AP Physics C Mechanics Summer Assignment

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AP Physics C Mechanics Summer Assignment 2018 2019 School Year Welcome to AP Physics C, an exciting and intensive introductory college physics course for students majoring in the physical sciences or

1 AP Physics C Mechanics Summer Assignment School Year Welcome to AP Physics C, an exciting and intensive introductory college physics course for students majoring in the physical sciences or engineering. Students must have prior exposure to physics topics (i.e. Academic Physics), be proficient in both algebra and trigonometry, and have experience or be concurrently enrolled in the AP Calculus AB course. AP Physics C is comprised of two courses: Mechanics, which is equivalent to the first semester of a university course; and Electricity & Magnetism, which is equivalent to the second semester of a university course. During the students will cover the Mechanics material, focusing on Newtonian Mechanics to include: Kinematics Newton s Laws of Motion Work-Energy-Power Linear Momentum Circular Motion Oscillations Gravity While succeeding in AP Physics C is not entirely dependent upon being an expert mathematician, being proficient with the practices and math skills addressed in this assignment will get you rolling in the right direction. This assignment is due the first day of school, is worth 100 pts, and your grade, teacher, parents, etc., will love you for completing it. Have a wonderful summer and I look forward to seeing you in late August. If you have any questions, please feel free to contact me at Jim.Hurrell@lcps.org. I ll do my best to get back to you as soon as possible. Mr. Hurrell

2 Table of Contents Topic Conversions Topic Introduction 3 6 Problems 7 9 Page (s) Scientific Notation Topic Introduction 10 Problems The Metric/SI System Topic Introduction Problems 16 Manipulating Algebraic Equations Topic Introduction Problems Significant Figures Topic Introduction Problems 25 Trigonometry Basis Topic Introduction 26 Problems 27 Vector Basis Topic Introduction Problems 31 2 P a g e

Conversions We perform conversions if we need to change the units of a quantity. For example, 1 foot equals 12 inches, the amount is the same, but how we express the amount is different.

3 Conversions We perform conversions if we need to change the units of a quantity. For example, 1 foot equals 12 inches, the amount is the same, but how we express the amount is different. To do a conversion you need a conversion factor. Conversion factor nuts and bolts Conversion factors come from commonly used equalities Any equality can make two conversion factors o Example 1 Equality: 12 in = 1 ft 12 in 1 ft Two conversion factors: ( ) or ( 1 ft 12 in ) o Example 2 Equality: 1 hr = 60 min Two conversion factors: ( 1 hr min ) or (60 ) 60 min 1 hr Since anything divided by itself is 1, a conversion factor also equals 1. Step-by-step Conversion Guide Step # Description 1 Write what you are given as a fraction with one unit on the top (aka numerator) and one unit on the bottom (aka denominator) 2 In parenthesis and without numbers, write the units you want to discard diagonal from itself. In the other part of the fraction write what you are converting to. 3 Put numbers into the parenthesis so that the top equals the bottom. This will be a common equality that you know. 4 Cancel out the units but not the numbers 5 Do the math. Multiply the numbers if they are both on top. Divide if the second one is on the bottom. 3 P a g e

4 Single conversion examples Example 1: Convert 55 mi/hr to mi/min Step # Description Details 1 Write what you are given as a fraction with one unit on the top (aka numerator) and one unit on the bottom (aka denominator) 55 mi 1 hr 2 In parenthesis and without numbers, write the units you want to discard diagonal from itself. In the other part of the fraction write what you are converting to. 3 Put numbers into the parenthesis so that the top equals the bottom Common equality used: 1 hr = 60 min 4 Cancel out the units but not the numbers 5 Do the math. Multiply the numbers if they are both on top. Divide if the second one is on the bottom. 55 mi 1 hr ( hr min ) 55 mi 1 hr ( 1 hr 60 min ) 55 mi 1 hr ( 1 hr 60 min ) 55 mi 1 hr ( 1 hr 55 mi ) = 60 min 60 min = mi min Example 2: Convert 25 m/s to ft/s Step # Description Details 1 Write what you are given as a fraction with one unit on the top (aka numerator) and one unit on the bottom (aka denominator) 25 m 1 s 2 In parenthesis and without numbers, write the units you want to discard diagonal from itself. In the other part of the fraction write what you are converting to. 3 Put numbers into the parenthesis so that the top equals the bottom Common equality used: 3.3 ft = 1 m 4 Cancel out the units but not the numbers 5 Do the math. Multiply the numbers if they are both on top. Divide if the second one is on the bottom. 25 m 1 s 25 m 1 s ( ft m ) 25 m 3.3 ft ( 1 s 1 m ) 25 m 3.3 ft ( 1 s 1 m ) 3.3 ft 82.5 ft ( ) = = ft 1 m 1 s s 4 P a g e

