9/5 Objectives (A day)

1. 9/5 Objectives (A day) • Introduction of AP physics • Lab safety • Sign in lab safety attendance sheet • Classical Mechanics • Coordinate Systems • Units of Measurement • Changing Units • Dimensional Analysis

2. Lab safety General guidelines • Conduct yourself in a responsible manner. • Perform only those experiments and activities for which you have received instruction and permission. • Be alert, notify the instructor immediately of any unsafe conditions you observe. • Work area must be kept clean.

3. Dress properly during a laboratory activity. Long hair should be tied back, jackets, ties, and other loose garments and jewelry should be removed. • When removing an electrical plug from its socket, grasp the plug, not the electrical cord. Hand must be completely dry before touching an electrical switch, plug, or outlet. • Report damaged electrical equipment immediately. Look for things such as frayed cords, exposed wires, and loose connections. Do not use damaged electrical equipment. Please sign in lab safety attendance sheet

4. Classical Mechanics • Mechanics is a study of motion and its causes. • We shall concern ourselves with the motion of a particle. This motion is described by giving its position as a function of time. Specific position & time → event Position (time) → velocity (time) → acceleration • Ideal particle • Classical physics concept • Point like object / no size • Has mass • Measurements of position, time and mass completely describe this ideal classical particle. • We can ignore the charge, spin of elementary particles.

5. Position • If a particle moves along a • straight line → 1-coordinate • curve/surface → 2-coordinate • Volume → 3-coordinate • General description requires a coordinate system with an origin. • Fixed reference point, origin • A set of axes or directions • Instruction on labeling a point relative to origin, the directions of axes and the unit of axes. • The unit vector

6. Rectangular coordinates - Cartesian Simplest system, easiest to visualize. To describe point P, we use three coordinates: (x, y, z)

7. Spherical coordinate • Nice system for motion on a spherical surface • need 3 numbers to completely specify location: (r, Φ, θ) • r: distance between point to origin • Φ: angle between line OP and z: latitude = π/2 - Φ. • θ: angle in xy plane with x – longitude.

8. Time • Time is absolute. The rate at which time elapse is independent of position and velocity.

9. Unit of measurement International system of units (SI) consists of 7 base units. All other units can be expressed by combinations of these base units. The combined base units is called derived units

10. Physical Dimensions • The dimension of a physical quantity specifies what sort of quantity it is—space, time, energy, etc. • We find that the dimensions of all physical quantities can be expressed as combinations of a few fundamental dimensions: length [L], mass [M], time [T]. • For example, • Energy: E = ML2/T2 • Speed: V = L/T

11. Derived units • Like derived dimensions, when we combine basic unit to describe a quantity, we call the combined unit a derived unit. • Example: • Volume = L3 (m3) • Velocity = length / time = LT-1 (m/s) • Density = mass / volume = ML3 (kg/m3)

12. SI prefixes • SI prefixes are prefixes (such as k, m, c, G) combined with SI base units to form new units that are larger or smaller than the base units by a multiple or sub-multiple of 10. • Example: km – where kis prefix, m is base unit for length. • 1 km = 103 m = 1000 m, where 103 is in scientific notation using powers of 10

13. SI uses prefixes for extremes prefixes for power of ten

14. Example: Convert the following 5 x 109 2 x 10-6 6 x 10-5 7 x 10-9 4 x 106

15. 1760 yd 0.9144 m 2 miles x x 1 mile 1 yd Unit conversions Note: the units are a part of the measurement as important as the number. They must always be kept together. Suppose we wish to convert 2 miles into meters. (1 miles = 1760 yards, 1 yd = 0.9144 m) = 3218 m

16. m 1000 m 1 hr x x = 22 s 1 km 3600 s 80 km hr example • Convert 80 km/hr to m/s. • Given: 1 km = 1000 m; 1 hr = 3600 s Units obey same rules as algebraic variables and numbers!!

17. L L = = L T2 Dimensional analysis • We can check for error in an equation or expression by checking the dimensions. Quantities on the opposite sides of an equal sign must have the same dimensions. Quantities of different dimensions can be multiplied but not added together. • For example, a proposed equation of motion, relating distance traveled (x) to the acceleration (a) and elapsed time (t). T2 Dimensionally, this looks like At least, the equation is dimensionally correct; it may still be wrong on other grounds, of course.

18. Another example use dimensional analysis to check if the equation is correct. d = v / t L = (L ∕ T ) ∕ T [L] = L ∕ T2

19. Significant Figures (Digits) • Instruments cannot perform measurements to arbitrary precision. A meter stick commonly has markings 1 millimeter (mm) apart, so distances shorter than that cannot be measured accurately with a meter stick. • We report only significant digits—those whose values we feel sure are accurately measured. There are two basic rules: • (i) the last significant digit is the first uncertain digit • (ii) when multiply/divide numbers, the result has no more significant digits than the least precise of the original numbers. The tests and exercises in the textbook assume there are 3 significant digits.

20. Scientific Notation and Significant Digits • Scientific notation is simply a way of writing very large or very small numbers in a compact way. • The uncertainty can be shown in scientific notation simply by the number of digits displayed in the mantissa 2 digits, the 5 is uncertain. 3 digits, the 0 is uncertain.

