Bài giảng vật lý đại cương chương 1

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.. Fundamental Q

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Textbook : Physics for scientists and engineers, Serway, 4 th edition

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Study

Suggested Study Procedure

1 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 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 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

investigations

These steps are called

the scientific method.

Chapter 1

Models

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 1

Hypotheses

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 1

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).

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 1

Numbers 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)

agreed to in 1960 by an international committee

main system used in this course

also called mks for the first letters in the units of the fundamental quantities

Systems of Measurements, cont

Defined in terms of a meter – the

distance traveled by light in a vacuum during a given time

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

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.

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 1

Dimensions 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

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 ?

2

r

Mm G

F =

Prefixes correspond to powers of 10

Each prefix has a specific name

Each prefix has a specific abbreviation

shown in the table.

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

Chapter 1

Mathematics 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 1

Graph 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.

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

Plane polar coordinate system

Origin and reference

line are noted

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 3

A high fountain of water is located at the center of a circular pool as shown in the figure below 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?

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 1

Rules for Determining Significant Zeros

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 6

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?