Physics Day 4AIM: How do we measure things?

LO: SI units and prefixes

LO: Dimensional Analysis aka Factor Label Method

LO: Scientific Notation

AGENDA

Do Now

Notes on Units

Worksheet

HW02 due 9.8

Do Now1/ Collect a Reference Table2/ Pick up a Physics Work Book and put your name on it.3/ Open the workbook and read the first two pages.

Mathematical Concepts

•Units: •Unit conversion,

•Dimensional Analysis

•Trigonometry

Units    

System

SI CGS BE

SI stands for the French phrase "Le Systeme International d'Unitus."

CGS - centimeter (cm), gram (g), and second.

BE - British Engineering.

Units    

System

SI CGS BE

Length meter (m)centimeter (cm)

foot (ft)

SI stands for the French phrase "Le Systeme International d'Unitus."

CGS - centimeter (cm), gram (g), and second.

BE - British Engineering.

Units    

System

SI CGS BE

Length meter (m)centimeter (cm)

foot (ft)

Masskilogram (kg)

gram (g) slug (sl)

SI stands for the French phrase "Le Systeme International d'Unitus."

CGS - centimeter (cm), gram (g), and second.

BE - British Engineering.

Units    

System

SI CGS BE

Length meter (m)centimeter (cm)

foot (ft)

Masskilogram (kg)

gram (g) slug (sl)

Time second (s) second (s) second (s)

SI stands for the French phrase "Le Systeme International d'Unitus."

CGS - centimeter (cm), gram (g), and second.

BE - British Engineering.

Units of length

• Early units of length were associated with the human body.

Units of length

• Early units of length were associated with the human body.

• The foot was originally defined to be the length of the royal foot of King Louis XIV.

Units of length

• Early units of length were associated with the human body.

• The foot was originally defined to be the length of the royal foot of King Louis XIV.

• These units are not reproducible.

Earlier Definition of meter Metre (meter) originated from the Greek word metron meaning “measure”.

Earlier Definition of meter Metre (meter) originated from the Greek word metron meaning “measure”.

In 1793, the meter was defined in terms of the distance measured along the earth's surface between the north pole and the equator.

Standard Meter Bar

In 1799, a platinum-iridium meter bar, was used to define meter.

Standard Meter Today

Since 1983, meter is defined using the speed of light, 299 792 458 m/s.

The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.

Standard Kilogram Today

The standard platinum-iridium kilogram is kept at the International Bureau of Weights and Measures in Sevres, France.

Units of time

• The Earth takes 24 hours to rotate once.

• Before 1956, the mean solar day was defined to be 24x60x60 = 86,400 seconds.

Standard Second Today

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

A cesium atomic clock.

 Physical Quantity

Unit

Name Symbol

Time second s

Length meter m

Mass kilogram kg

Electric current ampere A

Temperature kelvin K

Amount of substance

mole mol

Luminous intensity

candela cd

SI Base Units

Some SI Derived Units

• Area - m2

• Volume - m3

• Density - kg/m3

Sine, Cosine, and Tangent

.AB

BC

Hypotenuse

deOppositeSiSin

Sine, Cosine, and Tangent

.AB

BC

Hypotenuse

deOppositeSiSin

.AB

AC

Hypotenuse

deAdjacentSiCos

Sine, Cosine, and Tangent

.AB

BC

Hypotenuse

deOppositeSiSin

.AB

AC

Hypotenuse

deAdjacentSiCos

.AC

BC

deAdjacentSi

deOppositeSiTan

Pythagorean Theorem

.222 CBACAB

.22 CBACAB

Dimensional Analysis

• Dimensional Analysis– A systematic method for solving problems in

which units are carried thru the entire problem• units are multiplied together, divided into each other,

or cancelled

– Helps ensure that problems are solved correctly– Helps ensure that solutions have the proper units– Uses conversion factors

Conversion Factors

• Conversion Factor – a fraction whose numerator and denominator

are the same quantity expressed in different units

– used to change from one unit to another

Conversion Factors

• Examples of Conversion Factors

12 in = 1 ft

100 cm = 1 m

12 in or 1 ft1 ft 12 in

100 cm or 1 m1 m 100 cm

Every relationship can give two conversion factors that are the inverses of each other.

Dimensional Analysis - One Conversion Factor

Example: A lab bench is 175 inches long. What is its length in feet?

Example: A lab bench is 175 inches long. What is its length in feet?Given: 175 in.

Find: Length (ft)

Conversion factor:12 in or 1 ft 1 ft 12 in.

ft = 175 in X 1 ft = 14.583333 ft = 14.6 ft

12 in

Dimensional Analysis - One Conversion Factor

Dimensional Analysis - One Conversion Factor

Example: A marble rolled 50.0 mm. How many meters did it roll?

Conversion factor:1000 mm or 1 m 1 m 1000 mm

Dimensional Analysis - One Conversion Factor

Example: A marble rolled 50.0 mm. How many meters did it roll?

Given: 50.0 mm

Find: dist. (m)

m = 50.0 mm X 1 m = 0.05 m = 0.0500 m

1000 mm

Dimensional Analysis - One Conversion Factor

Example: In Germany, a salesman I was with drove at 185 km/hr. What was our speed in mi/hr?

Dimensional Analysis - One Conversion Factor

Example: In Germany, a salesman I was with drove at 185 km/hr. What was our speed in mi/hr?

Conversion factor:1.609 km or 1 mi 1 mi 1.609 km

Given: 185 km/hr

Find: mi/hr

mi = 185 km X 1 mi = 114.97825 mi

hr hr 1.609 km hr

Speed = 115 mi/hr

Exponentials