Physics Ch 1 What is Physics?
Physics is much more than equations and numbers. • Physics is the branch of knowledge that studies the physical world. • Physics is about what happens in the world all around us. You use physics every day! • Physics deals with the way nature behaves—natural laws.
Aristotle argued that heavy objects fall faster than light objects. Galileo stated that light and heavy objects fall at the same rate. A Physics Misconception
Early Views • Aristotle believed that all matter within reach was made up of 4 elements: Earth, Water, Air, and Fire. • Each element had a natural place. The highest was Fire, then Air, then Water, and finally, Earth. Motion occurred because an element wanted to reach its own natural place. • He also named a 5th element, Ether, which he believed stars were made from.
Scientific Method • The Greek teachings were accepted as truth until the 1600s. • Galileo Galilei (1564-1642) is called the Father of the Scientific Method. • Scientific method combines systematic experimentation with careful measurement and analysis of results. • Conclusions are then retested to find out if they are valid.
Physics Ch 2 Mathematical Toolkit
Language of Science • Mathematics is the language of Science. • The applications of physics principles usually involves the measurement of one or more quantities. • The metric system of measurement was created by French scientists in 1795. • It is convenient to use because units of different sizes are related by powers of 10.
International System of Units • The International System of Units (SI) is used throughout the world. The National Institute of Standards and Technology keeps the official standards for the units of length, mass, and time for the United States. • Fundamental Units—The basic 3 SI units used to describe other quantities • Derived units—Combinations of the fundamental units
Fundamental Units • The Three Basic or fundamental units are: • Second—the standard unit of time • Meter—the standard unit of length • Kilogram—the standard unit of mass The second was first defined as 1/86,400 of the mean solar day (average length of a day over a year). In 1967, the second was redefined in terms of the frequency of one type of radiation emitted by a cesium-133 atom. The meter was first defined as 10-7 of the distance from the north pole to the equator; In 1982, the meter was defined as the distance light travels in 1/299,792,458 second in a vacuum. The kilogram is the only unit not defined in terms of the properties of atoms. It is the mass of a platinum-iridium metal cylinder kept near Paris.
Scientific Notation • Scientific Notation is based on exponential notation. It is used to express either very large or very small numbers in a shortened form. • Scientific notation makes working with these numbers much easier.
Rules of Scientific Notation • The notation is based on powers of base number 10. The general format looks something like this: • N X 10x where N= number greater or equal to 1 but less than 10 and x=exponent of 10. Numbers Greater Than 10 • We first want to locate the decimal and move it either right or left so that there are only one non-zero digit to its left. • The resulting placement of the decimal will produce the N part of the standard scientific notational expression. • Count the number of places that you had to move the decimal to satisfy step 1 above. • If it is to the left as it will be for numbers greater than 10, that number of positions will equal x in the general expression.
Practice Problems • Express the following measurements in scientific notation: 1. a. 5800 m b. 450,000 m c. 302,000,000 m 2. a. 0.000508 kg b. 0.00000045 kg c. 0.003600kg d. 0.004 kg 3. a. 300,000,000 s b.186,000 s c. 93,000,000 s d. 86,000,000,000 m
Practice problem Answers 1.a. 5.8 x 103 m b. 4.5 x 10 5 m c. 3.02 x 108 m 2.a. 5.08 x 10-4 kg b. 4.5 x 10-7 kg c. 3.600 x 10-3 kg d. 4 x 10-3 kg 3. a. 3 x 108 s b. 1.86 x 105 s c. 9.3 x 107 s d. 8.6 x 1010 m
Milli (m) = 1/1,000 or 10-3 Centi (c) = 1/100 or 10-2 Deci (d) = 1/10 or 10-1 Kilo (k) =1,000 or 103 Hecto (h) 100 or 102 Deka (da) 10 or 101 Examples: Conversion between units. What is the equivalent of 500 millimeters in meters? 1 mm = 1 x 10-3 meter. Therefore, (500 mm)(1 x 10-3 m)/1mm = 500 x 10-3 m = 5 x 10-1 m Prefixes used with SI units
A very useful method of converting one unit to an equivalent unit is called the factor-label method of unit conversion. Just like fractions, if you multiply a number by an equivalent of 1, the value does not change. Example: To convert 2/3 to an equivalent fraction with a denominator of 12, you would multiply by an equivalent of 1: 2/3 x 4/4 = 8/12 Likewise, to change one unit to another, you must multiply by an equivalent of 1. 4 km = ? m (1 km = 103 m) (4/1 km)(1 x 103 m) = 4,000 m or 4 x 103 m Dimensional Analysis(Factor-Label Method)
