AP Physics 1 Summer Assignment 2018 Bayonne High School

Transcription

1 AP Physics 1 Summer Assignment 2018 Bayonne High School AP Physics 1 is an algebra based physics course through which one would develop a deep conceptual understanding of how the physical world works. Concepts from Algebra and Geometry are used in this course, so summer is a good time to review these concepts. You will be manipulating algebraic equations without numbers and use basic trigonometry when problem solving. You will also start studying Kinematics the study of motion using Physicsclassroom.com. Following is a summer assignment, which is to be turned in on the first day of school. Set aside 25+ hours, evenly spread through the summer to do this. You will take a quiz based on the summer assignment in the first week of school. It is important that you do all work by yourself and understand what you are doing. It is a good practice to ask for help after you have tried enough, but copying someone else's work is plagiarism and has historically led to poor results. In this course, concepts in Mechanics (Kinematics, Forces, Two Dimensional Motion, Momentum, Energy, Rotational Motion, Vibrations and Waves) and Simple Electrical Circuits (basic Electrostatics and DC Circuits) are developed through labs, followed by problem solving. You will communicate your ideas with your peers and the instructor through discussions and in writing. Active participation during class and about 5 hours of homework per week are expected for this class. We use the textbook College Physics by Randall Knight and Workbook 1 that goes with this textbook. You will receive a textbook and a workbook to keep during the school year. Following online resources can be used as references for this course, besides the class work and the textbook. 1. Physicsclassroom.com ( The tutorial section of this site is like an online textbook, complete with explanations, animations and questions. 2. HyperPhysics ( astr.gsu.edu/hbase/hframe.html) This site has the physics concepts presented in a concept map. You will be able to trace a concept or a principle in physics using the map. The site has great explanations and solved examples physics- 1- video- list This site has a set of YouTube videos by Mr. Anderson for AP Physics 1 class. Mr. Anderson s explanations are thorough and promote deep understanding of concepts. If you have any questions, please send me an at the following address. kopatel@bboed.org ***Note that my ID is "kopatel", not "kpatel"*** Page 1 of 18

2 PART A Math Review Significant Figures and Scientific Notation Review 1.) How many significant figures do the following numbers have? a.) Answer: d.) Answer: b.) Answer: e.) π Answer: c.) 206,000 Answer: Directions: Evaluate the following without using a calculator. Final answers should be in scientific notation with the correct number of significant figures. 2.) ( )( ) 3.) ( ) ) ) Unit Conversions Review 6.) Finish the SI prefix table below. Follow the example of the centi- prefix. You will need to remember these. Symbol Name Numerical Equivalent p n µ m c centi 10-2 k M G Page 2 of 18

3 Show your work for the following: 7.) 16.7 kilograms is how many grams? 8.) 560 nm is how many meters? 9.) 15 years is how many seconds? 10.) seconds is how many years? 11.) m/s is how many kilometers per hour? Page 3 of 18

4 Right Triangle Activity In this activity you will find patterns that lead to relationships between the sides and angles of a right triangle and define the patterns using math functions. Consider the right triangles A, B F in the following figures. Each right triangle has the same three angles, but varying lengths of sides. A B C Figure 1 D E F Figure 2 Label the angle between the base and the hypotenuse as θ (pronounce thay- tah ) in Figure 1 and as Φ (pronounce figh ) in Figure 2. For a right triangle the side opposite to the angle being considered is called the opposite and the side adjacent to the angle is called the adjacent. We're interested in finding the following ratios as the lengths of the sides change, keeping the same angle. For each of the triangles A to F, measure the three sides using a ruler; calculate the ratios using a calculator and record below. Be sure to measure each side in centimeters, to the nearest 10 th of a cm. Triangle Length of the adjacent side A Length of the opposite side Length of the hypotenuse Ratio (o / h) Ratio (a / h) Ratio (o / a) B C D E F Page 4 of 18

