(or as they want me to call it, Introduction to Physics) The Joy of Physics (or as they want me to call it, Introduction to Physics)

The Joy of Physics Introductory Notes

Unit Information Unit Objectives Essential Questions Measure with accuracy and precision (e.g., length, volume, mass, temperature, time) Convert within a unit (e.g., centimeters to meters). Use common prefixes such as milli-, centi-, and kilo-. Use scientific notation, where appropriate. Use of appropriate SI units (metric analysis) Essential Questions Why is it important to have a common system of measurement? Why is it important to use the Metric system for scientific work? How do you convert between Metric units and use scientific notation?

Thou shall not use the U.S. Conventional system! Go metric! These are some of the terms we will be using this year: Mass – grams or kilograms Volume – liters or cubic centimeters (cm3) Distance – meters, centimeters, millimeters, kilometers Temperature – celsius, kelvin Thou shall not use the U.S. Conventional system!

Go metric! Learn them! Use them!

Go metric! Giga – billion - 1 x 109 Mega – million – 1 x 106 You will be seeing/using these prefixes often this year. It is in your best interest to learn them and get accustomed to them! Giga – billion - 1 x 109 Mega – million – 1 x 106 Kilo - thousand – 1 x 103 centi – one hundredth – 1 x 10-2 milli – one thousandth – 1 x 10-3 micro – one millionth – 1 x 10-6 nano – one billionth 1 x 10-9

Simple Metric Approximations 1 cm – width of a fingernail 1 meter – distance from your nose to the end of your fingertips 1 g – mass of a paperclip 5 g – mass of a nickel 1 kg – small brick 2 mL – volume of a thimble 2 L – soda bottle

Accuracy vs. Precision Accuracy is how close a measurement is to the correct or accepted value of quantity measured. Precision is the degree of exactness of a measurement. Take a look at the next slide to see one way to examine accuracy vs. precision.

Let’s say you live approximately 10 miles from school Metric System What if you need to measure a longer distance, like from your house to school? Let’s say you live approximately 10 miles from school 10 miles = 16093 meters 16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage: 16093 meters = 16.093 kilometers (or 16.1 if rounded to 1 decimal place)

Metric System These prefixes are based on powers of 10. What does this mean? From each prefix every “step” is either: 10 times larger or 10 times smaller For example Centimeters are 10 times larger than millimeters 1 centimeter = 10 millimeters kilo hecto deca Base Units meter gram liter deci centi milli

Metric System Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length 1 centimeter = 10 millimeters Example not to scale 40 41 1 mm 40 41 1 cm

Metric Conversion Kilo- Hecto- Deka- Base Unit (meter, liter, gram) When converting within the metric system, just follow the steps! Kilo- Hecto- Deka- Deci- Cent- Milli- Base Unit (meter, liter, gram) To go down the steps, multiply by ten for each step. To go up the steps, divide by ten for each step. Examples: 43 meters = 430 decimeters= 4300 centimeters = 43000 millimeters 1750 grams = 175.0 dekagrams = 17.5 hectograms = 1.750 kilograms

Measurements Base measurement Derived Measurement A single number from a direct observation or measurement. Distance: meter Mass: gram Time: second Derived Measurement A measurement acquired from two or more base measurements. – Area: a = l x w – Density: d = m/v – Volume: v = l x w x h

Dimensional Analysis However, for converting from one set of units to a different set of units requires something else. 15 miles x 1 kilometer x 1000 meters = 25,000 m .6 mile 1 kilometer However, 15 miles x 1.6 kilometer x 1000 meters = 24,000 m 1 mile 1 kilometer Both answers are correct, but depending upon which conversion you use, you may get different answers.

Recommendations It’s that easy! Make certain that similar terms cancel out. Do any mathematical cancelling if possible. Multiply across the top and bottom and divide those two numbers. Be careful with which conversion you use. It’s that easy!

Dimensional Analysis The process of converting one set of units to another set. The number and label change, but the value remains the same Example: Converting hours to seconds 15 hours x 60 minutes x 60 seconds = 54,000 s 1 hour 1 minute So…..15 hours = 54,000 seconds. Same value, different label.

Useful Conversions 1 mile = 1.6 km 1 meter = 3.3 ft 1 kg = 2.2 lbs 1 inch =2.54 cm 1 oz = 28 g 1 lb = 454 g

Scientific Notation A way of writing numbers that makes it easier to work with very large or small numbers. 2 parts: base number and exponent 6.0223 x 1023 base exponent

Scientific Notation 6.0223 x 1023 Base number must be between 1 and 10. (may be a decimal) Exponent indicates how many times the number is multiplied by 10 (in this case 23 times)

Scientific Notation MEarth = 6,000,000,000,000,000,000,000,000 kg Examples: MEarth = 6,000,000,000,000,000,000,000,000 kg This is better written as 6.0 x 1024 kg You can do it with negatives also but this is a very small number: Melectron = 0.000000000000000000000000000000911 kg I think 9.11 x 10-31 works much better! Remember a positive exponent means a number larger than 1, a negative exponent means a number smaller than 1!

