ADVANCED PLACEMENT PHYSICS 1 MS. LAWLESS ALAWLESS@SOMERVILLESCHOOLS.ORG Purpose of Assignments: This assignment is broken into 8 Skills. Skills 1-6, and 8 are review of science and math literacy. Skill 7 is introducing a new skill required for physics which involves vectors or accounting for directional quantities. Required Assignment(s): DUE DATE: First Monday upon return to school in September For clarity THERE ARE ASTERISKS ALONG THE MARGINS TO INDICATE THAT WORK MUST BE DONE BY THE STUDENT IN THAT SECTION. It is recommended that this be done in the last half of the summer so that the skills are fresh when school starts. Each section should take an average of 15 minutes per section depending the students abilities. SECTION 7: VECTORS MAY TAKE 30-60 MINUTES. Packet will be graded on correctness and completion. Optional Assignment(s): There is no optional assignment. 1
Somerville High School AP Physics I Summer Packet. Due: September 11 TH 2017 This packet must be completed and turned in on the first MONDAY AT THE START OF SCHOOL. Student Name: Since questions are interspersed throughout we have indicated areas that require student action to answer the questions. These areas are indicated with asterisks along the margin. This packet is designed to test/practice the skills that are necessary to survive in AP Physics I. AP Physics I requires a strong proficiency in the fundamentals of math including the following: unit conversions, graphing, algebraic manipulation, linearizing an equation, geometry, trigonometry, etc. This packet contains some information and examples but should not be your only source. You can get help on these, if you need it by working with another student. Of course many websites are helpful. PhysicsClassroom.com is an excellent resource for all physics topics. 2
Skill #1: Algebraic Manipulation It is imperative that you have the ability to manipulate algebraic relationships in order to isolate variables. This includes standard simplification rules as well. In many cases you may be asked to solve problems and simplify without the use of numerical values. Please complete the following by solving for the appropriate variable and simplifying where necessary. Use the space at the bottom of the page for any work. 3
Skill #2: Unit Conversions We use the MKS (Meter, Kilogram, Second) version of the SI System in Physics but many measurements or data may be in other forms of these units or even in other systems altogether such as the English System. Remember that the prefix relates the correct power of 10. Example: 1 micrometer (μm) = 1 x 10-6 m. A measurement of 130 micrometers (μm) = 130 x 10-6 m. Putting this in standard scientific notation would yield a value of 1.3 x 10 4 m. Convert the following to the new unit shown. If you need a conversion factor you can find them on the internet. A metric prefix table can be found at the following link: http://www.nanotech now.com/metric prefixtable.htm 4
Skill #3 Scientific Notation Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0000000056, we write 5.6 x 10-9. So, how does this work? Here are some examples of scientific notation. 10000 = 1 x 10 4 24327 = 2.4327 x 10 4 1000 = 1 x 10 3 7354 = 7.354 x 10 3 100 = 1 x 10 2 482 = 4.82 x 10 2 10 = 1 x 10 1 89 = 8.9 x 10 1 (not usually done) 1 = 10 0 1/10 = 0.1 = 1 x 10-1 0.32 = 3.2 x 10-1 (not usually done) 1/100 = 0.01 = 1 x 10-2 0.053 = 5.3 x 10-2 1/1000 = 0.001 = 1 x 10-3 0.0078 = 7.8 x 10-3 1/10000 = 0.0001 = 1 x 10-4 0.00044 = 4.4 x 10-4 As you can see, the exponent of 10 is the number of places the decimal point must be shifted to give the number in long form. A positive exponent shows that the decimal point is shifted that number of places to the right. A negative exponent shows that the decimal point is shifted that number of places to the left. In scientific notation, the digit term (4.660 below) indicates the number of significant figures in the number. The exponential term only places the decimal point. As an example, 46600000 = 4.66 x 10 7 This number only has 3 significant figures. The zeros are not significant; they are only holding a place. As another example, 0.000530 = 5.30 x 10-4 This number has 3 significant figures. The zeros are only placeholders except for the last zero that shows that it is a measured or significant value. How to do calculations: On your scientific calculator: Make sure that the number in scientific notation is put into your calculator correctly. Read the directions for your particular calculator. For inexpensive scientific calculators: 1. Punch the number (the base number) into your calculator. 