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## CHAPTER 1 A PHYSICS TOOLKIT

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### In this chapter you will: Use mathematical tools to measure and predict. ... It is the mass of a Platinum-Iridium metal cylinder kept near Paris. ... – PowerPoint PPT presentation

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Title: CHAPTER 1 A PHYSICS TOOLKIT

1
CHAPTER 1 A PHYSICS TOOLKIT
•
• In this chapter you will
•
•  Use mathematical tools to measure and predict.
• Apply accuracy and precision when measuring.
• Display and evaluate data graphically.

2
CHAPTER 1 SECTIONS
• Section 1.1 Mathematics and Physics
• Section 1.2 Measurement
• Section 1.3 Graphing Data

3
SECTION 1.1 MATHEMATICS AND PHYSICS
• Objectives
• Demonstrate scientific methods.
• Use the metric system.
• Evaluate answers using dimensional analysis.
• Perform arithmetic operations using scientific
notation.

4
WHAT IS PHYSICS?
• Physics - is a branch of science that involves
the study of the physical world energy, matter,
and how they are related.
•
• Learning physics will help you to understand the
physical world.
•
• The goal of this course is to help you understand
the physical world.
•
• You can use the problem solving skills you use in
physics in many disciplines.
•
• Physics uses mathematics as a powerful language.
•
• Mathematics is the language of Physics.

5
MATHEMATICS IN PHYSICS
• In physics, equations are important tools for
modeling observations and for making predictions.
•
• Physicists rely on theories and experiments with
numerical results to support their conclusions.
• Example Problem 1 Electric Current
• V IR
• 120 .75 R
• 160 Ohms R
• Do Practice Problems p. 5 1-4

6
SI UNITS
• The example problem uses different units of
measurement to communicate the variables and the
result. It is helpful to use units that everyone
understands.
•
• Scientific institutions have been created to
define and regulate measures.
•
• The worldwide scientific community and most
countries currently use an adaptation of the
metric system to state measurements.
•
• Metric System system of measurement that is
based on powers of ten. It was created by French
scientists in 1795.
•
• The Système International dUnités, or SI- uses
seven base quantities, which are shown in the
table on next slide(Table 1-1 p. 5).
(International System of Units)

7
SI UNITS
8
SI UNITS
• Base Quantities (or Fundamental Units) set of
units on which a measurement system is based.
They were originally defined in terms of direct
measurements.
• Second standard unit of time.
•
• The second was first defined as 1/86,400 of the
mean solar day. Mean Solar Day is the average
length of the day over a period of one year.
•
• In 1967 the second was redefined in terms of the
frequency of one type of radiation emitted by a
Cesium-133 atom.

9
SI UNITS
• Meter standard SI unit of length.
• Meter was first defined as one-ten-millionth
(10-7) of the distance from the North Pole to the
equator measured along a line passing through
Lyons, France.
•
• In the 20th Century Physicists found that light
could be used to make very precise measurements
of distances.
•
• In 1960, the meter was redefined as a multiple of
a wavelength of light emitted by Krypton-86. By
1982, a more precise length measurement defined
the meter as the distance light travels in
1/299,792,458 second in a vacuum.

10
SI UNITS
• Kilogram standard SI unit of mass of an object.
•
• Kilogram is the only SI unit not defined in terms
of the properties of atoms. It is the mass of a
Platinum-Iridium metal cylinder kept near Paris.
•
• Derived Units are created by combining the base
units in various ways. The unit of a quantity
that consists of combinations of fundamental or
base units. A common derived unit is the meter
per second (m/s), which is used to measure speed.
•
• The SI system is regulated by the International
Bureau of Weights and Measures in Sèvres, France.
• This bureau and the National Institute of Science
and Technology (NIST) in Gaithersburg, Maryland,
keep the standards of length, time, and mass
against which our meter sticks, clocks, and
balances are calibrated.

