simple Harmonic MotionDamped Harmonic MotionForced Oscillations and ResonanceWavesSuperposition and InterferenceEnergy in Waves: Intensity

Physics of Hearing

- Calculate the intensity and the power of rays and waves.

All waves carry energy. The energy of some waves can be directly observed. Earthquakes can shake whole cities to the ground, performing the work of thousands of wrecking balls.

Loud sounds pulverize nerve cells in the inner ear, causing permanent hearing loss. Ultrasound is used for deep-heat treatment of muscle strains. A laser beam can burn away a malignancy. Water waves chew up beaches.

The amount of energy in a wave is related to its amplitude. Large-amplitude earthquakes produce large ground displacements. Loud sounds have higher pressure amplitudes and come from larger-amplitude source vibrations than soft sounds. Large ocean breakers churn up the shore more than small ones. More quantitatively, a wave is a displacement that is resisted by a restoring force. The larger the displacement

The energy effects of a wave depend on time as well as amplitude. For example, the longer deep-heat ultrasound is applied, the more energy it transfers. Waves can also be concentrated or spread out. Sunlight, for example, can be focused to burn wood. Earthquakes spread out, so they do less damage the farther they get from the source. In both cases, changing the area the waves cover has important effects. All these pertinent factors are included in the definition of

$I=\frac{P}{A}\\$

, where - Calculate the amount of energy that falls on a solar collector having an area of 0.500 m
^{2}in 4.00 h. - What intensity would such sunlight have if concentrated by a magnifying glass onto an area 200 times smaller than its own?

$P=\frac{E}{t}\\$

, the definition of intensity can be written as$\displaystyle{I}=\frac{P}{A}=\frac{\frac{E}{t}}{A}\\$

,
and this equation can be solved for E with the given information.$I=\frac{P}{A}\\$

Replace

$\frac{E}{t}\\$

:$\displaystyle{I}=\frac{\frac{E}{t}}{A}\\$

.
Solve for Substitute known values into the equation:

Calculate to find

$\displaystyle\frac{I\prime}{I}=\frac{\frac{P\prime}{A\prime}}{\frac{P}{A}}=\frac{A}{A\prime}\\$

(The powers cancel because *A*= 200*A*′- $\frac{I\prime}{I}=200\\$

Substitute known quantities:

Calculate to find

Calculate the new amplitude:

Recall that the intensity of the old amplitude was

Take the ratio of new intensity to the old intensity. This gives

$\frac{I\prime}{I}=4\\$

.Calculate to find

The intensity goes up by a factor of 4 when the amplitude doubles. This answer is a little disquieting. The two individual waves each have intensities of 1.00 W/m

- Intensity is defined to be the power per unit area: $I=\frac{P}{A}\\$and has units of W/m
^{2}.

- Two identical waves undergo pure constructive interference. Is the resultant intensity twice that of the individual waves? Explain your answer.
- Circular water waves decrease in amplitude as they move away from where a rock is dropped. Explain why.

**Medical Application.**Ultrasound of intensity 1.50 × 10^{2}W/m^{2}is produced by the rectangular head of a medical imaging device measuring 3.00 by 5.00 cm. What is its power output?- The low-frequency speaker of a stereo set has a surface area of 0.05 m
^{2}and produces 1W of acoustical power. What is the intensity at the speaker? If the speaker projects sound uniformly in all directions, at what distance from the speaker is the intensity 0.1 W/m^{2}? - To increase intensity of a wave by a factor of 50, by what factor should the amplitude be increased?
**Engineering Application.**A device called an insolation meter is used to measure the intensity of sunlight has an area of 100 cm2 and registers 6.50 W. What is the intensity in W/m^{2}?**Astronomy Application.**Energy from the Sun arrives at the top of the Earth’s atmosphere with an intensity of 1.30 kW/m^{2}. How long does it take for 1.8 × 10^{9}J to arrive on an area of 1.00 m^{2}?- Suppose you have a device that extracts energy from ocean breakers in direct proportion to their intensity. If the device produces 10.0 kW of power on a day when the breakers are 1.20 m high, how much will it produce when they are 0.600 m high?
**Engineering Application.**(a) A photovoltaic array of (solar cells) is 10.0% efficient in gathering solar energy and converting it to electricity. If the average intensity of sunlight on one day is 700 W/m^{2}, what area should your array have to gather energy at the rate of 100 W? (b) What is the maximum cost of the array if it must pay for itself in two years of operation averaging 10.0 hours per day? Assume that it earns money at the rate of 9.00 ¢ per kilowatt-hour.- A microphone receiving a pure sound tone feeds an oscilloscope, producing a wave on its screen. If the sound intensity is originally 2.00 × 10
^{−5}W/m^{2}, but is turned up until the amplitude increases by 30.0%, what is the new intensity? **Medical Application.**(a) What is the intensity in W/m^{2}of a laser beam used to burn away cancerous tissue that, when 90.0% absorbed, puts 500 J of energy into a circular spot 2.00 mm in diameter in 4.00 s? (b) Discuss how this intensity compares to the average intensity of sunlight (about 700 W/m^{2}) and the implications that would have if the laser beam entered your eye. Note how your answer depends on the time duration of the exposure.

3. 7.07

5. 16.0 d

6. 2.50 kW

8. 3.38 × 10