Physics for Scientists and Engineers - Introduction and Chapter 1 Notes

Physics: An Introduction

Overview of Physics

• Physics is a fundamental science concerned with the universe's basic principles.
• It forms the foundation of other physical sciences.
• Physics is divided into major areas:
  • Classical Mechanics
  • Relativity
  • Thermodynamics
  • Electromagnetism
  • Optics
  • Quantum Mechanics

Classical Physics

• Mechanics and electromagnetism are fundamental to classical physics.
• Classical physics was developed before 1900 and includes:
  • Mechanics: Major developments by Newton, continuing through the 19th century.
  • Thermodynamics
  • Optics
  • Electromagnetism: Developed until the late 19th century.
• Classical Mechanics is also called Newtonian Mechanics.

Modern Physics

• Modern Physics began near the end of the 19th century.
• It addresses phenomena that classical physics could not explain.
• Includes theories of relativity and quantum mechanics.

Importance of Classical Mechanics Today

• It is still important in many disciplines.
• A wide range of phenomena can be explained with classical mechanics.
• Many basic principles carry over into other phenomena.
• Conservation Laws apply directly to other areas.

Objective of Physics

• To find the limited number of fundamental laws governing natural phenomena.
• To use these laws to develop theories that can predict the results of future experiments.
• To express the laws in the language of mathematics.

Theory and Experiments

• Theory and experiments should complement each other.
• When discrepancies occur, the theory may be modified.
• The theory may apply to limited conditions. For example, Newtonian Mechanics is confined to objects traveling slowly with respect to the speed of light.
• The goal is to develop a more general theory.

Basic Quantities in Mechanics

• Three basic quantities are used in mechanics:
  • Length
  • Mass
  • Time
• Derived quantities can be expressed in terms of these basic quantities.

Standards of Quantities

• Standardized systems are agreed upon by some authority, usually a governmental body.
• SI (Systéme International) was agreed to in 1960 by an international committee.
• SI is the main system used.

Length

• Units:
  • SI: meter (m)
• Defined in terms of a meter – the distance traveled by light in a vacuum during a given time.

Approximate Values of Some Measured Lengths

• Distance from the Earth to the most remote known quasar: $1.4 X 10^{26}$ m
• Distance from the Earth to the most remote normal galaxies: $9 × 10^{25}$ m
• Distance from the Earth to the nearest large galaxy (M 31, the Andromeda galaxy): $2 X 10^{22}$ m
• Distance from the Sun to the nearest star (Proxima Centauri): $4 X 10^{16}$ m
• One lightyear: $9.46 × 10^{15}$ m
• Mean orbit radius of the Earth about the Sun: $1.50 × 10^{11}$ m
• Mean distance from the Earth to the Moon: $3.84 X 10^8$ m
• Distance from the equator to the North Pole: $1.00 × 10^7$ m
• Mean radius of the Earth: $6.37 x 10^6$ m
• Typical altitude (above the surface) of a satellite orbiting the Earth: $2 × 10^5$ m
• Length of a football field: $9.1 × 10^1$ m
• Length of a housefly: $5 × 10^{-3}$ m
• Size of smallest dust particles: $~10^{-4}$ m
• Size of cells of most living organisms: $~10^{-5}$ m
• Diameter of a hydrogen atom: $~10^{-10}$ m
• Diameter of an atomic nucleus: $~10^{-14}$ m
• Diameter of a proton: $~10^{-15}$ m

Mass

• Units:
  • SI: kilogram (kg)
• Defined in terms of a kilogram, based on a specific cylinder kept at the International Bureau of Standards.

