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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

- Perform unit conversions both in the SI and English units.
- Explain the most common prefixes in the SI units and be able to write them in scientific notation.

The range of objects and phenomena studied in physics is immense. From the incredibly short lifetime of a nucleus to the age of the Earth, from the tiny sizes of sub-nuclear particles to the vast distance to the edges of the known universe, from the force exerted by a jumping flea to the force between Earth and the Sun, there are enough factors of 10 to challenge the imagination of even the most experienced scientist. Giving numerical values for physical quantities and equations for physical principles allows us to understand nature much more deeply than does qualitative description alone. To comprehend these vast ranges, we must also have accepted units in which to express them. And we shall find that (even in the potentially mundane discussion of meters, kilograms, and seconds) a profound simplicity of nature appears—all physical quantities can be expressed as combinations of only four fundamental physical quantities: length, mass, time, and electric current.

Measurements of physical quantities are expressed in terms of

Length |
Mass |
Time |
Electric Current |
---|---|---|---|

meter (m) | kilogram (kg) | second (s) | ampere (A) |

Metric systems have the advantage that conversions of units involve only powers of 10. There are 100 centimeters in a meter, 1000 meters in a kilometer, and so on. In non-metric systems, such as the system of U.S. customary units, the relationships are not as simple—there are 12 inches in a foot, 5280 feet in a mile, and so on. Another advantage of the metric system is that the same unit can be used over extremely large ranges of values simply by using an appropriate metric prefix. For example, distances in meters are suitable in construction, while distances in kilometers are appropriate for air travel, and the tiny measure of nanometers are convenient in optical design. With the metric system there is no need to invent new units for particular applications.

The term order of magnitude refers to the scale of a value expressed in the metric system. Each power of 10 in the metric system represents a different order of magnitude. For example, 10

The fundamental units described in this chapter are those that produce the greatest accuracy and precision in measurement. There is a sense among physicists that, because there is an underlying microscopic substructure to matter, it would be most satisfying to base our standards of measurement on microscopic objects and fundamental physical phenomena such as the speed of light. A microscopic standard has been accomplished for the standard of time, which is based on the oscillations of the cesium atom.

The standard for length was once based on the wavelength of light (a small-scale length) emitted by a certain type of atom, but it has been supplanted by the more precise measurement of the speed of light. If it becomes possible to measure the mass of atoms or a particular arrangement of atoms such as a silicon sphere to greater precision than the kilogram standard, it may become possible to base mass measurements on the small scale. There are also possibilities that electrical phenomena on the small scale may someday allow us to base a unit of charge on the charge of electrons and protons, but at present current and charge are related to large-scale currents and forces between wires.

The standard for length was once based on the wavelength of light (a small-scale length) emitted by a certain type of atom, but it has been supplanted by the more precise measurement of the speed of light. If it becomes possible to measure the mass of atoms or a particular arrangement of atoms such as a silicon sphere to greater precision than the kilogram standard, it may become possible to base mass measurements on the small scale. There are also possibilities that electrical phenomena on the small scale may someday allow us to base a unit of charge on the charge of electrons and protons, but at present current and charge are related to large-scale currents and forces between wires.

Prefix | Symbol | Value^{[2]} |
Example (some are approximate) | |||
---|---|---|---|---|---|---|

exa | E | ${\text{10}}^{\text{18}}$ |
exameter | Em | ${\text{10}}^{\text{18}}\text{ m}$ |
distance light travels in a century |

peta | P | ${\text{10}}^{\text{15}}$ |
petasecond | Ps | ${\text{10}}^{\text{15}}\text{ s}$ |
30 million years |

tera | T | ${\text{10}}^{\text{12}}$ |
terawatt | TW | ${\text{10}}^{\text{12}}\text{ W}$ |
powerful laser output |

giga | G | ${\text{10}}^{9}$ |
gigahertz | GHz | ${\text{10}}^{9}\text{ Hz}$ |
a microwave frequency |

mega | M | ${\text{10}}^{6}$ |
megacurie | MCi | ${\text{10}}^{6}\text{ Ci}$ |
high radioactivity |

kilo | k | ${\text{10}}^{3}$ |
kilometer | km | ${\text{10}}^{3}\text{ m}$ |
about 6/10 mile |

hecto | h | ${\text{10}}^{2}$ |
hectoliter | hL | ${\text{10}}^{2}\text{ L}$ |
26 gallons |

deka | da | ${\text{10}}^{1}$ |
dekagram | dag | ${\text{10}}^{1}\text{ g}$ |
teaspoon of butter |