2. Push the EE or EXP button. Do NOT use the x (times) button!! 3. Enter the exponent number. Use the +/- button to change its sign. 4. Voila! Treat this number normally in all subsequent calculations. Ex. To check yourself, multiply 6.0 x 10 5 times 4.0 x 10 3 on your calculator. Your answer should be 2.4 x 10 9. Question 1 Write in scientific notation: 0.000467 and 32000000 Question 2 Express 5.43 x 10-3 as a number. Question 3 (4.5 x 10-14 ) x (5.2 x 10 3 ) =? Question 4 (6.1 x 10 5 )/(1.2 x 10-3 ) =? Question 5 (3.74 x 10-3 ) 4 =? Question 6 The fifth root of 7.20 x 10 22 =? 5
Skill #4 Calculations with Significant Figures (Sig.Figs.) Before you can determine how many sig figs to report in your final calculation you first need to be able to determine how many sig figs are in the individual numbers. The technical rules are: 1. All non-zero integers are significant, no matter where they are. 2. Leading zeros (zeros before other numbers) are never significant. 3. Captive zeros (zeros between other numbers) are always significant. 4. Trailing zeros (zeros after other numbers) are significant only if the number contains a decimal point. For example, 1000 has one significant figure (1). The number 1000.0 has four significant figures (1 and the three 0s). A way to remember this, which may help, is the "Atlantic-Pacific Rule". Imagine the U.S. bounded on the right by the Atlantic Ocean and on the left by the Pacific Ocean. If the decimal point is Absent, you begin at the Atlantic, on the right. You ignore all zeros until you hit a nonzero integer, and then count every number after that as significant. If the decimal point is Present, you begin at the Pacific, on the left. You do the same thing. So, what are we counting? We count the first nonzero digit we encounter and all subsequent digits. E.G.: 432.30 grams has 5 sig figs. 6,000 m has 1 sig fig. When dealing with Scientific notation you only count the sig figs in the base number. How many significant figures are in the following numbers? 1) 1230 2) 0.01010 3) 0.023 4) 9.210 5).02300 6).200 7) 2.300 8) 4.0 x 10 6 9) 3.20 x 10 4 The Basic Rules for math with sig figs are as follows: Adding and Subtracting: The answer has the same number of decimal places as the least given. Don t forget that the units must be the same if you are comparing decimal places. In other words you can t compare cm to km. Multiplying and Dividing: The answer has the same number of sig figs as the least given. Solve the following problems and be sure to include correct units and sig figs in your answer. 1) 7.301 cm +8.2 cm = 3) 4.32 m 2.3m = 2) 6.5 km + 4.35 m + 1300 cm = 4) 20.02 m / 4.20 sec = 6
Skill #5: Basic Geometry In Physics we use many basic principles of geometry. We look at circles when dealing with rotation, at triangles when dealing with right angle trigonometry and area under curves, and angular relationships when dealing with angular forces, refraction of light, etc. Below are some very basic geometric questions. 7
Skill #6: Right Angle Trigonometry We will constantly be using right angle trigonometry in most Physics topics such as vectors, forces, and optics. You should know the sine, cosine and tangent functions as well as the Pythagorean Theorem. We may run across situations where the law of cosines and law of sines will be useful but they are typically not necessary. Please answer the questions below. Here is a quick review of how to use Soh Cah Toa to find sides and angles of a Right Triangle. Every resultant (the sum of vectors) can be drawn as a right triangle. The study of trigonometry begins with the right triangle. The three main trig functions are sine, cosine, and tangent. The longest side of this right triangle (or any right triangle), the diagonal side, is called the hypotenuse. In the example above, the side that s 3 units long is referred to as the opposite side because it s on the opposite side of the triangle from angle x, and the side of length 4 is called the adjacent side because it s adjacent to, or touching, angle x. Be aware that the adjacent and opposite sides switch depending on which angle you of the smaller angles serves as reference angle. SohCahToa (pronounced so-cah-towah) is a meaningless mnemonic that helps you remember the definitions of the sine, cosine, and tangent functions. SohCahToa uses the initial letters of sine, cosine, and tangent, and the initial letters of hypotenuse (H), opposite (O), and adjacent (A), to help you remember the following definitions. Pythagorean Theorem: This is the last tool to use in solving right triangles. You can use this when you know any two sides of the right triangle. a 2 + b 2 = c 2 where a and b are the smaller sides and c is the hypotenuse. 8
