College Physics

Chapter 1Introduction

Physics 2010/2011

Instructor: Allen Hunley

Telephone: (931) 221-6116 (office)

E-Mail:allen.hunley@muhlenberg.kyschools.us

Office Hours: By appointment. (I am an adjunct member so I do not have an office at APSU.)

Textbook: College Physics (7th Edition)by Serway & Faughn Thomson Books/Cole (2006)

World Wide Web

CourseWeb Address: http://teacherweb.com/KY/MSHS/AllenHunley/

TextbookWeb Address: www.cp7e.com

(Physics Now Web Site, free if you purchased a new edition textbook)

Study

Suggested Study Procedure1. Read the assigned topics/materials before coming to the class/lab.2. Attend the class, take good notes, and actively participate in all the activities in the class.3. Reread the topics/materials.4. Work the assigned problems starting the first day that they are assigned - you will require time for this material to "sink in"!5. Ask questions in the interim.6. Use a three-hole binder for the course so that you can keep all the materials (notes, homework assignments, answer sheets, exams, labs, etc.) in it. This will help you to find all the necessary materials when you prepare for your exams.

Evaluation

Lecture and lab grades are combined. You will receive the same letter grade for the lecture course as for the lab course.

In summary, the distribution of credits among the various assignments is as following:

Guide to letter grades is:Homework Assignments 15 points A = 90 - 100Lab Activities 20 points B = 80 – 89Exams 50 points C = 70 – 79Final Exam 15 points D = 60 – 69Total 100 points F = 0 - 59

Laboratory

Laboratory activities are highly valued in physics and are incorporated into our classes. These activities may consist of traditional hands-on experiments or computer simulations. You will be working in groups with 2-3 students in each group. The grade is based entirely on the lab write-ups you turn in. These activities contribute 20% of your grade.

The aims of the class

• On of the aims of this class is to teach you to think in a physics way.

• As you see each concept, try to get a mental picture of how it works.

• You will learn as much about how to solve problems as you do about the laws of physics themselves.

• So you will need to approach this class differently from many of the other classes you are taking. Simply memorizing solutions will not help.

• Doing lots of homework problems is the best way to do well in the class. As you do each problem, think of what strategy you are using to solve the problem.

The Branches of Physics

Physics

Physics attempts to use a small number of basic concepts, equations, and assumptions to describe the physical world.

These physics principles can then be used to make predictions about a broad range of phenomena.

Physics discoveries often turn out to have unexpected practical applications, and advances in technology can in turn lead to new physics discoveries.

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

Chapter 1The Scientific Method

There is no single procedure that scientists follow in their work. However, there are certain steps common to all good scientific investigations.

These steps are called the scientific method.

Chapter 1Models

Physics uses models that describe phenomena.

A model is a pattern, plan, representation, or description designed to show the structure or workings of an object, system, or concept.

A set of particles or interacting components considered to be a distinct physical entity for the purpose of study is called a system.

Chapter 1Hypotheses

Models help scientists develop hypotheses.

A hypothesis is an explanation that is based on prior scientific research or observations and that can be tested.

The process of simplifying and modeling a situation can help you determine the relevant variables and identify a hypothesis for testing.

Chapter 1Hypotheses, continued

Galileo modeled the behavior of falling objects in order to develop a hypothesis about how objects fall.

If heavier objects fell faster than slower ones,would two bricks of different masses tied together fall slower (b) or faster (c) than the heavy brick alone (a)? Because of this contradiction, Galileo hypothesized instead that all objects fall at the same rate, as in (d).

Chapter 1Controlled Experiments

A hypothesis must be tested in a controlled experiment.

A controlled experiment tests only one factor at a time by using a comparison of a control group with an experimental group.

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

Chapter 1Numbers as Measurements

In SI, the standard measurement system for science, there are seven base units.

Each base unit describes a single dimension, such as length, mass, or time.

The units of length, mass, and time are the meter (m), kilogram (kg), and second (s), respectively.

Derived units are formed by combining the seven base units with multiplication or division. For example, speeds are typically expressed in units of meters per second (m/s).

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

Mass Units

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

Defined in terms of kilogram, based on a specific cylinder kept at the International Bureau of Weights and Measures

Mass

The SI unit for mass is the kilogram.

A kilogram is defined as the mass of a special platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures in France.

Time Units

seconds, s in all three systems 9,192,631,700 times the period of

oscillation of radiation from the cesium atom.

Fundamental Quantities and Their Dimension

Length [L] Mass [M] Time [T]

other physical quantities can be constructed from these three

Chapter 1Dimensions and Units

Measurements of physical quantities must be expressed in units that match the dimensions of that quantity.

In addition to having the correct dimension, measurements used in calculations should also have the same units.

