Welcome to AP Physics C

Transcription

1 Welcome to AP Physics C SUMMER ASSIGNMENT 2017 PHYSICS Pearson Education, Inc., 2013 (ebook) Randall D. Knight California Polytechnic State University San Luis Obispo ISBN: Price: $49.97 MasteringPhysics with Pearson etext (1-year access) for MasteringPhysics Purchase (in August) Media Access Card for Classical Mechanics and Electricity & Magnetism ISBN: Price: $39.99 AP Advantage: Physics C (optional) Workbook Edition Peoples Education, 2004 James Mooney The Taft School Watertown, CT ISBN: Price: $22.00 Copyright 2017 R McCall. All rights reserved. Printed in the USA. Page 1

2 Materials: A composition notebook for daily work, and homework problems A small amount of college ruled paper A scientific graphing calculator (TI-83, TI-84, etc.) A clear plastic metric ruler Pencils (NO PENS!) to be brought to class every day (mechanical pencils preferred) USB Flash drive (for downloading online physics information) You have embarked upon a wonderful adventure! You have made a great decision and a powerful commitment in taking AP Physics C!! This summer assignment has a two-fold purpose: First, to decrease the amount of new material that you will have to master during the school year for the AP Exam in May Second, to present an opportunity for you to earn some early strong grades as you begin the first quarter with confidence. AP Physics C Summer Assignment: Download the summer textbook (Physics with Calculus by Craig Fletcher) and the bound quadrille notebook. These items will make the summer assignment easier and clearer. 2. Read Chapters 1-4. This is UNIT 1. Please complete the summer assignment. You have plenty of time. DON T WAIT UNTIL THE LAST MINUTE!! 3. A problem quiz that will cover each chapter will be during the second week of class. 4. Attached to this summer assignment is Summer Calculus Worksheet. 5. Another attachment to this summer assignment is the IN-CLASS EXAMPLE PROBLEMS from Chapters 1-4 to complete. The IN-CLASS EXAMPLE PROBLEMS are included in this packet. The most important thing in this problem assignment is your completely worked-out solutions. The problems will be graded on your worked out solutions. Incomplete or absent work = NO CREDIT! Show me ALL the steps! 6. All the worked-out solutions to the IN-CLASS EXAMPLE PROBLEMS, the worked-out solutions to the Summer Calculus Worksheet, and the detailed notes from chapter 4 are due the first day of class at the beginning of class! You will not receive credit if you do not turn in these on the first day of class. There are NO EXCUSES. 7. When submitting your summer assignment, please complete your work in Notability and submit it into Schoology on August 9 th, our first day of class. Questions??? Contact Mr. McCall mccallr@bishopmoore.org Copyright 2017 R McCall. All rights reserved. Printed in the USA. Page 2

3 UNIT 1: PHYSICS BASICS, MOTION, & VECTORS READING & NOTES, PROBLEMS, AND ANSWERS For the summer assignment, please download this Physics with Calculus textbook pdf by Craig Fletcher. CHAPTER 1 MATH REVIEW Read Chapter 1. Review the math concepts. Try answering the questions on p Check your worked-out solutions against the Solutions to Ch 1 link. CHAPTER 2 DERIVATIVES Read Chapter 2. Remember your AP Calculus AB course. Consider how we will use calculus in physics next year. Please make note of the examples given in this chapter. CHAPTER 3 INTEGRALS Read Chapter 3. Remember your AP Calculus AB course. Consider how we will use calculus in physics next year. Please make note of the examples given in this chapter. CHAPTER 4 KINEMATICS Read Chapter 4. Take detailed notes on Ch 4. Pay close attention to the author s notes and observations. Complete IN-CLASS EXAMPLE PROBLEMS on pages 4-7 of this packet. Copyright 2017 R McCall. All rights reserved. Printed in the USA. Page 3