WARNING: BE SURE YOU CALCULATOR IS IN DEGREE MODE. Solve the following right triangles. (Don t forget units) (Note that triangles are not drawn to scale.) 1) 2) 3) 100N Θ Θ 1.75 m 34 dx Fx v Θ1 15 F Θ 5.2 m/s dy Θ2 3.5 m/s Θ1 = Θ2 = V = Dx = Dy = Θ = Fx = F = Θ = 9
Skill #7: Vectors There are two classifications of quantities we will study: Vectors and Scalars. Scalar quantity: This is a quantity that represents only the magnitude (amount/size) of a measurement. Mass, volume, time and temperature are some examples of scalars. Vector quantity: Most of the quantities that we will study in Physics are vectors. Vectors are different that standard scalar quantities because they have both a magnitude and a direction. Vectors are represented by a variable with an arrow above it as in the examples shown below When a vector is drawn in space it is represented by an arrow and labeled with the variable that it represents. The length of the arrow corresponds to the magnitude of the vector while the orientation of the arrow represents the vector s direction. Negative vectors have the same magnitude as their positive counterparts but a direction turn of 180. IMPORTANT! It is very important to understand that in Physics a negative sign ( ) does not represent the actual value of a number but its direction. In Math 2 is smaller than +2 but in Physics the negative just indicates opposite direction. Example: If student A moves forward at 2 miles per hour (2 mph) and student B moves backwards at 3 mph (-3 mph) The student moving -3 mph is moving faster, just in the opposite direction. Resultant: When you add numbers together you get a result. When you add vectors together, you get a resultant. Vectors can be added together to form larger vectors called Resultants. The examples below are adding only two vectors together, but you can add more than two vectors together. To add them tip to tail just draw the first vector, then start from where you left off (at the tip of the arrow) and draw the next vector from there. The ANSWER or RESULTANT is always draw from where your first vector started to where you last vector ended. (Start at the start and end at the end). If you need to subtract vectors, just add the opposite a b is the same as a + (-b). VECTORS ALWAYS INDICTAE DIRECTION AND SHOULD NEVER BE DRAWN WITHOUT A DIRECTIONAL ARROW!!! 10
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Component Vectors: A resultant vector is mathematically made up of the sum of the component vectors of all of the vectors that make the resultant. Each individual vector, including the resultant can be thought of as being made up of an (X, Y) set of vectors called the components. Any vector can be represented by its x and y components. Perhaps you noticed that the x and y components are always at right angles and so they form a right triangle. Trigonometry and Vectors: Now we know how to visually represent vector components. We need to know how to solve right triangles. Every resultant (the sum of vectors) can be drawn as a right triangle. 12
Skill #8: Graphing and Analysis Graphical construction & analysis are very important skills to have in Physics. You will be asked to convert equations to linear form, correctly graph data, apply best fit lines to your data and determine slope/intercept values. You will also be asked to interpret graphs to obtain specific information. Complete the problems below 1) Plot the following data on the grid provided. a. Be sure to title the graph. Graphs are always titled as y vs. x. b. Label the axes and include units. c. Choose major and minor divisions that are easy to read and interpolate. d. NEVER, NEVER use cut outs (skip numbers on an axis). Always start at zero. 2) Draw a best-fit line. Distance (meters) 3) Choose two points that are ON THE LINE (not your necessarily your original points) and calculate the slope of your nest fit line. Be sure to include the units for your slope. 4) What is the y-intercept (don t forget units)? Time (seconds) 2.1 0.0 3.6 0.2 4.2 0.3 6.1 0.5 8.0 0.8 9.9 1.0 5) For this graph, write out the slope-intercept equation for this line. 13
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