5 Notice that there is a pattern in the ratios. Describe the pattern in your own words in the following space. Now use your scientific calculator to determine the sine, cosine, and tangent of the angle θ and angle Φ. This is done using the sin, cos, or tan keys on your calculator. For example, let s say θ = 30 and you want to find the sine of 30. Depending on your type of calculator, you will either push the sin button and then type 30, or type 30 and then press the sin button. If you have done it correctly, the display should read 0.5 as an answer. Be sure that your calculator is set to the DEGREE mode. Check if the ratios you found in the previous activity make sense. Trigonometry Review Directions: Use the figure below to answer problems Simplify as much as you can. For problems 12-18, write your answer using the given variables a, b, c and θ. To find θ, when let s say sin θ is given, use the inverse operation, sin - 1, on the calculator. a b c θ 12.) Find c if given a and b. 13.) Find a if given b and c. 14.) Find a if given c and θ. 15.) Find b if given a and θ. Page 5 of 18

6 16.) Find c if given b and θ. 17.) Find θ if given b and c. 18.) Find θ if given a and b. 19.) If a = 2.0 cm and c = 7.0 cm, what is b? 20.) If c = 10.0 m and θ = 60, what is b? 21.) If a = 12.0 km and θ = 30, what is b? 22.) Using the properties of triangles, show that A = C in the figure below. Answer: Page 6 of 18

7 23.) For what range of angles (in radians) does sin θ θ? This is known as the small angle approximation, typically used when simplifying problems. Use your calculator in radian mode to figure this out. 24.) Complete the table below without using a calculator. θ sin θ cos θ tan θ 90 degrees = π / 2 radians θ = arc length / radius (when θ is measured in radians) 25.) 360 degrees = radians. 26.) 4.5 revolutions = radians. 27.) Find the length of an arc with a radius of 6.0 m swept across 2.5 radians. 28.) Find the length of an arc with a radius of 10.0 m swept across 100 degrees. Page 7 of 18

8 Algebra Review You will be working with variables without numbers during this course, so make sure you can do the following problems. Use a high school Algebra textbook or an online resource for reference. Directions: Solve the following equations for the given variable and conditions. Simplify as much as possible. Example: 2x + xy = z. Solve for x. x(2 + y) = z x = z 2 + y **Please note that (a + b) / b a b cannot be cancelled out this way. It is in fact equal to (a/b) +1 **Also, (a 2 + b 2 ) a + b (a + b) 2 = a 2 + 2ab + b 2 29.) v 1 + v 2 = 0. Solve for v1. a = Δv / Δt. Solve for Δt. 30.) 31.) v f 2 = v i 2 + 2ad A.) Solve for vi. B.) Solve for d. 32.) d f = d i + v o t at 2 A.) Solve for vo. B.) Solve for t, if vo = 0. Page 8 of 18

9 C.) Solve for t, if di = df. a 33.). Solve for v. c = v 2 r 34.) mgsinθ = µmgcosθ. Solve for θ. 35.) 1 2 mv 2 f + mgh f = 1 2 mv 2 i + mgh i A.) Solve for hf, if hi = 0 and vf = 0. B.) Solve for vf, if hf = 0. Page 9 of 18

10 36.) m 1 v i,1 + m 2 v i,2 = (m 1 + m 2 )v f. Solve for vi,2. 37.) m 1 v i,1 + m 2 v i,2 = m 1 v f,1 + m 2 v f,2. Solve for vf,2 if vi,1 = ) (F 1 sinθ)r 1 + ( F 2 sinφ)r 2 = 0. Solve for r2. Page 10 of 18

11 39.) kx + m( g) = 0. Solve for m. F g = G m 1m 2. Solve for r. 40.) r 2 L L cosθ = v2 41.) 2 Solve for L. 42.) mv 2 R = G Mm. Solve for v. T = 2π L. Solve for g. R 2 43.) g Page 11 of 18

12 44.) 1. Solve for x if vf = 0. 2 mv 2 f kx 2 = 1 2 mv 2 i + mgh i 1 45.) = Solve for RT. R T R 1 R 2 Miscellaneous Directions: Simplify without using a calculator. Remember to show all of your work ) 47.) Page 12 of 18

13 48.) Consider z = x, c = ab, l = m n, or r = s2. y t 2 a.) As x increases and y stays constant, z. b.) As y increases and x stays constant, z. c.) As x increases and z stays constant, y. d.) As a increases and c stays constant, b. e.) As c increases and b stays constant, a. f.) As b increases and a stays constant, c. g.) As n increases and m stays constant, l. h.) As l increases and n stays constant, m. i.) If s is tripled and t stays constant, r is multiplied by. j.) If t is doubled and s stays constant, r is multiplied by. Systems of equations Conceptual Question: 49.) How many equations are needed to solve a.) for 1 unknown variable? b.) for 2 unknown variables? c.) for 3 unknown variables? Use the equations in each problem to solve for the specified variable in the given terms. Simplify as much as possible. 50.) F f = µf N and F N = mgcosθ. Solve for µ in terms of Ff, m, g, and θ. Page 13 of 18