Practice Problems • Convert each of the following to its equivalent in meters. a. 1.1 cm b. 76.2 mm c. 2.1 km • Convert each of the following to its equivalent in kilograms. a. 147 g b. 11 mg c. 478 mg
Answers to Practice Problems • 1. a. 1.1 x 10-2 m b. 7.62 x 10-2 m c. 2.1 x 103 m • a. 1.47 x 10-1 kg b. 1.1 x 10-5 kg c. 4.78 x 10-4 kg
Operations with Scientific Notation • Addition/Subtraction: • Just like in math class, you can only add or subtract like terms. For ex: 2X + 3X = 5X but 2X2 + 3X cannot be added. • Therefore, 5 x 10-7 kg + 3 x 10-7kg = 8 x 10-7 kg • If 2 amounts are not like terms, you can change the scientific notation of one quantity to make them match. For ex: • 1.9 x 10-7 – 3.8x 10-8 can be rewritten as 1.9 x 10-7 – .38 x 10-7 The answer is 1.52 x 10-7 or just 1.5 x 10-7
Operations with Scientific Notation • Multiplication/Division: • In math (2x3)(3x) = 6x3+1 or 6x4 • Also, 12x6/3x2 = 4x6-2 or 4x4 • Likewise,(3 x 106 m)(2 x 103 m) = 6 x 109 m2 • (8 x 106 m)/(2 x 104 s) = 4 x 102 m/s
Precision is the degree of exactness to which the measurement of a quantity can be reproduced. Accuracy is the extent to which a measured value agrees with the standard value of a quantity Parallax is the apparent shift in the position of an object when it is viewed from various angles Eye Level Not All is Certain • Rule: Always Read measuring instruments at eye level.
Significant Digits • Because the precision of all measuring devices is limited, the number of digits that is valid for any measurement is also limited. The valid digits are called significant digits.
Rules for Significant Digits • Rules for determining which digits in a measurement are significant are: • Every nonzero digit in a recorded measurement is significant. • Zeroes appearing between nonzero digits are significant. The Zeroes in front of (before) all nonzero digits are merely placeholders; they are not significant. 0.0000099 only has two significant figures. • Zeroes at the end of the number if a decimal point is present and also zeroes to the right of the decimal are significant. The measurements 1241.20 m, 210.100 m and 5600.00 all have six significant digits. • Zeroes at the end of a measurement and to the left of an omitted decimal point are ambiguous. They are not significant if they are only place holders: 6,000,000 live in New York—the zeroes are just to represent the magnitude of how many people are in N.Y. But the zeroes can be significant if they are the result of precise measurements.
Practice Problems 1. State the number of significant digits in each measurement. • 2804 m b. 2.84 m c. 0.0029 m d. 0.003068 m e. 4.6 x 105 m f. 4.06 x 105 • 75 m h. 75.00 mm i. 0.007060 kg j. 1.87 x 106 ml k. 1.008 x 108 m l. 1.20 x 10-4 m
Answers • 1.a 4 b. 3 c. 2 d. 4 e. 2 f. 3 g. 2 h. 4 i. 4 j. 3 k. 4 l. 3
Operations using significant digits • Rules for addition and subtraction: • The sum or difference of any 2 measurements cannot be more precise than the least precise measurement. • First add or subtract as indicated. Then, round off the answer to the lowest number of decimal places in the original measurements. • For ex: 24.686 m The answer can only be precise 2.343 m to the nearest hundredth 3.21 m because the least precise 30.239 m measurement is precise to only 2 decimal places. The best answer is 30.24 m
Operations for multiplication/division • In multiplication or division, first do the operation. Then note the factor with the least number of significant digits. That is how many significant digits will be in the answer. • For example: Multiply 3.22 cm by 2.1 cm. • The answer is 6.762 cm2 • The least precise factor is 2.1 with only 2 significant digits; therefore the answer must be rounded to 6.8 cm2.
Solving Equations Using Algebra • General Rule: To move a number or variable from one side of the equation to the other, do the operation opposite to what is done to it in the equation. • Ex: Solve for the variable. x - 5 = 2. • x - 5 = 2 x - 5 + 5 = 2 + 5 5 is added to both sides x = 7
More Examples. • Solve for the variable. 1. x/2 = 5. 2. 10 - 3x = 7.
Solving with radicals • Solve the radical equation.
Graphing Terms • The independent variable (x) is the variable that the experimenter manipulates or controls. • The dependent variable (y) is the responding variable. Its value changes when the independent variable changes. • The independent variable is graphed on the horizontal axis and the dependent variable is graphed on the vertical axis.
Graphing Relationships • A linear relationship is a straight line and is written in the form: y = mx + b where m is the slope and b is the y-intercept. • An inverse relationship is written in the form xy = k or y = k(1/x) or kx-1 where k is a constant. • A quadratic relationship is written in the form y = kx2.
Graphing relationships • Linear Inverse Quadratic