AP PHYSICS C SUMMER ASSIGNMENT

Transcription

1 AP PHYSICS C SUMMER ASSIGNMENT Below is a list of requirements to complete over the summer. Do not procrastinate and enjoy your physics early and often. 1. Complete the attached Summer Assignment for all three Topics of Study (found on pages 2-6). You will be required to purchase a copy of The AP Physics C Companion by Dan Fullerton (available at Also, you will be required to read Chapter 1: Introduction and Chapter 2: Background Skills while working through the summer assignment. It is suggested to do your reading while doing the problems on the summer assignment and not in one sitting, but in smaller segments. Please turn in your summer assignment showing all work and answers any time before Friday, July 31 st. You can drop them off at the school to be placed in my mailbox, send it using an unladen European swallow or a snowy owl to my house (and if you know my address, I ll be a little concerned you re stalking me), or you could scan in and send via You are required to bring a scientific calculator (which you all probably have) and dry erase markers on the first day of school. The best calculators to purchase are either the Texas Instruments TI-30X IIS (about $12), the Texas Instruments TI-84 Plus Graphing Calculator (about $85), or the Texas Instruments Nspire CX CAS Graphing Calculator (about $130). Any will suffice for this course of study but a graphing calculator will definitely help out. 3. If you have any questions about the assignment or need any help at all, please feel free to me at robert.ayton@redeemerlions.com or through the contact page at and I will help you out. If you work hard, I guarantee you will succeed in AP Physics C next year and have some fun along the way. Lastly, keep an eye out at my website for any updates to content or messages. Thank you and I am looking forward to next school year, Mr. Ayton

2 Questions labeled TQ will be questions about the text you read in Chapter 2: Background Skills. These TQ s can be answered in one word, one phrase, or a complete sentence. Questions labeled CQ are conceptual questions and must be answered also in one word, one phrase, one value, or complete sentences. Questions labeled QQ s are quantitative questions and the equation, substitution with units, and solve with units must be shown on your paper. Significant Figures CQ1. How many significant figures are in the value 63.2 m/s? CQ2. How many significant figures are in the value kj? CQ3. How many significant figures are in the value sec? CQ4. How many significant figures are in the value kg? Scientific Notation QQ5. Express the number 307,000 in scientific notation to three significant figures. QQ6. Express the number in scientific notation to three significant figures. QQ7. Expand the number 4.40 x 10-4 to the correct amount of significant figures. QQ8. Expand the number 1.30 x Accuracy and Precision TQ10. What is the difference between accuracy and precision? Metric System TQ11. Why is AP Physics known as the mks system? QQ12. Convert 340,000 J to kj. QQ13. Convert 20 km/hr to m/s. QQ14. Convert 480 micrometers to meters. CQ15. A Newton is equivalent to what in terms of SI Units? CQ16. Since KE = ½ mv 2. What are the SI Units of Kinetic Energy (equivalent to a Joule)?

3 Trigonometry and Triangles, Vectors and Scalars TQ17. What is the difference between a scalar quantity and a vector quantity? TQ18. What are four examples of a scalar quantity? TQ19. What are four examples of a vector quantity? TQ20. You can add vectors by adding the components or by what kind of method? QQ21. A ball is thrown at 20 m/s at 30 o. What is the x-component of the velocity? QQ22. A projectile is launched at 12 m/s at 40 o. What is the y-component of the velocity? QQ23. A boat is heading across at stream from one side to the other at 4.0 m/s. The river is flowing downstream at 2.0 m/s. What is the magnitude of the boat s resultant velocity with respect to the starting point? Vector Notation TQ24. If vector u has dimensions of 5 m in the +x direction, 4 m in the -y direction, and 3 m in the +z direction, what is this vector in ordered set notation? TQ25. Write the vector u found in TQ24 in unit vector notation. QQ26. Calculate the magnitude of vector u found in TQ24. QQ27. If vector A is < -3 m, 3 m, -2 m > and vector B is < 5 m, 4 m, -2 m >, what is vector R if vector R is the sum of A and B? Use the vectors below for problems CQ28 and CQ29: CQ28. Draw the resultant vector, R, which is the result of A + B. CQ29. Draw the resultant vector, R, which is the result of A - B. QQ30. A person walks 10 meters at an angle of 60 degrees north of east. He then walks 8 meters 30 degrees north of west. What is the person s magnitude of the displacement from his starting position? QQ31. What is the person s angle of direction from his starting position in problem QQ30?

