Unit 1 Introduction

Measurement

To make a measurement, we must...  know what we are trying to measure  have some standard with which to compare  must have some method of making this comparison

SI Units  French scientists adopted the metric system in  Major Benefit: Units are related by __________________.  There are seven base units. We will be concerned with only five for now.

Fundamental SI Units for Physics  length  time  _________________________  mass  _________________________  Light (Candela)

How might you define a second? Class discussion

Time

“The ____________ between two occurrences.”  The SI unit of time is the second.  Originally defined as 1/86 400th of the average length of a day.  Redefined as the duration of periods of the radiation corresponding to the transition between two hyperfine level of the fundamental state of the atom of Cesium-133 isotope.

Length

“The ______________ between two points.”  The SI unit of length is the meter.  Originally defined as 1/ of the distance between the North Pole and the equator through Paris, France.  Redefined as times the wavelength of the orange-red Krypton 86 isotope at bar and 15 oC.  Currently defined as the distance light travels through a vacuum in 1/ th of a second.

Temperature

“A measure of the ______ of a substance.”  Heat is a form of energy which is the result of molecular motion.  Temperature scales:  Kelvin (Absolute scale) (SI UNIT)  Celsius  Fahrenheit

Mass

“A measure of the __________in an object.”  The SI unit of mass is the kilogram.  Originally defined as the mass of 1 Liter of water at 3.98 oC.  Now defined as the mass of a piece of metal kept at the International Bureau of Weights and Measures in Sevres, France.

Which weighs more, a ton of feathers or a ton of lead?

Mass vs. Weight  “A measure of the amount of __________ in an object.”  Does not change from place to place.  SI unit is the kilogram.  “A measure of the ______________ force between objects.”  Changes from place to place.  SI unit is the Newton.

Quantity

“The ____________ of substance one has.”  In the scientific community, substances are referred to in moles (SI unit).  One mole is 6.02 x 1023 particles (Avogadro's #).  12 g of Carbon-12

The Mole  A mole of _________ would spread over the surface of the earth, and produce a layer about 50 miles thick.  A mole of _______, spread over the United States, would produce a layer 3 inches deep.  A mole of dollars could not be spent at the rate of a billion dollars a day over a _________ years.  This shows you just how big a mole is. This number is so large that it is usually only represented in scientific notation

Scientific Notation  A method of expressing _________________ as powers of ten.  Mostly useful when expressing rather large or small numbers/quantities.  Example:  2.03x102 = _______________  = _______________

Advantages of Scientific Notation  Easily able to express very large or small numbers.  Number of molecules in 18 mL of water   The mass of an electron  kg

Converting between decimals & scientific notation #Direction to move decimal # of places Positive or negative 100Left Left n/a Right Right

Converting Between Scientific Notation & Decimals #Direction to move decimal # of places Smaller or greater than “1” 1.0x10 3 right3greater x10 2 right2greater x10 0 n/a x10 -2 left2smaller x10 -3 left3smaller.001

To express a Decimal Number in S.N. (#.##X10#)  Example:  605 =  We always move the decimal so that we have only ONE digit to the _______ of the decimal.  = 6.05 (we had to move the decimal two places)  For every place holder the decimal moves, you +/- 1 from the exponent/power on the “10.”  6.05x10 2

Multiplying two #’s expressed in scientific notation.  Multiply the digits.  ___________________________  If necessary, re-write in proper scientific notation.  Check the number of significant digits.

Dividing two #’s expressed in scientific notation.  _________________________  Subtract the exponents.  If necessary, re-write in proper scientific notation.  Check the number of significant digits.

Prefixes  We use prefixes as a __________________ way of expressing large multiples of 10.  For instance we use the prefix kilo- to represent 1000 or 10 3

Prefix Table

Prefix Responsibility

Derived Units  “Units which are the result of combinations of two or more fundamental units.”

Derived Units  What are some other units that are not base units, but units that we see on a regular basis?  Examples: – Newton (N)kg * m/s 2 – Joules (J)N * m – Density ( ρ ) g/cm 3

Measurement Reliability

Accuracy and Precision  ______________:  “How closely a measurement is to the true correct value for the quantity.”  _______________:  “How closely a set of measurements are to each other.”

Accurate or Precise?

Significant Digits/Figures The reliable digits in a measurement based on the accuracy of the measuring instrument.

Rule of Thumb  Whenever making a measurement, you are permitted one “guessed” digit.  The guessed digit is the last significant digit in a number.

Significant Digit Demonstration  Graduated Cylinder and Beaker

Rules to determine the number of significant digits.  Non-zero numbers are significant.  123 cm  Zeros between two significant digits are significant.  103 cm  Final zeros after a decimal point are significant.  in.  Zeros used solely for spacing the decimal point are not significant.  miles/sec.  miles/sec

During Addition and Subtraction  Your answer should be rounded off to the decimal place value as the measurement with the guessed digit in the _____________ decimal place.

Add the following values cm cm

Add the following values. 241 cm + 64,300 cm

During Multiplication and Division  The final answer should have the same number of significant digits as the measurement having the smallest number of significant digits.

Multiply the following values. 44 m x 2 m

Rules for Rounding Numbers  If the digit to the immediate right of the last significant figure is less than five, do not change the last significant figure.   _____________

Rules for Rounding Numbers  If the digit to the immediate right of the last significant figure is greater than ________, round up the last significant figure.   ______________

Rules for Rounding Numbers  If the digit to the immediate right of the last significant figure is equal to five and is followed by a nonzero digit, round up the last significant figure.   _______________

Rules for Rounding Numbers  If the digit to the immediate right of the last significant figure is equal to five and is not followed by a nonzero digit, look at the last significant figure. If it is an odd digit, round it up. If it is an even digit, do not round up.   _______________   _______________

Percent Error – Two common versions

Percent Error Example problem  Determine the percent error for the density of Al found experimentally to be equal to 2.60 g/cm 3 if the actual density is 2.70 g/cm 3.

Parallax  The apparent shift in objects when viewed from different _____________.  Can be used to discern the distance of the object(s) being observed.

Dimensional Analysis

 “A problem solving method that focuses on the units that are used to describe matter.”  Simply put, it is the analysis of the units in a problem to see if the math was done right.

Dimensional Analysis  Example Problem:  A person is traveling 70.0 mph for 10.0 seconds. How far did they travel in feet?

Conversion Factor  “A ratio of equivalent values used to express the same quantity in different units; is always equal to 1 and changes the units of a quantity without changing its value.”

Dimensional Analysis  How many inches are in 2.7 feet?

Question  It is possible to use dimensional analysis to convert between units?  Since 1 m = 1000 mm, how many mm are there in 3.45 m?

Example  How many cm 3 are in 3.2 m 3 ?

Example  In Canada, a car travels along Highway 401 at a speed of km/h. What is the car’s speed in m/s?

Scientific Process Review

REVIEW…  Data Representation  Types of Graphs  What constitutes a good graph?  Independent vs. Dependent Variables

Variables  Independent (x-axis) – the variable(s) being manipulated by the scientist.  Dependent (y-axis) – the variable(s) that are the observed result of the independent variables being manipulated by the scientist.  Note: You will not always have a clear independent and dependent variable. Usually this happens when you are dealing with rates (units per given time). In this case time always goes on the x-axis.