— | — | ${\text{10}}^{0}$ (=1) |
||||

deci | d | ${\text{10}}^{-1}$ |
deciliter | dL | ${\text{10}}^{-1}\text{ L}$ |
less than half a soda |

centi | c | ${\text{10}}^{-2}$ |
centimeter | cm | ${\text{10}}^{-2}\text{ m}$ |
fingertip thickness |

milli | m | ${\text{10}}^{-3}$ |
millimeter | mm | ${\text{10}}^{-3}\text{ m}$ |
flea at its shoulders |

micro | µ | ${\text{10}}^{-6}$ |
micrometer | µm | ${\text{10}}^{-6}\text{ m}$ |
detail in microscope |

nano | n | ${\text{10}}^{-9}$ |
nanogram | ng | ${\text{10}}^{-9}\text{ g}$ |
small speck of dust |

pico | p | ${\text{10}}^{-\text{12}}$ |
picofarad | pF | ${\text{10}}^{-\text{12}}\text{ F}$ |
small capacitor in radio |

femto | f | ${\text{10}}^{-\text{15}}$ |
femtometer | fm | ${\text{10}}^{-\text{15}}\text{ m}$ |
size of a proton |

atto | a | ${\text{10}}^{-\text{18}}$ |
attosecond | as | ${\text{10}}^{-\text{18}}\text{ s}$ |
time light crosses an atom |

Let us consider a simple example of how to convert units. Let us say that we want to convert 80 meters (m) to kilometers (km).

The first thing to do is to list the units that you have and the units that you want to convert to. In this case, we have units in

Next, we need to determine a

Now we can set up our unit conversion. We will write the units that we have and then multiply them by the conversion factor so that the units cancel out, as shown:

$80\overline{)\text{m}}\times \frac{\text{1 km}}{1000\overline{)\text{m}}}=0\text{.080 km.}\\$

Note that the unwanted m unit cancels, leaving only the desired km unit. You can use this method to convert between any types of unit.Lengths in meters | Masses in kilograms (more precise values in parentheses) | Times in seconds (more precise values in parentheses) | |||
---|---|---|---|---|---|

${\text{10}}^{-\text{18}}$ |
Present experimental limit to smallest observable detail | ${\text{10}}^{-\text{30}}$ |
Mass of an electron $\left(9\text{.}\text{11}\times {\text{10}}^{-\text{31}}\text{ kg}\right)$ |
${\text{10}}^{-\text{23}}$ |
Time for light to cross a proton |

${\text{10}}^{-\text{15}}$ |
Diameter of a proton | ${\text{10}}^{-\text{27}}$ |
Mass of a hydrogen atom $\left(1\text{.}\text{67}\times {\text{10}}^{-\text{27}}\text{ kg}\right)$ |
${\text{10}}^{-\text{22}}$ |
Mean life of an extremely unstable nucleus |

${\text{10}}^{-\text{14}}$ |
Diameter of a uranium nucleus | ${\text{10}}^{-\text{15}}$ |
Mass of a bacterium | ${\text{10}}^{-\text{15}}$ |
Time for one oscillation of visible light |

${\text{10}}^{-\text{10}}$ |
Diameter of a hydrogen atom | ${\text{10}}^{-5}$ |
Mass of a mosquito | ${\text{10}}^{-\text{13}}$ |
Time for one vibration of an atom in a solid |

${\text{10}}^{-8}$ |
Thickness of membranes in cells of living organisms | ${\text{10}}^{-2}$ |
Mass of a hummingbird | ${\text{10}}^{-8}$ |
Time for one oscillation of an FM radio wave |

${\text{10}}^{-6}$ |
Wavelength of visible light | $\text{1}$ |
Mass of a liter of water (about a quart) | ${\text{10}}^{-3}$ |
Duration of a nerve impulse |

${\text{10}}^{-3}$ |
Size of a grain of sand | ${\text{10}}^{2}$ |
Mass of a person | $\text{1}$ |
Time for one heartbeat |

$\text{1}$ |
Height of a 4-year-old child | ${\text{10}}^{3}$ |
Mass of a car | ${\text{10}}^{5}$ |
One day $\left(8\text{.}\text{64}\times {\text{10}}^{4}\text{s}\right)$ |