Scientific Notation on the calculator 6.0223 x 1023 On your calculator type in 6.0223 Find the EE (or EXP) button and press it Type in 23 That’s it!

Rules for Exponents Product Rule na x nb = na+b Here ares some rules to follow when using exponents. Product Rule na x nb = na+b Quotient Rule na/nb = na-b Power rule (na)b = nab

Scalar vs. Vector Quantities Some measurements are straightforward and do not involve direction and express magnitude (size) alone. These are called scalar quantities (or scalars). ex: mass, length Other measurements involve magnitude and direction. These are called vector quantities. ex: force, velocity, acceleration, momentum

The Joy of Physics Vectors

Vectors In diagrams, vectors are shown as arrows, drawn to scale and in the proper direction. ex: 15 m/s The arrow has both a tail and a head.

Vector Addition in One Dimension When vectors lie in the same plane you simply add them, making sure to note any with negative values (such as the 50 m west in the image to the right). The answer is called the resultant and is in purple below the component vectors.

Properties of Vectors A few key points to be aware of regarding vectors: They can be moved parallel to themselves in a diagram. They can be added in any order. To subtract a vector, add the opposite.

Vectors in Two Dimensions Things do not always move simply in one dimension. Often there are two forces or velocities in different directions. An example: a plane flying north at 300 km/h north is being pushed by wind moving at 50 km/h east. Putting the tails together you might get a diagram like this: 300 km/h 50 km/h

Three Ways to Solve Parallelogram method Pythagorean theorem SOH CAH TOA

Parallelogram Method If you have drawn your vectors to scale and put the tails together, you can draw parallel lines to make a complete parallelogram (dashed lines). Then you draw the resultant from the tails of your component vectors to where the new heads meet (red line). Then you measure the resultant. 300 km/h 50 km/h

Pythagorean Method The Pythagorean theorem states a2 + b2 = c2, where a and b are sides of a right triangle and c is the hypotenuse. Thinking graphically this would be: Δx2 + Δy2 = d2 In this instance we want to rearrange the components so that the resultant is going in the proper direction. 300 km/h 50 km/h 300 km/h 50 km/h

Pythagorean Theorem Let a = 50 km/h Let b = 300 km/h 502 + 3002 = c2 2500 + 90000 = c2 92,500 = c2 C = 304 km/h Therefore, the resultant velocity is 304 km/h. 300 km/h 50 km/h

SOH CAH TOA This method utilizes trigonometric functions: (sine, cosine and tangent) and can be used to find angles and/or sides. SOH CAH TOA is an acronym that describes how the functions work. Sine (of an angle) = Opposite side / Hypotenuse Cosine (of an angle) = Adjacent side / Hypotenuse Tangent (of an angle) = Opposite side / Adjacent

SOH CAH TOA Which to use? This depends upon which information you have and what you are looking for.

SOH CAH TOA Looking at our example (no longer drawn to scale): The angle here is represented by the symbol theta (θ). The 300 km/h side is opposite the angle and the 50 km/h is adjacent to the angle. 300 km/h 50 km/h θ

SOH CAH TOA Using the other angle: The 300 km/h side is adjacent to the angle and the 50 km/h is opposite the angle. The hypotenuse is always opposite the right angle. 300 km/h 50 km/h θ

Finding an angle For this diagram, we will look for θ. We have the opposite and adjacent sides to the angle so we will use tangent (TOA). Tan θ = 300 km/h / 50 km/h Tan θ = 6 θ = (6) Tan-1 θ = 80.5˚ 300 km/h 50 km/h θ

Finding a Side Here we will look for the resultant (hypotenuse) and we have the side opposite the angle. Therefore we will use the sine function (SOH). Sin 50˚= 40 / H H = 40 / Sin 50˚ H = 52 N 40 N θ = 50˚

Internet Resources Metric System http://www.khanacademy.org/search?page_search_query=metric+system Vectors http://www.khanacademy.org/science/physics/v/introduction-to-vectors-and- scalars http://thenewboston.org/watch.php?cat=35&number=8 http://www.physicsclassroom.com/Class/vectors/u3l1a.cfm Scientific Notation http://www.khanacademy.org/searchpage_search_query=scientific+notation