4 Dot Product TQ32. Is the dot product of two vectors a scalar or a vector result? TQ33. What is the mathematical formula definition of a dot product? QQ34. Find the dot product of the following vectors. A = <2, 4, 5> and B = <4, 3, 1>. QQ35. Find the angle between the following vectors. A = <2, 4, 5> and B = <4, 3, 1>. TQ36. What is the dot product of perpendicular vectors? TQ37. What is the dot product of parallel vectors? TQ38. What is the product rule for derivatives of a dot product? QQ39. If A = <3, 2> and B = <-2, By>, find the value of By such that the two vectors are perpendicular. Cross Product TQ40. Is the cross product of two vectors a scalar or a vector result? TQ41. What is the mathematical formula definition of a cross product? TQ42. In the cross product right hand rule, if you point your fingers in the direction of vectors A and B, what tells you your direction of the cross product? Need arrows above A and B QQ43. Find the cross product, A B, for the following vectors. A = <2, 4, 5> and B = <4, 3, 1>. Graphing CQ44. In a graph of acceleration vs. time, what is the independent and dependent variables? CQ45. Given the following data describing the speed of a cart as a function of time, determine the mathematical relationship and explain how you determined this? Time (sec) Speed (m/s) CQ47. What type of mathematical relationship is kinetic energy as a function of velocity? CQ46. Given the following data describing the speed of an object as a function of its height dropped, determine what one would have to plot in order to linearize the graph. Height (m) Speed (m/s) CQ47. What is the slope of your linearized graph in CQ46? What does this number represent?

5 Calculus TQ48. What is differential or derivative calculus find? TQ49. What is the derivative of distance with respect to time? TQ50. What is integral calculus? TQ51. What is the integral of acceleration with respect to time? Calculus Notation TQ52. If a function is represented as y = f(x), what are three different ways to write the derivative of that function? Derivatives of Constants CQ53. What is the derivative of y = 5? Derivatives of Polynomials QQ54. Find the following derivative: y = 4x 3 Rules for Derivatives QQ55. Find the following derivative by first simplifying the square root: y = 3 x QQ56. Find the following derivative: y = 12x 2 + 3x + 15 QQ57. Find the following derivative by using the product rule: f(x) = (3x 2 + x)(6x + 5) QQ58. Find the following derivative by using the quotient rule: y = 4x+4 Derivatives of Trig Functions QQ59. Find the following derivative: f(x) = 4 sin 2x QQ60. Find the following derivative: y = 8 tan x x+5 QQ61. Find the following derivative using the product rule: y = sin(x) cos(2x) Derivatives of Exponential and Logarithmic Functions QQ62. Find the following derivative: f(x) = e 2x QQ63. Find the following derivative: y = ln(2x)

6 The Chain Rule QQ64. Find the following derivative using the chain rule: f(x) = cos(2x 3 ) QQ65. Find the following derivative using the chain rule: y = (3x 2 ) 3 Integration TQ66. What is the integral sign? QQ67. Find the following integral: (x 2 + 3x + 5) dx QQ68. Find the following integral: (4x 4 + 3x 2 + 2x + 4) dx x=3 QQ69. Find the following definite integral: (4x 2 + 2x + 5) x=1 dx QQ70. Find the area under the curve y = x 2 from x = 0 to x = 4. Integrals of Trig Functions QQ71. Find the area under the graph y = sin x between x = 0 and x = π 2. Integrals of Exponential and Logarithmic Functions QQ72. Find the following integrals: y = 5e x QQ73. Find the following integral: x2 x 2 +4 dx QQ74. The velocity of a cart as a function of time is given by the following equation v(t) = 7t 3 5. The cart starts at a position of 0 and at time 0. Calculate the instantaneous acceleration of the cart at t = 2.0 seconds. QQ75. Calculate the distance the cart in QQ74 traveled from t = 0.0 seconds to t = 2.0 seconds.