A Physics Toolkit
Chapter 1
Pgs 2 - 29
Chapter Objectives

Use mathematical tools to measure and
predict.

Apply accuracy and precision when
measuring.

Display and evaluate data graphically.
Chapter 1. 1 Mathematics &
Physics

Demonstrate scientific methods.

Use metric system.

Evaluate answers using dimensional
analysis.
Chapter 1.1 Vocabulary
Physics
 Dimensional analysis
 Scientific method
 Hypothesis
 Scientific law
 Scientific theory

What is physics?
 Branch
of science that involves
the study of the physical world,
energy, matter and how they are
related
 What
are some of the topics
studied in physics?
Do Now: What is the difference
between Science and Technology ?

Science: Scientia meaning knowledge


Systematic way to build and organize
knowledge in the form of testable
explanations and predictions about the
universe.
Technology: application of knowledge

is the making, modification, usage, and knowledge of
tools, machines, techniques, crafts, systems, methods
of organization, in order to solve a problem, improve a
preexisting solution to a problem, achieve a goal or
perform a specific function.
Physics
Electromagnetism
Mechanics
Kinematics
Dynamics
Static
Electricity
Current
Optics
Magnetism
Light
Mirrors
Lenses
Mathematics
 The
language of Physics
 Why
do you think mathematics is so
important in physics?
 Equations:
tool for modeling
observations and for making
predictions.
SI: Système International d’Unités

SI is based on the power of 10
 SI has 7 base units
 We will concentrate on only the first three for
now
Page 5 in textbook
SI Prefixes
Only Need
to know
these 3
Page 6 in textbook
Discussion:

Why do scientists use the metric system,
instead of the English or some other
system?

Why is it important to have an agreed
upon system of units?
Dimensional Analysis

Every measured or
calculated quantity is
associated with a
dimension
 Units used to express
the dimension do not
affect it
 Any equation must be
dimensionally consistent
Dimensional Analysis
Method of treating units as algebraic
quantities, which can be cancelled.
 Conversion Factor: is a multiplier that is
equal to one



Example: 1 kg = 1000 g
Choose a conversion factor that will cancel
the units

May need to use more than one conversion
factor
Practice

Convert 1 year into minutes.
Do Now: Convert 1,000,000
seconds into days.
Practice

A car is moving at a speed of 90 km/h.
What is the speed of the car in m/s?

You are riding your bicycle down the hill at
15 m/s. What is your speed in km/h?
Do Now: What is the scientific
Method?
Systematic method of
observing, experimenting, and
analyzing to answer questions
about the natural world
Scientific Method
Scientific Method

Hypothesis- educated guess about variables

Must be testable
Models
Ideas, equations,
structures, or
systems used to
describe a
phenomenon
Laws
Rule of nature
that sums up
related
observations to
describe a
pattern in nature
Theories
Explanation
based on many
observations
supported by
experimental
results
Do Now: Complete the following
conversions using Dimensional Analysis
120 km/h into mph
 120 km/h into m/s
 65 mph into km/h
 65 mph into m/s


Conversion Factor
1 mile = 1.610 km
•
•
•
•
74.5 mph
33.3 m/s
104.7 km/h
29.1 m/s
Chapter 1.2 Measurement

Distinguish between accuracy and
precision
Chapter 1.2 Vocabulary
Measurement
 Precision
 Accuracy

Measurements

Comparison between an
unknown quantity and a
standard
 NIST- National Institute
of Standards and
Technology
 CGPM – General
Conference on Weights
and Measures
NIST-F1 Cesium Fountain Atomic Clock
The Primary Time and Frequency Standard for the
United States


Measurement of elapsed time
consists of counting the
repetitions of any
phenomenon that repeats
itself as a measure of time
1967 – CGPM adopted a
definition of a second based
on a characteristic frequency
of the radiation emitted by a
cesium atom
Standard of Length

Meter

Length of the path traveled by light in
vacuum during a time interval of
1/299,792,458 seconds
Standard of Mass : Prototype
Kilogram No. 20
Think, Pair, Share

How would you criticize the statement: “one
you have picked a standard, by the very
meaning of ‘standard’ it is invariable”?
Accuracy vs. Precision
Accuracy
Precision
Describes how well the The degree of
results of a
exactness of a
measurement agree
measurement
with the “real” or
accepted value
Precision
Millimeter
Centimeter
What is the measurement at the red line in
meter, centimeters, and millimeters?
 What determines the precision of a
measurement?
 How does the last digit differ from the
other digits in a measurement?

Precision & Significant Figures

Increasing the precision of measurements
decreases the experimental uncertainty

When reporting data, make sure to use correct
significant figures as to accurately represent
the precision used in making the
measurements
Chapter 1.3 Graphing Data
Graph the relationship between
independent and dependent variables
 Interpret graphs
 Recognize common relationships in
graphs

Do Now: What is the purpose of
collecting data during a lab?
Chapter 1.3 Vocabulary
Independent Variable
 Dependent Variable
 Line of best fit
 Linear relationship
 Quadratic relationship
 Inverse relationship

Experimental Design

Purpose?