5 Multiple conversion examples Notes: When performing more than one conversion, you can do: o Method 1: Perform each conversion independently OR o Method 2: Perform all of the conversions in one long chain Both methods will provide the same answer, but once you master the chain approach, I think you will find it to be the most efficient Convert 700 hours to weeks performing one conversion at a time Conversion 1: (hours to days) Note: Since our starting point is a single unit (hours), just write it over 1. Conversion 2: (days to weeks) 700 hr 1 ( 1 days ) = days 24 hr days 1 ( 1 week ) = 4.17 weeks 7 days Convert 700 hours to weeks using the chain method 700 hr 1 ( 1 days 24 hr week 700 weeks ) (1 ) = = 4.17 weeks 7 days P a g e

6 Railroad Tracks Method (My Favorite) This method of converting units is sometimes called the Factor Label method, but engineers prefer trains so they changed the name to the "Railroad Tracks" method (woo woo). Very similar to the chains method, just a different look. Draw up a set of "Railroad Tracks" as shown below (Train is not required ) With the original value in the top "row" of the first "column" and the original units in the top or bottom row of this column just the way you would normally put them above or below the line. Then write each conversion factor into the following columns in such a way that the units cancel out, leaving the units you want. Note: Each time you add a conversion factor you are actually multiplying by 1.0 because the top and bottom are equal, just in different units. Then multiply or divide all the conversion factors depending on whether they are above or below the line. Railroad Tracks Examples: Convert 700 hours to weeks 700 hr 1 days 1 week 1 24 hr 7 days 24 * 7 = 700 weeks = 4.17 weeks Convert 25 m/s to mi/hr = = m 1 mi 60 s 60 min 25* 60 * 60 mi mi s 1609 m 1 min 1 hr 1609 hr hr 6 P a g e

7 Perform the following conversions given the following equalities: 5280 ft = 1 mi 12 in = 1 ft 1 in = 2.54 cm ( m) 1 m = 3.3 ft Note: ft = feet mi = miles in = inches cm = centimeters m = meters SHOW ALL WORK (1) Convert 7.5 mi to ft (2) Convert 7.5 mi to in (3) Convert 5 ft to m (4) Convert 7 weeks to days 7 P a g e

8 (5) Convert 3500 seconds to minutes (6) Convert 22 m/sec to m/min (7) Convert 60 mph (miles/hr) to m/hr (8) Convert 180 m/min to m/hr (9) Convert 15 in/min to ft/min 8 P a g e

9 (10) Convert 15 in/min to ft/sec (11) Convert 650 cm/min to cm/sec (12) Convert 650 cm/min to in/sec (13) Convert 12 mph to m/s 9 P a g e

10 Scientific Notation Scientific Notation is a neat and compact way of writing large and small numbers while using only significant digits (addressed in the next section) and powers of ten. The conventional form for scientific notation is: N 10 P Where: N = a number in the form of x.xx (digit in the ones, tenths, and hundredths place) P = the powers of ten telling you which direction to move the decimal place and how many times Examples Expanded Form Scientific Notation Comments x 10-3 The negative three power of ten indicates that the decimal point should be moved three places to the left 324, x 10 5 The positive power of five indicates that the decimal point should be moved five places to the right. In this case, zeros are needed as placeholders When dividing, divide the decimals while keeping the correct number of significant figures. When dividing powers of ten, subtract the bottom power of ten s exponent from the top power of ten s exponent. If multiplying, add powers of ten = ( ) ( ) = Before adding or subtracting numbers in scientific notation, all numbers need to have the same power of ten. ( ) + ( ) = = P a g e