Masses of Various Objects (Approximate Values)

• Observable Universe: $~10^{52}$ kg
• Milky Way galaxy: $~10^{42}$ kg
• Sun: $1.99 × 10^{30}$ kg
• Earth: $5.98 X 10^{24}$ kg
• Moon: $7.36 X 10^{22}$ kg
• Shark: $~10^3$ kg
• Human: $~10^2$ kg
• Frog: $~10^{-1}$ kg
• Mosquito: $~10^{-5}$ kg
• Bacterium: $~1 × 10^{-15}$ kg
• Hydrogen atom: $1.67 x 10^{-27}$ kg
• Electron: $9.11 X 10^{-31}$ kg

Standard Kilogram

• The National Standard Kilogram No. 20 is an accurate copy of the International Standard Kilogram kept at Sèvres, France.
• It is housed under a double bell jar in a vault at the National Institute of Standards and Technology.

Time

• Units:
  • seconds (s)
• Defined in terms of the oscillation of radiation from a cesium atom.

Approximate Values of Some Time Intervals

• Age of the Universe: $5 × 10^{17}$ s
• Age of the Earth: $1.3 × 10^{17}$ s
• Average age of a college student: $6.3 x 10^8$ s
• One year: $3.2 × 10^7$ s
• One day (time interval for one revolution of the Earth about its axis): $8.6 × 10^4$ s
• One class period: $3.0 × 10^3$ s
• Time interval between normal heartbeats: $8 × 10^{-1}$ s
• Period of audible sound waves: $10^{-3}$ s
• Period of typical radio waves: $~10^{-6}$ s
• Period of vibration of an atom in a solid: $~10^{-13}$ s
• Period of visible light waves: $~10^{-15}$ s
• Duration of a nuclear collision: $10^{-22}$ s
• Time interval for light to cross a proton: $10^{-24}$ s

Number Notation

• When writing numbers with many digits, spacing in groups of three will be used (no commas).
• Examples:
  • 25 100
  • 5. 123 456 789 12

Reasonableness of Results

• When solving a problem, check if the answer seems reasonable.
• Reviewing tables of approximate values for length, mass, and time will help test for reasonableness.

Systems of Measurements

• US Customary:
  • Everyday units
  • Length is measured in feet.
  • Time is measured in seconds.
  • Mass is measured in slugs.
  • Often uses weight, in pounds, instead of mass as a fundamental quantity.

Prefixes

• Prefixes correspond to powers of 10.
• Each prefix has a specific name and abbreviation.
• Prefixes can be used with any base units.
• They are multipliers of the base unit.
• Examples:
  • 1 mm = $10^{-3}$ m
  • 1 mg = $10^{-3}$ g

Model Building

• A model is a system of physical components.
• Steps:
  • Identify the components.
  • Make predictions about the behavior of the system.
  • The predictions will be based on interactions among the components and/or interactions between the components and the environment.

Models of Matter

• Some Greeks thought matter is made of atoms.
• JJ Thomson (1897) found electrons and showed atoms had structure.
• Rutherford (1911) discovered the central nucleus surrounded by electrons.
• The nucleus has structure, containing protons and neutrons.
• The number of protons gives the atomic number.
• The number of protons and neutrons gives the mass number.
• Protons and neutrons are made up of quarks.

Modeling Technique

• An important technique is to build a model for a problem.
• Steps:
  • Identify a system of physical components for the problem.
  • Make predictions of the behavior of the system based on the interactions among the components and/or the components and the environment.

Density

• Density is an example of a derived quantity.
• It is defined as mass per unit volume.
• The formula for density is: $\rho \equiv \frac{m}{V}$
• Units are kg/m$^3$

Densities of Various Substances

• Platinum: $21.45 × 10^3$ kg/m$^3$
• Gold: $19.3 × 10^3$ kg/m$^3$
• Uranium: $18.7 × 10^3$ kg/m$^3$
• Lead: $11.3 × 10^3$ kg/m$^3$
• Copper: $8.92 × 10^3$ kg/m$^3$
• Iron: $7.86 × 10^3$ kg/m$^3$
• Aluminum: $2.70 × 10^3$ kg/m$^3$
• Magnesium: $1.75 × 10^3$ kg/m$^3$
• Water: $1.00 × 10^3$ kg/m$^3$
• Air at atmospheric pressure: $0.0012 × 10^3$ kg/m$^3$

