#1 NAME: AP Physics B Summer Homework (Show work) #2 Fill in the radian conversion of each angle and the trigonometric value at each angle on the chart. Degree 0 o 30 o 45 o 60 o 90 o 180 o 270 o 360 o Radian sin cos tan csc sec cot 1
Constant Acceleration --------oooo-------------------------- #3 Please memorize the following units and formulas. This will be quizzed. 2
Kinematics (From ramseyjn online resources) #1 Read the online reference notes about kinematics. Use the information provided to answer the following problems and questions. For each problem, list the original equation used, show correct substitution, and arrive at the correct answer with the correct units. All velocities must be reported in m/s, displacements in meters, and time in seconds. a. You begin a trip and record the odometer reading. It says 45545.8 miles. You drive for 35 minutes. At the end of that time the odometer reads 45569.8 miles. What was your average speed in miles per hour? b. A high speed train travels from Paris to Lyons at an average speed of 227 km/h. If the trip takes 2.0 h, how far is it between the two cities? c. Give an example of two cars that have the same speed but different velocities. d. You are driving down the road at a constant velocity. What are 3 ways you could safely change your velocity? e. You nose out another runner to win the 100.0 m dash. If your total time for the race was 11.80 s and you aced out the other runner by 0.001 s, by how many meters did you win? f. The speed of sound is 344 m/s. You see a flash of lightning and then hear the thunder 1.5 seconds later. How far away from the lightning strike are you? g. A train travels from Denver to Bougainvillea in 5 hours and 37 minutes. If the average speed for the train was 76.5 km/h, how much distance did it cover? #2 Use the kinematics equations to solve each of the problems below. Read each problem, think about what is given and what is not given, and decide which equation you can eliminate to come to a solution. The last two problems require you to use two of the equations to solve it. One equation will first be used to solve for a variable you need in the other equation. a. A car traveling at 7.0 m/s accelerates at 2.5 m/s 2 to reach a speed of 12.0 m/s. How long does it take for this acceleration to occur? b. A person pushes a stroller from rest and accelerates at a rate of 0.50 m/s 2. What is the velocity of the stroller after it has traveled 4.75 m? 3
c. An airplane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s 2 for 15.0 s before takeoff. How long must the runway be for the plane to be able to take off? d. A bus slows down with an acceleration of -1.8 m/s 2. How long does it take the bus to slow from 9.0 m/s to a complete stop? e. A car with an initial speed of 4.3 m/s accelerates uniformly at 3.0 m/s 2 for 5.0 s. How far has the car gone? f. A train slows down with a constant acceleration from an initial velocity of 21 m/s to 0 m/s in 21.0 s. How far does it travel before stopping? g. A sailboat starts from rest and accelerates at a rate of 0.21 m/s 2 over a distance of 280 m. Find the time it takes the boat to travel this distance. Unit Conversion Factors #1 To convert km/h to m/s, multiply by unit conversion factors so that the units you don t want cancel out and the units you want remain. Show your work as in the following example: #3 How many seconds are in a year? #4 Convert the speed of light, 3x10 8 m/s, to km/day. #5 The SI unit for liquid volume is 1 milliliter, approximately the volume of a large drop of water. The corresponding SI unit for solid volume is 1 cm 3. 1 drop 1 ml = 1 cm 3. a) How many liters can a 1 m 3 tank hold? b) How many drops of water is this? 4
Moving Man Distance vs. Time Graphs Procedure do the following activity using this web site http://phet.colorado.edu/simulations/index.php?cat=motion Then click on The Moving Man Getting started. After Moving Man is open leave the position graph open but close all of the other graphs, velocity and acceleration. Your screen should look like screen 1. Making observations. By either clicking on the man or the slider cause the man to move back and forth and observe what shows up on the graph. Using the axes provided below make a sketch of the graph that is produced by each action described next to each axis. (From Northview HS online resources) 5
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Moving Man Velocity vs. Time Graphs Procedure Do the following activity using this web site http://phet.colorado.edu/simulations/index.php?cat=motion Then click on The Moving Man. Getting started. After The Moving Man is open leave the position graph and the velocity graph open but close the acceleration graph. Your screen should look like screen 1.. Making observations. By either clicking on the man or the slider cause the man to move back and forth and observe what shows up on the graphs. Using the axis provided below make sketches of Distance vs. Time and Velocity vs. Time graphs for the actions described next to each axis. 7
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Graphing Techniques (Problems by Yav at Ann Sobrato HS) Graph the following sets of data using proper graphing techniques. The first column refers to the y-- axis and the second column to the x-- axis 1. Plot a graph for the following data recorded for an object falling from rest: a. What kind of curve did you obtain? b. What is the relationship between the variables? c. What do you expect the velocity to be after 4.5 s? d. How much time is required for the object to attain a speed of 100 ft/s? 2. Plot a graph showing the relationship between frequency and wavelength of electromagnetic waves: a. What kind of curve did you obtain? b. What is the relationship between the variables? 9
