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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

- Make reasonable approximations based on given data.

$\frac{\text{2 m}}{\text{1 person}}\times \frac{\text{2 person}}{\text{1 story}}\times \text{39 stories = 156 m}\\$

.The U.S. federal deficit in the 2008 fiscal year was a little greater than $10 trillion. Most of us do not have any concept of how much even one trillion actually is. Suppose that you were given a trillion dollars in $100 bills. If you made 100-bill stacks and used them to evenly cover a football field (between the end zones), make an approximation of how high the money pile would become. (We will use feet/inches rather than meters here because football fields are measured in yards.) One of your friends says 3 in., while another says 10 ft. What do you think?

volume of stack = length × width × height

volume of stack = 6 in. × 3 in. × 0.5 in

volume of stack = 9 in.^{3}

$1 × 10^{12 }(a trillion dollars)/ $1 × 10^{4} per stack = 1 × 10^{8} stacks.

$\begin{array}{}\text{Area}={\text{5,000 yd}}^{2}\times \frac{3\text{ft}}{\text{1 yd}}\times \frac{3\text{ft}}{\text{1 yd}}\times \frac{\text{12}\text{in}\text{.}}{\text{1 ft}}\times \frac{\text{12}\text{in}\text{.}}{\text{1 ft}}=6,480,000\text{ in}{\text{.}}^{2},\\ \text{Area}\approx 6\times {\text{10}}^{6}\text{in}{\text{.}}^{2}\text{.}\end{array}\\$

This conversion gives us 6 × 10(4) Calculate the total volume of the bills. The volume of all the

$9\text{in}{\text{.}}^{3}/\text{stack}\times {\text{10}}^{8}\text{ stacks}=9\times {\text{10}}^{8}\text{in}{\text{.}}^{3}\\$

(5) Calculate the height. To determine the height of the bills, use the equation:$\begin{array}{lll}\text{volume of bills}& =& \text{area of field}\times \text{height of money:}\\ \text{Height of money}& =& \frac{\text{volume of bills}}{\text{area of field}},\\ \text{Height of money}& =& \frac{9\times {\text{10}}^{8}\text{in}{\text{.}}^{3}}{6\times {\text{10}}^{6}{\text{in.}}^{2}}=1.33\times {\text{10}}^{2}\text{in.,}\\ \text{Height of money}& \approx & 1\times {\text{10}}^{2}\text{in.}=\text{100 in.}\end{array}\\$

The height of the money will be about 100 in. high. Converting this value to feet gives

$\text{100 in}\text{.}\times \frac{\text{1 ft}}{\text{12 in}\text{.}}=8\text{.}\text{33 ft}\approx \text{8 ft.}\\$

Using mental math and your understanding of fundamental units, approximate the area of a regulation basketball court. Describe the process you used to arrive at your final approximation.

An average male is about two meters tall. It would take approximately 15 men laid out end to end to cover the length, and about 7 to cover the width. That gives an approximate area of 420 m

Scientists often approximate the values of quantities to perform calculations and analyze systems.

1. How many heartbeats are there in a lifetime?

2. A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?

3. How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of 10^{-22}.)

4. Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of 10^{-27} and the mass of a bacterium is on the order of 10^{-15}).

7. (a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is ten times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human?

8. Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?

**approximation:** an estimated value based on prior experience and reasoning

3. 2 × 10

5. 50 atoms

7. 10