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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.

CHAPTER 1 SECTIONS

- Section 1.1 Mathematics and Physics
- Section 1.2 Measurement
- Section 1.3 Graphing Data

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.

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.

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

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)

SI UNITS

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.

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.

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.

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

SI UNITS (also Deka Hecto)

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

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.

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

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.

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

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.

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