College Physics

Chapter 1Introduction

Theories and Experiments The goal of physics is to develop

theories based on experiments A theory is a “guess,” expressed

mathematically, about how a system works

The theory makes predictions about how a system should work

Experiments check the theories’ predictions

Every theory is a work in progress

Fundamental Quantities and Their Dimension Length [L] Mass [M] Time [T]

other physical quantities can be constructed from these three

Units To communicate the result of a

measurement for a quantity, a unit must be defined

Defining units allows everyone to relate to the same fundamental amount

Systems of Measurement Standardized systems

agreed upon by some authority, usually a governmental body

SI -- Systéme International agreed to in 1960 by an international

committee main system used in this text also called mks for the first letters in the

units of the fundamental quantities

Systems of Measurements, cont cgs – Gaussian system

named for the first letters of the units it uses for fundamental quantities

US Customary everyday units often uses weight, in pounds, instead

of mass as a fundamental quantity

Length Units

SI – meter, m cgs – centimeter, cm US Customary – foot, ft

Defined in terms of a meter – the distance traveled by light in a vacuum during a given time of 1/299792458 second. This establishes the speed of light at 299792458 m/sec or its accepted value of 3.00 x 108 m/s.

Mass Units

SI – kilogram, kg cgs – gram, g USC – slug, slug

Defined in terms of kilogram, based on a specific cylinder of platinum and iridium alloy kept at the International Bureau of Weights and Measures located in Sevres, France.

Standard Kilogram

Time Units

seconds, s in all three systems

9192631700 times the period of oscillation of radiation from a cesium atom

Approximate Values Various tables in the text show

approximate values for length, mass, and time: See Page 3 Note the wide range of values Lengths – Table 1.1 Masses – Table 1.2 Time intervals – Table 1.3

Prefixes Prefixes correspond to powers of 10 Each prefix has a specific name Each prefix has a specific abbreviation See table 1.4 found on page 4

Common prefixes to remember:

109 giga, G 106 mega, M 103 kilo, k101 deka, da 10-1 deci, d 10-2 centi, c10-3 milli, m 10-6 micro, 10-9 nano, n

Structure of Matter Matter is made up of molecules

the smallest division that is identifiable as a substance

Bodies of mass smaller than the molecule will not have characteristics of a unique substance

Molecules are made up of atoms correspond to elements

More structure of matter Atoms are made up of

nucleus, very dense, contains protons, positively charged, “heavy” neutrons, no charge, about same mass as

protons protons and neutrons are made up of quarks

orbited by electrons, negatively charges, “light”

fundamental particle, no structure

Structure of Matter

Structure of Matter

Quarks – up, down, strange, charm, bottom, and top.

Up, Charm, and Top have a charge of + that of a proton.

Down, Strange, and Bottom have a charge of - that of a proton.

The proton has two up quarks and one down quark. + - = + 1.

The neutron has two down quarks and one up quark. - - + = 0.

The other quarks are indirectly observed and not well understood.

Dimensional Analysis Technique to check the

correctness of an equation Dimensions (length, mass, time,

combinations) can be treated as algebraic quantities add, subtract, multiply, divide

Both sides of equation must have the same dimensions

Dimensional Analysis, cont. Cannot give numerical factors: this is its

limitation Dimensions of some common quantities are

listed in Table 1.5 on page 5. Example: [a] = [v]/[t]; L/T = {x}/{t2}

T x = at2

Uncertainty in Measurements There is uncertainty in every

measurement, this uncertainty carries over through the calculations need a technique to account for this

uncertainty We will use rules for significant figures

to approximate the uncertainty in results of calculations

Significant Figures A significant figure is one that is reliably

known All non-zero digits are significant Zeros are significant when

between other non-zero digits after the decimal point and another

significant figure can be clarified by using scientific notation

Operations with Significant Figures Accuracy – number of significant figures When multiplying or dividing two or

more quantities, the number of significant figures in the final result is the same as the number of significant figures in the least accurate of the factors being combined