11
SI UNITS
• The ease of switching between units is another
feature of the metric system.
•
• Prefixes are used to change SI units by powers
of 10.
•
• To convert between SI units, multiply or divide
by the appropriate power of 10.
•
• Prefixes are used to change SI units by powers of
10, as shown in the table.
•
• See Table 1-2 for the Prefixes. Notice once we
reach three then we use factors of 3 such as 6,
9, 12, etc.
•
• To use the SI units effectively you need to know
the meanings of the prefixes. Make sure you know
the Prefixes listed in Table 1-2. And Deka and
Hecto.
•
• When using the prefixes we usually use powers of
1, 2 or factors of 3.
•
• Note 101 is deka with symbol da and 102 is
hecto with symbol h
• Extra Credit. Find the Prefixes for 104 , 105 ,
10-4 , 10-5

12
SI UNITS (also Deka Hecto)
13
DIMENSIONAL ANALYSIS
• You often will need to use different versions of
a formula, or use a string of formulas, to solve
a physics problem.
•
• To check that you have set up a problem
correctly, write the equation or set of equations
you plan to use with the appropriate units.
•
• Dimensional Analysis - method of treating units
as algebraic quantities, which can be cancelled.
It can be used to check that an answer will be in
the correct units. It is also used in choosing
conversion factors.
•
• Conversion Factor - is a multiplier equal to 1.
For example, because 1 kg 1000 g, you can
construct the following conversion factors
•
•
• Choose a conversion factor that will make the
units cancel, leaving the answer in the correct
units.
• Do Practice Problems p 7 5-8

14
SIGNIFICANT DIGITS
• Significant Digits - the valid digits in a
measurement.
•
• Uncertain Digit - the last digit given for any
measurement.
• Rules for Significant Digits
• 1. All Non-Zero Digits are Significant.
• 2. Final Zeros after the Decimal Point are
Significant.
• 3. Zeros between significant digits are
Significant.
• 4. Zeros used only as placeholders are NOT
Significant.

15
SIGNIFICANT DIGITS
• Note s such as 1000 are normally written in
scientific notation so you can tell how many
significant digits.
• 1 103 has 1, 1.0 103 has 2, 1.00 103 has
3, and 1.000 103 has 4
• Also Counting s and Conversion Factors are EXACT
so they have INFINITE Significant Digits
• When you perform any arithmetic operation, it is
important to remember that the result never can
be more precise than the least-precise
measurement.
•
• To add or subtract measurements, first perform
the operation, then round off the result to
correspond to the least-precise value involved.
•
• To multiply or divide measurements, perform the
calculation and then round to the same number of
significant digits as the measurement with the
least number of significant digits.
•
• Note that significant digits are considered only
when calculating with measurements.
• Do Practice Problems p. 8 9-12

16
SCIENTIFIC METHODS
• Scientific Method a systematic method of
observing, experimenting, and analyzing to answer
questions about the natural world.
•
• Written, oral, and mathematical communication
skills are vital to every scientist.
•
• Hypothesis - an educated guess about how
variables are related.
• A hypothesis can be tested by conducting
experiments, taking measurements, and identifying
what variables are important and how they are
related. Based on the test results, scientists
establish models, laws, and theories.

17
SCIENTIFIC METHODS
• Scientific Method Steps
• 1. State the Problem
• 2. Gather Information
• 3. Form a Hypothesis
• 4. Test the Hypothesis
• 5. Analyze Data
• 6. Draw Conclusions

18
SCIENTIFIC METHODS
• Scientific Models - are based on experimentation.
•
• Scientific Law - is a rule of nature that sums up
related observations to describe a pattern in
nature. A well established rule about the
natural world that sums up, but does not explain
a pattern in nature.
• Scientific Theory - is an explanation based on
many observations supported by experimental
results. An explanation based on numerous
observations, supported by experimental results,
that may explain why things work the way they do.

19
QUESTION 2
• A car is moving at a speed of 90 km/h. What is
the speed of the car in m/s? (Hint Use
Dimensional Analysis)
• 90 km 1 h 1000 m 25
m/s
• h 3600 s 1 km