21. Percent error • Measurements made during laboratory work yield an experimental value • Accepted value is the measurements determined by scientists and published in the reference table. • The difference between and experimental value and the published accepted value is called the absolute error. • The percent error of a measurement can be calculated by (absolute error) experimental value – accepted value Percent error = X 100% accepted value

22. Lab period • Lab report format

23. Class work Homework • Read and sign the Lab Requirement Letter – be sure to include both your signature and your parent or guardian’s signature. • Read and sign the Student Safety Agreement – both your signature and your guardian’s signature. • Reading assignment: 1.1 – 1.6, p. 29: #1.1, 1.3, 1.9

24. 9/6 do now • The micrometer (1 μm) is often called the micron. How many microns make up 1.0 km? • Homework questions? • Quiz tomorrow – on homework assignments

25. Objectives (B day) • Sign up on mastering physics – do assignments • Math review – class work

26. Register Mastering Physics (See instructions at mastering physics sign up info) • Go to http://www.masteringphysics.com • Register with the access code in the front of the access kit in your new text, or pay with a credit card if you bought a used book. • WRITE DOWN YOUR NAME AND PASSWORD • Log on to masteringphysics.com with your new name and password. • The VC zip code is 12549 • The Course ID: MPLABARBERA1010 Mastering physics due by 11:00 pm tonight

27. 9/7 do now (A day) • quiz

28. 9/7 Objectives (A day) • Vector review • Lab report requirement

29. There are two kinds of quantities… • Vectors have both magnitude and direction • displacement, velocity, acceleration • Scalars have magnitude only • distance, speed, time, mass

30. A A θ θ y Magnitude: |R| = √x12 +y12 Direction: θ = tan-1(y1/x1) y1 p(x1, y1) x o x1 Two ways to represent vectors • Geometric approach • Vectors are symbolized graphically as arrows, in text by bold-face type or with a line/arrow on top. Magnitude: the size of the arrow Direction: degree from East Algebraic approach • Vectors are represent in a coordinate system, e.g. Cartesian x, y, z. The system must be an inertial coordinate system, which means it is non-accelerated. θ

31. A -A Equal and Inverse Vectors Equal vectors have the same length and direction. Inverse vectors have the same length, but opposite direction.

32. Graphical Addition of Vectors: “Head and tail ” & “parallelogram” Head and tail method Parallelogram method E E C is called the resultant vector! E is called the equilibrantvector!

33. Vector Addition Laws • Commutative Law:a + b = b + a • Associative Law: (a + b)+ c = c + (b + a)

34. Subtract vectors: adding a negative vector

35. Component Addition of Vectors • Resolve each vector into its x- and y-components. Ax = Acos Ay = Asin Bx = Bcos By = Bsin etc. • Add the x-components together to get Rx and the y-components to get Ry.

36. Component Addition of Vectors • Calculate the magnitude of the resultant with the Pythagorean Theorem (|R| = Rx2 + Ry2). • Determine the angle with the equation  = tan-1 Ry/Rx.

37. Bx By A Ax |R| = Rx2 + Ry2. B R Ry Ay  = tan-1 Ry/Rx Rx Algebraic Addition of Vectors Ax = AcosA Ay = AsinA Bx = BcosB By = BsinB Rx = Ax + Bx Ry = Ay + By θB θ θA

41. Homework • Reading assignment: 1.7 – 1.9 • p. 30 #31, 41, 43

42. Lab Period • Lab 1:Vector Addition • Objective: To compare the experimental value of a resultant of several vectors to the values obtained through graphical and analytical methods. • Equipment: A force table set

43. 9/10 do now vi vf The direction of the change in velocity is best shown by A B C B E

44. Objectives (B day) • Quiz corrections – count as a grade • Homework questions? • Unit vector

45. ^ ^ ^ ^ ^ ^ i i k j k j Unit vectors • A unit vector is a vector that has a magnitude of 1, with no units. Its only purpose is to point, or describe a direction in space. • Unit vector is denoted by “^” symbol. • For example: • represents a unit vector that points in the direction of the + x-axis • unit vector points in the + y-axis • unit vector points in the + z-axis y x z

46. Any vector can be represented in terms of unit vectors, i, j, k Vector A has components: Ax, Ay, Az A = Axi + Ayj + Azk • In two dimensions: A = Axi + Ayj

47. The magnitude of the vector is |A| = √Ax2 + Ay2 The magnitude of the vector is |A| = √Ax2 + Ay2 + Az2 Magnitude and direction of the vector • In two dimensions: The direction of the vector is θ = tan-1(Ay/Ax) • In three dimensions:

48. Adding Vectors By Component s = a + b Where a = axi + ayj & b = bxi + byj s = (ax + bx)i + (ay + by)j sx = ax + bx; sy = ay + by s = sxi + syj s2 = sx2 + sy2 tanf = sy / sx

49. example A =(3i + 4j ) m Given vector: • Determine • The x, y, z component of A • the magnitude A • the direction of vector A with +x

50. example • Is the vector A = i + j + k a unit vector? • Can a unit vector have any components with magnitude greater than unity? Can it have any negative components? • If A = a (3.0 i + 4.0 j ) where a is a constant, determine the value of a that makes A a unit vector.