Operations with Significant Figures, cont. When adding or subtracting, round the

result to the smallest number of decimal places of any term in the sum

If the last digit to be dropped is less than 5, drop the digit

If the last digit dropped is greater than or equal to 5, raise the last retained digit by 1

Conversions When units are not consistent, you may

need to convert to appropriate ones Units can be treated like algebraic

quantities that can “cancel” each other See the inside of the front cover for an

extensive list of conversion factors Example:

2.5415.0 38.1

1

cmin cm

in

Examples of various units measuring a quantity

Order of Magnitude Approximation based on a number of

assumptions may need to modify assumptions if more

precise results are needed Order of magnitude is the power of 10

that applies Examples: 27~30, 1006950~1000000

Coordinate Systems Used to describe the position of a

point in space Coordinate system consists of

a fixed reference point called the origin

specific axes with scales and labels instructions on how to label a point

relative to the origin and the axes

Types of Coordinate Systems Cartesian – (x,y) or (x,y,z) Plane polar - (r,)

x

yr

s

Cartesian coordinate system

Also called rectangular coordinate system

x- and y- axes Points are labeled

(x,y)

Plane polar coordinate system Origin and

reference line are noted

Point is distance r from the origin in the direction of angle , ccw from reference line

Points are labeled (r,)

Trigonometry Review

sin

cos

tan

opposite side

hypotenuse

adjacent side

hypotenuse

opposite side

adjacent side

More Trigonometry Pythagorean Theorem

To find an angle, you need the inverse trig function for example,

Be sure your calculator is set appropriately for degrees or radians

2 2 2r x y

1sin 0.707 45

Problem Solving Strategy

Problem Solving Strategy Read the problem

Identify the nature of the problem Draw a diagram

Some types of problems require very specific types of diagrams

Problem Solving cont. Label the physical quantities

Can label on the diagram Use letters that remind you of the quantity

Many quantities have specific letters Choose a coordinate system and label it

Identify principles and list data Identify the principle involved List the data (given information) Indicate the unknown (what you are looking

for)

Problem Solving, cont. Choose equation(s)

Based on the principle, choose an equation or set of equations to apply to the problem

Substitute into the equation(s) Solve for the unknown quantity Substitute the data into the equation Obtain a result Include units

Problem Solving, final Check the answer

Do the units match? Are the units correct for the quantity

being found? Does the answer seem reasonable?

Check order of magnitude Are signs appropriate and

meaningful?

Problem Solving Summary Equations are the tools of physics

Understand what the equations mean and how to use them

Carry through the algebra as far as possible Substitute numbers at the end

Be organized

What is the % uncertainty in the measurement 3.76 0.25?

Answer: 0.25/3.76 x 100% = 6.6%

What is the % uncertainty in the measurement 11.3 0.9?.

Answer: 0.9/11.3 x 100% = 8%

Sample Problems

In calculating the area of a piece of notebook paper you get measurements of (21.1 .1) cm for the width and (27.5 .2) cm for the length. Determine the area and the uncertainty. If the actual value of the area is 603 cm 2, determine the percent error from your calculation.

Answer: (21.1)(27.5) (21.1)(.2) (25.5)(.1) + (.1)(.2) =

580. (4.22 + 2.55) = (580 7) cm 2

% error = (603 – 580) x 100 = 3.8%

603

Sample Problems

An airplane travels at 950 km/h. How long in seconds does it take to travel 1 km?

Answer: (950 km/h)(1h/3600sec) = .26sec

Use dimensional analysis to determine if the equation vf

2 = vo 2 + 2as is consistent.

Answer: [L] 2 = [L] 2 + [L][L]

[T] 2 [T] 2 [T] 2

[L] 2 = [L] 2

[T] 2 [T] 2 The equation is consistent.

Sample Problems