${\text{10}}^{2}$ |
Length of a football field | ${\text{10}}^{8}$ |
Mass of a large ship | ${\text{10}}^{7}$ |
One year (y) $\left(3\text{.}\text{16}\times {\text{10}}^{7}\text{s}\right)$ |

${\text{10}}^{4}$ |
Greatest ocean depth | ${\text{10}}^{\text{12}}$ |
Mass of a large iceberg | ${\text{10}}^{9}$ |
About half the life expectancy of a human |

${\text{10}}^{7}$ |
Diameter of the Earth | ${\text{10}}^{\text{15}}$ |
Mass of the nucleus of a comet | ${\text{10}}^{\text{11}}$ |
Recorded history |

${\text{10}}^{\text{11}}$ |
Distance from the Earth to the Sun | ${\text{10}}^{\text{23}}$ |
Mass of the Moon $\left(7\text{.}\text{35}\times {\text{10}}^{\text{22}}\text{ kg}\right)$ |
${\text{10}}^{\text{17}}$ |
Age of the Earth |

${\text{10}}^{\text{16}}$ |
Distance traveled by light in 1 year (a light year) | ${\text{10}}^{\text{25}}$ |
Mass of the Earth $\left(5\text{.}\text{97}\times {\text{10}}^{\text{24}}\text{ kg}\right)$ |
${\text{10}}^{\text{18}}$ |
Age of the universe |

${\text{10}}^{\text{21}}$ |
Diameter of the Milky Way galaxy | ${\text{10}}^{\text{30}}$ |
Mass of the Sun $\left(1\text{.}\text{99}\times {\text{10}}^{\text{30}}\text{ kg}\right)$ |
||

${\text{10}}^{\text{22}}$ |
Distance from the Earth to the nearest large galaxy (Andromeda) | ${\text{10}}^{\text{42}}$ |
Mass of the Milky Way galaxy (current upper limit) | ||

${\text{10}}^{\text{26}}$ |
Distance from the Earth to the edges of the known universe | ${\text{10}}^{\text{53}}$ |
Mass of the known universe (current upper limit) |

Suppose that you drive the 10.0 km from your university to home in 20.0 min. Calculate your average speed (a) in kilometers per hour (km/h) and (b) in meters per second (m/s). (Note: Average speed is distance traveled divided by time of travel.)

**Strategy**

**Solution for (a)**

**Discussion for (a)**

**Solution for (b)**

**Discussion for (b)**

First we calculate the average speed using the given units. Then we can get the average speed into the desired units by picking the correct conversion factor and multiplying by it. The correct conversion factor is the one that cancels the unwanted unit and leaves the desired unit in its place.

(1) Calculate average speed. Average speed is distance traveled divided by time of travel. (Take this definition as a given for now—average speed and other motion concepts will be covered in a later module.) In equation form,

$\text{average speed =}\frac{\text{distance}}{\text{time}}\\$

.(2) Substitute the given values for distance and time.

$\text{average speed =}\frac{\text{10}\text{.}0\text{ km}}{\text{20}\text{.}0\text{ min}}=0\text{.}\text{500}\frac{\text{ km}}{\text{ min}}\\$

.(3) Convert km/min to km/h: multiply by the conversion factor that will cancel minutes and leave hours. That conversion factor is 60 min/hr. Thus,

$\text{average speed =}0\text{.}\text{500}\frac{\text{ km}}{\text{ min}}\times \frac{\text{60}\text{ min}}{1\text{ h}}=\text{30}\text{.}0\frac{\text{ km}}{\text{ h}}\\$

.To check your answer, consider the following:

(1) Be sure that you have properly cancelled the units in the unit conversion. If you have written the unit conversion factor upside down, the units will not cancel properly in the equation. If you accidentally get the ratio upside down, then the units will not cancel; rather, they will give you the wrong units as follows:

$\frac{\text{ km}}{\text{min}}\times \frac{1\text{ hr}}{\text{60}\text{ min}}=\frac{1}{\text{60}}\frac{\text{ km}\cdot \text{hr}}{{\text{ min}}^{2}}\\$

,which are obviously not the desired units of km/h.

(2) Check that the units of the final answer are the desired units. The problem asked us to solve for average speed in units of km/h and we have indeed obtained these units.