11 Write the following numbers in scientific notation: (1) 5800 m (2) mm (3) kg (4) 560 g (5) 4,320,000 cm 2 (6) m/s (7) m 11 P a g e

12 (8) (5.8 x 10-6 ) (2 x 10 4 ) (9) (0.8 x 10 4 ) (1.28 x 10 6 ) (10) (3.8 x 10-6 ) (2.37 x 10-3 ) (11) (12) (13) ( ) ( ) (14) ( ) + ( ) 12 P a g e

SI/Metric System The International System of Units, universally abbreviated SI (from the French Le Système International d Unités), is the modern metric system of measurement.

The dimension of a measurement is indicated by the unit following the number.

13 SI/Metric System The International System of Units, universally abbreviated SI (from the French Le Système International d Unités), is the modern metric system of measurement. There are two quantities required for every measurement: Dimension: The physical quantity being measured, such as length, mass, or force. The dimension of a measurement is indicated by the unit following the number. Unit: This indicates the size of the measurement that is made, for example a mile is larger than a foot which is larger than an inch. The significant difference between the Metric system and British system of measurement is the way in which they indicate the size of a measurement. In the British system, different units are used to measure larger amounts. When an inch becomes too small a foot is used instead. In the metric system of measurement, instead of changing the units, prefixes are applied to base units to indicate larger or smaller amounts. The SI system is a component of the metric system; the only difference is that the SI system uses certain standard units for measurements. This is meant to better standardize the measurements throughout different sciences. These are referred to as SI Units and are used to make all other units of measurement in different combinations. The SI UNITS are shown below with the corresponding English (aka British) for reference. 13 P a g e

14 All other quantities in the metric system are different combinations of SI units and are called derived quantities. Below is a table listing some other quantities that are defined in terms of the seven base units. 14 P a g e

15 Below is a list of some derived quantities that have special names The common SI prefixes that will be used in AP Physics to form decimal multiples and submultiples of SI units are provided below. 15 P a g e

16 Below is a complete list of SI prefixes. Convert the following metric measurements: 1000 mg = g 198g = kg 8 mm = cm 160 cm = mm 75 ml = L 6.3 cm = mm 109 g = kg 50 cm = m 5.6 m = cm 250 m = km 5 L = ml 26,000 cm = m 14 km = m 16 cm = mm 56,500 mm = km 1 L = ml 65 g = mg 27.5 mg = g 480 cm = m 2500 m = km 923 cm = m 27 g = kg 355 ml = L km = cm 16 P a g e

17 Manipulating Algebraic Equations The types of algebraic equations you will be manipulating in AP Physics are ones expressed in terms of variable symbols (such as d, v, and a) and constants (such as r, g, and π). Often in science and mathematics you are given an equation and asked to solve it for a particular variable symbol or letter called the unknown. The symbols which are not the particular variable we are interested in solving for are called literals, and may represent variables or constants. Literal equations are solved by isolating the unknown variable on one side of the equation, and all of the remaining literal variables on the other side of the equation. Sometimes the unknown variable is part of another term. A term is a combination of symbols such as the products ma or πr 2. In this case the unknown (such as r in πr 2 ) must be factored out of the term before we can isolate it. The following rules, examples, and exercises will help you review and practice solving literal equations. PROCEDURE Note: In general, we solve a literal equation for a particular variable by following the basic procedure below. 1. Recall the conventional order of operations, that is, the order in which we perform the operations of multiplication, division, addition, subtraction, etc.: a. Parenthesis b. Exponents c. Multiplication and Division d. Addition and Subtraction This means that you should do what is possible within parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. If some parentheses are enclosed within other parentheses, work from the inside out. 2. If the unknown is a part of a grouped expression (such as a sum inside parentheses), use the distributive property to expand the expression. 3. By adding, subtracting, multiplying, or dividing appropriately, a. move all terms containing the unknown variable to one side of the equation, and b. move all other variables and constants to the other side of the equation. Combine like terms when possible. 4. Factor the unknown variable out of its term by appropriately multiplying or dividing both sides of the equation by the other literals in the term. 5. If the unknown variable is raised to an exponent (such as 2, 3, or ½), perform the appropriate operation to raise the unknown variable to the first power, that is, so that it has an exponent of one. 17 P a g e