c. What is the wavelength of an electromagnetic wave of frequency 350 Hz? d. What is the frequency of an electromagnetic wave of wavelength 375 m? Ideas of Calculus The following questions are basic ideas of calculus that are often used in physics. This has been discussed in Precalculus Honors. In particular, the slope of the secant line between two points on a position-time curve represents x/ t, which is average velocity. The slope of the tangent line at a point in the position-time curve represents the limit dx/dt, which is instantaneous velocity. (Recall how we discussed difference quotients in class.) Finally, the area under the velocity-time curve can be split into rectangular boxes. Their areas represent v t, or displacement. For more information, please see the following references: Physics Tutorial http://www.physicsclassroom.com/class/1dkin/ (It is mandatory to read Lessons 1~4 of One-Dimensional Kinematics. This is a thorough explanation of all the ideas above. Keep clicking next section until you finish reading Lesson 4.) Mandatory review/reading on tangents, secants, and difference quotients: PrecalculusH class notes P. 3~4 at http://www.oz.nthu.edu.tw/~g9561701/precalculus/ch2_notes_precalc.pdf Optional reading for more information on an introduction to calculus: Read Precalculus, 6 th edition by Stewart, Redlin, and Watson. Sections 2.4 (Average rate of a function), 13.3 (tangents), p. 884 (Focus on Modeling: Interpretations of Area) #1 A car is moving with the following velocity (m/s) vs. time (s) graph. a) Describe the motion of the car. b) Use the area under the curve to find the displacement of the car. (Since x = v t) #2 10
#3 If an object is dropped from a high cliff or a tall building, then the distance after t seconds is given by the function d(t) = 16t 2. a) Find its average speed over the interval t=a and t=a+h. b) Find its instantaneous speed at time a. #4 f(t) = -- 5 t 2 + t + 1. a) Find the slope of the secant line of f on [1, 3]. b) Find the slope of the tangent line at t=a. Projectile Motion: Kinematics and Parametric Equations/Vectors Review the idea of parametric equations and vectors as they apply to projectile motion. Here are some references (choose one if you need to review) Precalculus 6 th edition by Stewart, Redlin, Watson. P. 575 (Focus on Modeling: The Path of a Projectile) or... Pages 6~8 of this link http://www.mhhe.com/math/precalc/barnettpc2/student/olc/graphics/barnett01paga_s/ch10/download s/pc/ch10section5.pdf (from a free online Precalculus Book of McGrawHill http://www.mhhe.com/math/precalc/barnettpc2/student/olc/ ) http://www.animations.physics.unsw.edu.au//jw/projectiles.htm#45 http://www.animations.physics.unsw.edu.au/mechanics/chapter2_projectiles.html Hint: g = 32 ft/s 2 11
Expressions Solve for the variable or simplify into scientific notation (or proper fractions for variables). Include units as needed. Vectors Motion and forces are described using vectors, so it is very important to be familiar with vector math. If review is needed, you may choose from the following references: Precalculus 6 th edition by Stewart, Redlin, and Watson. Chapter 9 My summary of the above in Precalculus H Vector Notes A thorough online resource: http://www.animations.physics.unsw.edu.au/jw/vectors.htm #1 a)sketch v 2u b) Sketch 2v+u #2 #3 12
Trigonometry Trigonometry is very important in physics, for modeling waves as well as for using right triangles to find components of forces. 1 #1 y 1 cos( 2x ) 2 2 3 a) Amplitude = b) Period = c) Phase Shift = d) Graph one period with the 5 important points below. The x and y axes should be clearly labeled: 13
Please practice modeling with sine and cosine with the next four problems. #2 Spring Mass System A mass suspended from a spring is pulled down a distance of 2 ft from its rest position, as shown in the figure. The mass is released at time t = 2 and allowed to oscillate. If the mass returns to this position after 3 s, find an equation that describes its motion. y = position above the ground t = time in seconds y(t) = #3 Ferris Wheel A ferris wheel has a radius of 10 m, and the bottom of the wheel passes 1 m above the ground. If the ferris wheel makes one complete revolution every 20 s, find an equation that gives the height above the ground of a person on the ferris wheel as a function of time. #4 As the tides change, the water level in a bay varies sinusoidally. At high tide today at 8 A.M., the water level was 15 feet; at low tide, 6 hours later at 2 P.M., it was 3 feet. Model the water level as a function of time using a sinusoid. #5 Note that if the hypotenuse of a right triangle is known, the opposite side corresponds to sine and the adjacent side corresponds to cosine. Practice applying right triangles to the following two pictures. Label the vector components of the tension and weight as indicated. 14
#6 A winch of radius 2 ft is used to lift heavy loads. If the winch makes 8 revolutions every 15 s, find the speed at which the load is rising. Hint: s = r Newton s Laws #1 #2 The traffic light is in static equilibrium. #3 a) Find the system s acceleration (Hint: Newton s second law) b) Find the magnitude of the contact force (Hint: Newton s third law) More Laws and Conservation of Energy #1 A tennis ball of mass 0.145 kg is thrown upwards with an initial velocity of 20.0 m/s. Ignoring air resistance, what is the maximum height the tennis ball will reach? Hint: kinetic energy at the bottom is transformed into potential energy at the top. 15
#2 Two iceboats hold a race on a frictionless horizontal lake. The two iceboats have masses m and 2m. Each iceboat has an identical sail, so the wind exerts the same constant force F on each iceboat. The two iceboats start from rest and cross the finish line a distance s away. Describe your reasoning in the following questions. the answers could be: the 1m boat, 2m boat, or both are the same. a) Which iceboat crosses the finish line with greater kinetic energy? (Use the Work-KE Theorem) b) Which iceboat wins the race? (Use Newton s Second Law) c) Which iceboat spends more time along the surface? d) Which iceboat has the greater change in momentum? (Use the Impulse-Momentum theorem) e) If the iceboat of mass m has momentum of 350 kg.m/s at the finish line, how much momentum does the 2m iceboat have? f) If the iceboats go off a ledge at the finish line and the 2m iceboat reaches the ground 10 m from the ledge, at what distance does the 1m iceboat reach the ground? g) Which iceboat spends more time in the air, from the edge of the cliff to the ground? 16