4 APC Physics UNIT 1 DISPLACEMENT, VELOCITY, & ACCELERATION PHYSICS BASICS, MOTION, AND VECTORS IN ANY DIMENSION CH 1-4 IN-CLASS EXAMPLE PROBLEMS 1. The velocity of an object as a function of time is given by v = 3t 2-2t + 5 (measured in m/s). Find the average acceleration of the object between t = 3.0 s and t = 5.0 s. DERIVATIVES IN PHYSICS 2. The position of an object as a function of time is given by x = -4t 2 + 5t 3. a) Find a function for the object s velocity as a function of time. b) What is its velocity at t = 2.0 s? c) At what time(s) is the object at rest? 3. The position of an object as a function of time is given by x = t 3. At what time(s) is the object moving at a velocity of 8.5 m/s? 4. The position of an object as a function of time is given by x = 5t(lnt). What is its velocity at t = 2.0 s? MAXIMUM AND MINIMUM 5. The position of an object as a function of time is given by x = 5t 2 2t 3 a) Find the object s acceleration function. b) What is the object s maximum position? c) What is the maximum velocity of the object? Copyright 2017 R McCall. All rights reserved. Printed in the USA. Page 4

5 KINEMATICS AND FREE-FALL 6. A car, initially moving with a positive velocity of 22.0 m/s, applies its brakes for 28.0 meters, slowing at a rate of 7.60 m/s 2. a) For how much time are the brakes applied? b) What is the car's final speed after braking? 7. A model rocket is launched straight upward from rest at ground level. It accelerates with a constant upward acceleration of 2.0 m/s 2 until its engines stop at an altitude of 150 m. Assuming no parachute opens up, and no air resistance in general, how much total time does it take for the rocket to reach its highest point? INTEGRALS IN PHYSICS 8. An object is moving as indicated in the velocity-time graph shown to the right. Find the object's displacement during the 50.0 s interval. 9. The acceleration of an object is given by a = 2t - 12t 2, and its velocity at t = 0 is 5.0 m/s. What is its velocity at t = 4.0 s? VECTORS 10. A toy airplane first flies for 350 m at an angle of 13 above the horizontal, and then flies for m at an angle of 29 below the horizontal. What is the plane's resultant displacement? Copyright 2017 R McCall. All rights reserved. Printed in the USA. Page 5

6 11. Vector A = (5i + 3j)m and Vector B = (3i 4j)m. a) Find A+B in unit vector notation. b) Find A-B in unit vector notation. c) Now give A-B as a magnitude and angle. UNIT VECTORS IN MOTION 12. An object s velocity is initially v = 2i - 5j, and then 5.0 seconds later it is v = 6i + 3j, all in m/s. In unit-vector notation, what is the object's acceleration during the 5.0 seconds? 13. An object has an initial velocity given by v = 8i m/s, and then undergoes an acceleration given by a = (-2i + 4j) m/s 2. Calculate the object's velocity (in unit-vector notation) at t = 3.0 s. 14. A particle moves so that its position (in meters) as a function of time (seconds) is r = 3i + 6tj - 3t 2 k. In unit-vector notation, find its velocity at t = 4.0 s. 15. An object is initially located at the origin, moving with an initial velocity of (-5i + 3j) m/s. The object's acceleration in m/s 2 is given by a = (2t+3)i + 6t 2 j. Find the magnitude and direction of the object's velocity at t = 3.0 seconds. 16. A particle leaves the origin with a constant acceleration of (5i - 2j)m/s 2, and an initial velocity of (3i + 4j)m/s. Find the particle's position vector (in unit-vector notation) when it reaches its maximum y-coordinate. Copyright 2017 R McCall. All rights reserved. Printed in the USA. Page 6

7 PROJECTILE MOTION 17. A projectile is launched horizontally at 12.0 m/s from the top of the building that is 40.0 m tall. How far does the projectile move horizontally before it lands on the ground? 18. A ball is launched from a cliff at an initial angle of 35 to the horizontal, at a speed of 30.0 m/s. What is its speed at the time it has moved m in the horizontal direction? CIRCULAR MOTION 19. An Earth satellite moves in a circular orbit km from the center of the Earth, with a period of 98.0 minutes. Find the magnitude of the satellite's speed and acceleration. 20. A particle moves along a circular path over a horizontal xy plane at a constant speed. At time t1 = 3.00s, its acceleration vector is given by (3i-5j) m/s 2. At time t2 = 7.00 s its acceleration is given by (-3i+5j) m/s 2. Find the radius of the particle's circular path. Copyright 2017 R McCall. All rights reserved. Printed in the USA. Page 7