18 EXAMPLES 1. F = ma [Solve for a] F = ma Step 1: Divide both sides by m F m = a Step 2: Since the unknown variable (in this case a) is usually placed on the left side of the equation, we can switch the two sides: a = F m 2. v = d t [Solve for t] v = d t Step 1: Multiply each side by t tv = d Step 2: Divide both sides by v t = d v 3. U = 1 2 kx2 [Solve for x] U = 1 2 kx2 Step 1: Multiply both sides by 2 2U = kx 2 Step 2: Divide both sides by k 2U k = x2 18 P a g e

19 Step 3: Take the square root of both sides (For many physics problems the positive root is the only practical solution, therefore we will ignore the negative root in this example) 2U k = x x = 2U k 4. T = 2π L g [Solve for L] T = 2π L g Step 1: Divide both sides by 2π T 2π = L g Step 2: Square both sides T 2 4π 2 = L g Step 3: Multiply both sides by g gt 2 4π 2 = L L = gt2 4π 2 19 P a g e

20 5. F = Gm 1m 2 r 2 [Solve for r] F = Gm 1m 2 r 2 Step 1: Multiply both sides by r 2 Fr 2 = Gm 1 m 2 Step 2: Divide both sides by F r 2 = Gm 1m 2 F Step 3: Take the square root of both sides r = Gm 1m 2 F 6. F = qvb sin θ [Solve for Ɵ] F = qvb sin θ Step 1: Divide both sides by qvb F = sin θ qvb Step 2: Take the inverse sine of both sides θ = sin 1 ( F qvb ) 20 P a g e

21 PROBLEMS For each of the following equations, solve for the variable in bold print. Be sure to show each step you take to solve the equation for the bold variable. 1. v = at [Solve for a] 2. P = F A [Solve for A] 3. λ = h p [Solve for h] 4. F(Δt) = m v [Solve for t] 5. U = Gm 1m 2 r [Solve for m 1] 6. C = 5 (F 32) [Solve for F] 9 21 P a g e

22 7. x = x o + v o t at2 [Solve for a] 8. n 1 sin θ 1 = n 2 sin θ 2 [Solve for Ɵ 2] 9. mg sin θ = μmg cos θ ( M+m ) [Solve for Ɵ] m 10. v rms = 3RT M [Solve for M] 11. F = 1 4πε o Kq 1q 2 r 2 [Solve for r] s i + 1 s o = 1 f [Solve for f] 22 P a g e

23 Significant Figures Significant figures: More simply known as number of digits, represents to what certainty a quantity is known Rules of the road o Leading zero When writing a number using decimal notation where all the significant figures are to the right of the decimal point always include one zero to the left of the decimal point CORRECT INCORRECT How to determine how many significant digits there are in a number Rules o The leftmost digit which is not a zero is the most significant digit o If the number does not have a decimal point, the rightmost digit which is not a zero is the least significant digit o If the number does have a decimal point, the rightmost significant digit is the least significant digit, even if it's a zero o Every digit between the least and most significant digits should be counted as a significant digit Examples: The following numbers all have three significant digits o When Adding or Subtracting numbers Steps 1: Perform the indicated mathematical operations 2: Find the number which is known to the fewest decimal places 3: Round the result to that decimal place Examples 1: = 423 2: = : = : = P a g e