(3) Check the significant figures. Because each of the values given in the problem has three significant figures, the answer should also have three significant figures. The answer 30.0 km/hr does indeed have three significant figures, so this is appropriate. Note that the significant figures in the conversion factor are not relevant because an hour is *defined* to be 60 minutes, so the precision of the conversion factor is perfect.

(4) Next, check whether the answer is reasonable. Let us consider some information from the problem—if you travel 10 km in a third of an hour (20 min), you would travel three times that far in an hour. The answer does seem reasonable.

There are several ways to convert the average speed into meters per second.

(1) Start with the answer to (a) and convert km/h to m/s. Two conversion factors are needed—one to convert hours to seconds, and another to convert kilometers to meters.

(2) Multiplying by these yields

$\text{Average speed}=\text{30}\text{.}0\frac{\text{km}}{\text{h}}\times \frac{1\text{h}}{\text{3,600 s}}\times \frac{1,\text{000}\text{m}}{\text{1 km}}$

,$\text{Average speed}=8\text{.}\text{33}\frac{\text{m}}{\text{s}}\\$

.If we had started with 0.500 km/min, we would have needed different conversion factors, but the answer would have been the same: 8.33 m/s.

You may have noted that the answers in the worked example just covered were given to three digits. Why? When do you need to be concerned about the number of digits in something you calculate? Why not write down all the digits your calculator produces? The module Accuracy, Precision, and Significant Figures will help you answer these questions.

2. One cubic centimeter is equal to one milliliter. What does this tell you about the different units in the SI metric system?

2. The fundamental unit of length (meter) is probably used to create the derived unit of volume (liter). The measure of a milliliter is dependent on the measure of a centimeter.

- Physical quantities are a characteristic or property of an object that can be measured or calculated from other measurements.
- Units are standards for expressing and comparing the measurement of physical quantities. All units can be expressed as combinations of four fundamental units.
- The four fundamental units we will use in this text are the meter (for length), the kilogram (for mass), the second (for time), and the ampere (for electric current). These units are part of the metric system, which uses powers of 10 to relate quantities over the vast ranges encountered in nature.
- The four fundamental units are abbreviated as follows: meter, m; kilogram, kg; second, s; and ampere, A. The metric system also uses a standard set of prefixes to denote each order of magnitude greater than or lesser than the fundamental unit itself.
- Unit conversions involve changing a value expressed in one type of unit to another type of unit. This is done by using conversion factors, which are ratios relating equal quantities of different units.

1. Identify some advantages of metric units.

2. A car is traveling at a speed of 33 m/s. (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h speed limit?

3. Show that 1.0 m/s = 3.6 km/h. Hint: Show the explicit steps involved in converting 1.0 m/s = 3.6 km/h.

4. American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)

5. Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)

6. What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)

7. Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)

8. The speed of sound is measured to be 342 m/s on a certain day. What is this in km/h?

9. Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

10. (a) Refer to

- physical quantity:
- a characteristic or property of an object that can be measured or calculated from other measurements

- units:
- a standard used for expressing and comparing measurements

- SI units:
- the international system of units that scientists in most countries have agreed to use; includes units such as meters, liters, and grams

- English units:
- system of measurement used in the United States; includes units of measurement such as feet, gallons, and pounds

- fundamental units:
- units that can only be expressed relative to the procedure used to measure them

- derived units:
- units that can be calculated using algebraic combinations of the fundamental units

- second:
- the SI unit for time, abbreviated (s)

- meter:
- the SI unit for length, abbreviated (m)

- kilogram:
- the SI unit for mass, abbreviated (kg)

- metric system:
- a system in which values can be calculated in factors of 10

- order of magnitude:
- refers to the size of a quantity as it relates to a power of 10

- conversion factor:
- a ratio expressing how many of one unit are equal to another unit

3.

5. length: 377 ft; 4.53 × 10^{3} in. width: 280 ft; 3.3 × 10^{3} in.

7. 8.847 kn

9. (a) 1.3 × 10^{−9} m (b) 40 km/My

$\frac{\text{1.0 m}}{s}=\frac{1\text{.}\text{0 m}}{s}\times \frac{\text{3600 s}}{\text{1 hr}}\times \frac{1 km}{\text{1000 m}}\\$

5. length: 377 ft; 4.53 × 10

7. 8.847 kn

9. (a) 1.3 × 10