Atomic Mass

• The atomic mass is the total number of protons and neutrons in the element.
• Can be measured in atomic mass units (u).
• 1 u = $1.6605387 x 10^{-27}$ kg

Basic Quantities and Their Dimension

• Dimension denotes the physical nature of a quantity.
• Dimensions are denoted with square brackets.
  • Length [L]
  • Mass [M]
  • Time [T]

Dimensional Analysis

• Dimensional Analysis is a technique to check the correctness of an equation or to assist in deriving an equation.
• Dimensions (length, mass, time, combinations) can be treated as algebraic quantities (add, subtract, multiply, divide).
• Both sides of an equation must have the same dimensions.

Symbols

• The symbol used in an equation is not necessarily the symbol used for its dimension.
• Some quantities have one symbol used consistently (e.g., time is t).
• Some quantities have many symbols, depending upon the specific situation (e.g., lengths may be x, y, z, r, d, h, etc.).

Dimensional Analysis Example

• Given the equation: $x = \frac{1}{2} a t^2$
• Checking dimensions on each side:
  • $\frac{L}{T^2} T^2 = L$
• The T$^2$’s cancel, leaving L for the dimensions of each side.
• The equation is dimensionally correct.

Conversion of Units

• When units are not consistent, convert to appropriate ones.
• Units can be treated like algebraic quantities that can cancel each other out.

Conversion Example

• Always include units for every quantity; carry the units through the entire calculation.
• Multiply the original value by a ratio equal to one.
• Example:
  • 15.0 in = ? cm
  • $15.0 \text{ in} = 15.0 \text{ in} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 38.1 \text{ cm}$

Significant Figures

• A significant figure is one that is reliably known.
• Zeros may or may not be significant.
• Those used to position the decimal point are not significant.
• To remove ambiguity, use scientific notation.
• In a measurement, the significant figures include the first estimated digit.

Significant Figures Examples

• 0.0075 m has 2 significant figures (leading zeros are placeholders).
  • Can write $7.5 x 10^{-3}$ m for 2 significant figures.
• 10.0 m has 3 significant figures (the decimal point gives information about the reliability of the measurement).
• 1500 m is ambiguous.
  • Use $1.5 x 10^3$ m for 2 significant figures.
  • Use $1.50 x 10^3$ m for 3 significant figures.
  • Use $1.500 x 10^3$ m for 4 significant figures.

Operations with Significant Figures – Multiplying or Dividing

• When multiplying or dividing, the number of significant figures in the final answer is the same as the number of significant figures in the quantity having the lowest number of significant figures.
• Example: 25.57 m x 2.45 m = 62.6 m$^2$
  • The 2.45 m limits your result to 3 significant figures.

Operations with Significant Figures – Adding or Subtracting

• When adding or subtracting, the number of decimal places in the result should equal the smallest number of decimal places in any term in the sum.
• Example: 135 cm + 3.25 cm = 138 cm
  • The 135 cm limits your answer to the units decimal value.

Operations With Significant Figures – Summary

• The rule for addition and subtraction is different than the rule for multiplication and division.
• For adding and subtracting, the number of decimal places is the important consideration.
• For multiplying and dividing, the number of significant figures is the important consideration.

Rounding

• The last retained digit is increased by 1 if the last digit dropped is 5 or above.
• The last retained digit remains as it is if the last digit dropped is less than 5.
• If the last digit dropped is equal to 5, the retained digit should be rounded to the nearest even number.
• Saving rounding until the final result will help eliminate the accumulation of errors.

Problem Solving Tactics

• Explain the problem with your own words.
• Make a good picture describing the problem.
• Write down the given data with their units. Convert all data into the SI system.
• Identify the unknowns.
• Find the connections between the unknowns and the data.
• Write the physical equations that can be applied to the problem.
• Solve those equations.
• Check if the values obtained are reasonable (order of magnitude and units).

Reasonableness of Results (Revisited)

• When solving a problem, you need to check your answer to see if it seems reasonable
• Reviewing the tables of approximate values for length, mass, and time will help you test for reasonableness