24 o When Multiplying or Subtracting numbers Steps 1: Perform the indicated mathematical operations 2: Find the number with the fewest significant figures 3: Result will have the same number of significant figures as is the number with the fewest significant figures. Examples 1: 13.1 x 2.25 = : x 2.25 = : x = : x 2.3 = : 1.00 x = P a g e

25 PROBLEMS How many significant figures in the following numbers? 1. 1,245m m 3. 10,000m x 1023m x 1014m m 7. 1, Problems 9 13: Perform the following Calculations and record your answers in the proper number of significant figures = m m m = x x x 10 6 = x 10 5 = x 10 3 = x 10 3 ( )(1.3 x 10 6 ) 25 P a g e

Trigonometry Basics The focus of this packet will be right-triangle trigonometry Examine the right triangle pictured below o o o o o o Remember a right triangle has a 90 angle and that the sum of all

The right angle is marked and the other two angles are marked with a and b.

26 Trigonometry Basics The focus of this packet will be right-triangle trigonometry Examine the right triangle pictured below o o o o o o Remember a right triangle has a 90 angle and that the sum of all of the angles in any triangle is equal to 180 The two short sides of this right triangle have been labeled A and B The longest side of a right triangle is known as the hypotenuse. The right angle is marked and the other two angles are marked with a and b. Notice that the right angle is opposite to the hypotenuse and that angle a is opposite to side A and angle b is opposite to side B. We use the Pythagorean Theorem to calculate the length of any side of a right triangle when the length of the other two sides is known Pythagorean s Theorem Hypotenuse 2 = A 2 + B 2 o We use trigonometric relationships to calculate the length of any side of a right triangle when the length of one side and one angle is known. 26 P a g e

27 PROBLEMS Your calculator must be in degree mode! Show all your work. 1. Ɵ = 55 and c = 32, solve for a and b 2. Ɵ = 45 and a = 15, solve for b and c 3. B = 17.8 m and Ɵ = 65, solve for a and c 27 P a g e

Vector Basics General Information o Some quantities can be described with a single number (with units) giving its size or magnitude. Such quantities are called scalar quantities.

28 Vector Basics General Information o Some quantities can be described with a single number (with units) giving its size or magnitude. Such quantities are called scalar quantities. Examples of scalar quantities are time, temperature, and mass. o Many quantities not only have a magnitude but also a direction. Such quantities are called vectors. An example of a vector quantity is displacement. Displacement describes how far you ve traveled and in which direction you have traveled. For example, a car has traveled 2 km due east. Other vector quantities are velocity, acceleration, and force. o An arrow is used to represent a vector. 2 km due east The length of the arrow represents the magnitude and the which way the arrow points is the direction of the quantity. Sign Conventions o Positive and negative signs are typically used to indicate the direction of a vector mathematically. (In Physics, positive and negative signs do NOT mean positive or negative numbers, as in a number line.) Positive sign: to the east or north (right or up) Negative sign: to the west or south (left or down) Adding Vectors o Head-Tail Method Graphically adding vectors Place the tail of the 2 nd vector at the head of the 1 st vector 28 P a g e

29 o Adding Mathematically Vectors that are in the same direction o Vectors that are perpendicular to each other Note: Use methods presented in the Trigonometry Basics section of this packet 29 P a g e

30 o Vectors That Are Not Perpendicular to Each Other All vectors have an x-component and a y-component. Whenever adding vectors that are not going in the same direction or not perpendicular to each other, you must determine the x-component and y- component of each vector and add their components together. 30 P a g e

31 PROBLEMS 1. Determine the x and y components of each of the force vectors shown below. 2. Are the following quantities vectors or scalars? Explain. a. The cost of a theater ticket b. The current in a river 3. Write each combination of vectors as a single vector. See the figure below. 31 P a g e

AP Physics Math Review Packet

AP Physics Math Review Packet The science of physics was developed to help explain the physics environment around us. Many of the subjects covered in this class will help you understand the physical world