8 SUMMER CALCULUS WORKSHEET Use what you know from previous calculus classes, or what you have learned from the lecture videos on Calculus Review to complete the following problems. POWER RULE DERIVATIVES For each of the following functions, find the derivative ( dy )with respect to x: dx 1) y = 5x 2 2) y = 4x 3) y = 8x 3 4) y = 2 5) y = 2x 1 6) y = 4x 3 + 2x 1 OTHER COMMON DERIVATIVES For each of the following functions, find the derivative ( dy ) with respect to x: dx 7) y = cos x 8) y = e x 9) y = ln x CHAIN RULE DERIVATIVES Use the chain rule to help you find the derivative ( dy ) for each of the following functions: dx 10) y = (x 2 + 4) 3 11) y = e 3x 12) y = sin(3x + 1) PRODUCT RULE DERIVATIVES Use the product rule to help you find the derivative ( dy ) for each of the following functions: dx 13) y = (x 2 )(2x 7) 14) y = 2x 3 e x 15) y = (5x 2 + 3x)(ln x) Copyright 2017 R McCall. All rights reserved. Printed in the USA. Page 8

9 MAXIMUM AND MINIMUM VALUES Find the maximum y-coordinate reached by the following functions: 16) y = 3x x 17) y = 2x 2 20x + 12 INDEFINITE INTEGRALS Use the idea of un-doing a derivative to find the following indefinite integrals: 18) 3x 2 dx 19) (8x 3 + 2x) dx 20) (5x 3 1)dx DEFINITE INTEGRALS Evaluate each of the following definite integrals: 2 21) (6x 2 + 3)dx ) (4x + 1)dx 1 CALCULUS AND GRAPHS Use calculus ideas to find the required graphical values of the following functions: 23) Find the instantaneous slope of the function y = x 2 + 3x 5 at the point (2,5). 24) For the same function used in problem 23, find the area under the curve between x = 0 and x = 2. Copyright 2017 R McCall. All rights reserved. Printed in the USA. Page 9

10 1 st SEMESTER: (approximately 16 weeks) AP PHYSICS C COURSE SYLLABUS UNIT 1: Physics Basics, Motion, and Vectors TEST #1 Chapters 1-4 (approximately 11 days) UNIT 2: Forces, and Circular Motion TEST #2 Chapters 5-8 (approximately 14 days) UNIT 3: Work and Energy TEST #3 Chapters (approximately 14 days) UNIT 4: Linear Momentum & Center of Mass TEST #4 Chapters 9 (approximately 13 days) UNIT 5: Rotational Motion & Static Equilibrium TEST #5 Chapters 12 (approximately 12 days) UNIT 6: Gravitation & Oscillations TEST #6 Chapters (approximately 12 days) Cumulative Semester Exam (UNITS 1-6) Copyright 2017 R McCall. All rights reserved. Printed in the USA. Page 10

11 2 nd SEMESTER: (approximately 17 weeks) UNIT 7: Electric Forces, Fields, and Gauss s Law TEST #1 Chapters (approximately 15 days) UNIT 8: Electric Potential and Capacitors TEST #2 Chapters (approximately 17 days) UNIT 9: Electric Currents, Resistance and Circuits TEST #3 Chapters (approximately 13 days) UNIT 10: Magnetism and Electromagnetic Induction TEST #4 Chapters (approximately 12 days) AP PHYSICS C REVIEW (approximately 15 days) MECHANICS TOPICS TEST #5 ELECTRICITY AND MAGNETISM TOPICS TEST #6 AP PHYSICS C EXAM MAY 7 TH (MONDAY AFTERNOON) Copyright 2017 R McCall. All rights reserved. Printed in the USA. Page 11