For example, when determining area by multiplying length and width, be sure the measurements are expressed in the same units.

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

Example 1

T

L T

The following equation was given by a student during an examination:

Do a dimensional analysis and explain why the equation can’t be correct.

20 atvv

ν has dimensions a has dimensions t has dimension

2T

L

Example 2

Newton’s law of universal gravitation is represented by

where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units kg ∙ m/s2. What are the SI units of the proportionality constant G?

2r

MmGF

Prefixes

Prefixes correspond to powers of 10

Each prefix has a specific name Each prefix has a specific

abbreviation See table 1.4

Chapter 1SI Prefixes

In SI, units are combined with prefixes that symbolize certain powers of 10. The most common prefixes and their symbols are shown in the table.

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

Chapter 1

Sample Problem

A typical bacterium has a mass of about 2.0 fg. Express

this measurement in terms of grams and kilograms.Given:

mass = 2.0 fg

Unknown: mass = ? g mass = ? kg

Chapter 1Sample Problem, continued

Build conversion factors from the relationships given in

Table 3 of the textbook. Two possibilities are:

Only the first one will cancel the units of femtograms to

give units of grams.

–15

–15

1 10 g 1 fg and

1 fg 1 10 g

–15–151 10 g

(2.0 fg) = 2.0 10 g1 fg

Chapter 1Sample Problem, continued

Take the previous answer, and use a similar process to

cancel the units of grams to give units of kilograms. –15 –18

3

1 kg(2.0 10 g) = 2.0 10 kg

1 10 g

Converting UnitsExample 3

Convert the following:

a. 25m to cm

b. 345m to Km

c. 550cm to Km

d. 0.3 m/s to Km/hr

Chapter 1Mathematics and Physics

Tables, graphs, and equations can make data easier to understand.

For example, consider an experiment to test Galileo’s hypothesis that all objects fall at the same rate in the absence of air resistance.

In this experiment, a table-tennis ball and a golf ball are dropped in a vacuum. The results are recorded as a set of numbers corresponding to the times of the

fall and the distance each ball falls. A convenient way to organize the data is to form a table, as shown on the next

slide.

Chapter 1Data from Dropped-Ball Experiment

A clear trend can be seen in the data. The more time that passes after each ball is dropped, the farther the ball falls.

Chapter 1Graph from Dropped-Ball Experiment

One method for analyzing the data is to construct a graph of the distance the balls have fallen versus the elapsed time since they were released. a

The shape of the graph provides information about the relationship between time and distance.

We can use the following equation to describe the relationship between the variables in the dropped-ball experiment:

(change in position in meters) = 4.9 (time in seconds)2

With symbols, the word equation above can be written as follows:y = 4.9(t)2

The Greek letter (delta) means “change in.” The abbreviation y indicates the vertical change in a ball’s position from its starting point, and t indicates the time elapsed.

This equation allows you to reproduce the graph and make predictions about the change in position for any time.

Chapter 1Equation from Dropped-Ball Experiment

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 Cartesian Plane polar

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

Example 4

A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (2.0, 1.0), where the units are meters, what is the distance of the fly from the corner of the room?

Example 5

For the triangle shown in Figure P1.39, what are (a) the length of the unknown side, (b) the tangent of θ, and (c) the sine of φ?

Example 6

A high fountain of water is located at the center of a circular pool as shown in Figure P1.41. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 15.0 m. Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation at the bottom of the fountain to be 55.0°. How high is the fountain?

Example 7A surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, he walks 100 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is 35.0°. How wide is the river?

Chapter 1

Accuracy and Precision

Accuracy is a description of how close a measurement is to the correct or accepted value of the quantity measured.

Precision is the degree of exactness of a measurement.

A numeric measure of confidence in a measurement or result is known as uncertainty. A lower uncertainty indicates greater confidence.

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

Chapter 1Rules for Determining Significant Zeros

Example 8

How many significant digits are in each of the following:

a.) 0.007

b.) 1.09

c.) 100

d.) 0.8090

Operations with Significant Figures 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

Operations with Significant Figures, cont.

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

Rules for Calculating with Significant Figures

Example 9

A fisherman catches two striped bass. The smaller of the two has a measured length of 93.46 cm (two decimal places, four significant figures), and the larger fish has a measured length of 135.3 cm (one decimal place, four significant figures). What is the total length of fish caught for the day?

Example 10

Using your calculator, find, in scientific notation with appropriate rounding,

(a) the value of (2.437 × 104)(6.5211 × 109)/(5.37 × 104)

and

(b) (3.14159 × 102)(27.01 × 104)/(1 234 × 106).

Derived Units

Derived units are combinations of the base units (mks).

Area is measured in m2

Volume is measured in m3

Speed is measured in m/s