14 51.) F 1 + F 2 = F T and F 1 d 1 = F 2 d 2. Solve for F1 in terms of FT, d1, and d2. 52.) ΣF = mac and a c = v 2. Solve for r in terms of ΣF, m, and v. r 53.) T = 2π L and T = 1. Solve for L in terms of π, g, and f. g f Page 14 of 18

15 Graphing Equations 54.) If r = c x*t was graphed on an r vs. t graph, what would the following be? Slope: y- intercept: 55.) On the y vs. x graphs below, neatly sketch the relationships given. a.) y = mx + b, if m > 0 and b = 0. b.) y = mx + b, if m < 0 and b > 0. c.) y = x 2 d.) y = x e.) y = 1/x f.) y = 1/x 2 g.) y = 1 x h.) y = sin(x) Page 15 of 18

16 Marbles in Cylinder Lab You received a graduated cylinder with three identical marbles and an unknown amount of water already in it. You placed extra identical marbles in the cylinder and obtained the data below. Use the data to graph a best- fit line showing the relationship between the water level and the number of marbles. Scale your axes appropriately, so the y- intercept is visible on the graph. Label your axes and include units. From the graph, determine a mathematical relationship (equation) for the water level for any number of marbles. Lastly, explain the meaning of the slope and y- intercept of your relationship in words. Number of Marbles Water level (ml) in Water ) Graph below 57.) Mathematical relationship using given variables (not just in terms of x and y): 58.) Explanation of the relationship in words: (Include the meaning of the slope and y- intercept.) Page 16 of 18

17 PART B - Kinematics Go to the following website and read as much as possible from the unit, One Dimensional Kinematics. Tutorial Make your own notes from the reading and write down any questions that you have as you work that can be brought up during a class discussion. Go to the following websites and answer all questions from the sections listed below from the Concept Builders on Physicsclassroom.com. Builders/Relationships- and- Graphs Builders/Kinematics Answer all questions from the following sections on paper (only write the answers; the questions may be printed, although printing is optional.) Relationships and Graphs Using Graphs Learning Goal: To analyze a graph in order to determine its slope (along with appropriate units), to use words to describe the relationship between plotted quantities, and to extrapolate in order to predict an unknown quantity. Which One Doesn't Belong Learning Goal: To use an understanding of the various types of relationships in order to identify which representation is not consistent with the other representations. 1- Dimensional Kinematics Distance vs. Displacement Learning Goal: To analyze a multi- stage motion and to determine the distance and the displacement for that motion. Acceleration Learning Goal: To identify whether an object accelerates or not, to determine the direction of the acceleration, and to determine the acceleration value if given simple numerical data. Name That Motion Learning Goal: To use an understanding of the language of kinematics in order to Page 17 of 18

18 accurately match an animation of a motion to the corresponding verbal description of that motion. Motion Diagrams Learning Goal: To construct the motion diagram for a given motion, showing properly- spaced dots, velocity vectors, and acceleration vectors. Graph That Motion Learning Goal: To use an understanding of the principles of kinematic graphing in order to accurately match an animation of a motion to the corresponding position- time graph or velocity- time graph of that motion. Match That Graph Learning Goal: To analyze the position- time graph for an object's motion and to match it to the corresponding velocity- time graph... or vice versa. Position- Time Graphs - Conceptual Analysis Learning Goal: To analyze a position- time graph and associate the graph features with motion characteristics of a moving object. Position- Time Graphs - Numerical Analysis Learning Goal: To analyze a position- time graph in order to determine the object s disance traveled, displacement, and velocity. Dots and Graphs Learning Goal: To analyze a dot diagram and match the motion that it describes to the appropriate position- time or velocity- time graph. Which One Doesn't Belong? Learning Goal: To interpret various representations of an object s motion in order to identify which representation is not like the others. Page 18 of 18