Determine relationship between two
different variables
Controlled Experiments
Manipulate only one variable in an
experiment
 Observe its effect on a second variable
 Hold ALL other variables in the experiment
CONSTANT

Variables

Any factor that might affect the behavior of an
experimental setup.
 Independent Variables




Factor that is changed or manipulated during the
experiments
Always plotted on the x-axis
Time is usually the independent variable
Dependent Variables


Factor that depends on the independent variable
Always plotted on the y-axis
Recording Data

Raw data is recorded (ink) on a data table
immediately as it is collected in the lab.
 Data Table


Independent variable in leftmost column of the data
table
Every column is labeled with the name of the
variable being measured with the units in
parentheses below the variable name.



Values in table do not have units.
Same number of decimal places in each column
Construct data table before collecting the data
Preparing the Data
Raw data might have to be “prepared”
before graphing
 If multiple trials were done, average the
trials together to determine a
representative value.
 An entry in your formal table that is a
result of a calculation must include an
explanation of the column and a
SAMPLE CALCULATION

Graphing Data

Purpose

Determine the relationship between the two
variables

Usually scatter graphs
 Graphs




Title: DEPENDENT VARIABLE vs. INDEPENDENT
VARIABLE
Scaled
Axis: labeled with the QUANTITY and the UNITS
Line of best fit: shows overall tendency
Graphical Analysis

Four Basic Relationships
No relation
 Linear Relations (Direct Relationship)
 Square Relations
 Inverse Relations


Develop mathematical model

Equation
No Relation
Changing the independent variable has
NO effect on the dependent variable.
 The dependent variable stays the same
 Graph is a horizontal line

Slope = 0
 Equation: y = constant

Linear Relations
Graph forms a straight line with a
nonzero slope
 Equation: y = mx + b


m is the slope of the line


Can be positive or negative
b is the y-intercept
Direct Relations
A special linear relationship
 As one factor increases by a certain
factor, the other variable must also
increase by the same factor
 MUST go through the origin of the axes

Y-intercept: b = 0
 Must have data point (0,0)

Square Relations
Non-Linear
 Parabolic or Quadratic


Top/bottom opening parabolas
Equation: y = ax2 + bx + c
 If vertex is at the origin (0,0), then y = ax2



Side opening parabolas
Linearize the graph to determine whether
or not the graph is truly a parabola
Inverse Relations
As the independent variable increases
the dependent variable decreases
 Equation y = a/x

Linearizing Graphs

Manipulate the data according to the
relation you think it might be


If you have predicted the right relation and
manipulate it accordingly, it will result in a
linear graph
Test Plot:

graph made with mathematically
manipulated data for the purpose of testing
whether or not our guess about a
mathematical relation might hold true
•Dependent Variable
•Graph
•Hypothesis
•Mathematical Model
Experiment
•Measurement
Independent
Variable
Spaghetti Bridge: Formal Lab Report

Objective:
to measure the strength of spaghetti by using
it to make a bridge across two tables.
Questions:
1. What are the possible variables that you can have in
building a spaghetti bridge?
2. What two variables are you going to be looking at to find
a relationship?
3. Identify your variables listed in number 1 as either
independent variables, dependent variables, or controls.
4. Write a hypothesis.
5. What are the materials that you will be using?
6. Write a procedure to test your hypothesis. Remember
that you need to collect measurable data. You need 5
data points and 3 trials for each data point.
7. Draw your data table.
8. When done, show to Mrs. Faria to get your materials.
Post Lab Questions:
1.Create a graph (dependent variable
vs independent variable)
2.Draw a line of best fit.
3.What relationship do you see
between the two variables.
4.Write an equation that best fits your
line.
5.What is the physical meaning of the
slope of your line.
Lab Questions
1. (6) What are the possible variables that you can have in building a
spaghetti bridge? Identify each variable as independent, dependent, or as
a control.
2. (5) Create a graph (dependent variable vs independent variable)
3. (2) Draw a line of best fit.
4. (2) What relationship do you see between the two variables.
5. (2) Write an equation that best fits your line.
6. (3) What is the physical meaning of the slope of your line. If it is not a line,
then describe what the graph is showing.
Spaghetti Lab Points
Format 2 pts
 Objective 1 pt
 Hypothesis 1 pt
 Materials 1 pt
 Procedure 5 pts
 Data Table 5 pts
 Questions 20 pts

Practice Problems

5, 6, 7, 8, 13, 17, 18, 21, 23, 24, 26, 37,
39, 40, 43, 45, 46, 57, 61, 67, 69, 84, 85,
89