Grade 11 - Physics

1. Grade 11 - Physics Motion

2. Scientific Notation • Reasons for use: It is difficult to work with very large or very small numbers when they are written in common decimal notation • Scientific notation expresses number in the form [ a x 10n ]

3. Scientific Notation

4. Significant Digits • There are two types of quantities that are used in science – exact values and measurements • Exact values – defined quantities such as 10 cars in the parking lot • Measurements – are NOT exact because there is uncertainty or error associated with measurement • The following rules should be used for significant digits:

5. Significant Digits • If a decimal point is present, zeros to the left of the first non zero digit are not significant [leading zeros] ie 0.00054 • If a decimal point is not present, zeros to the right of the non zero digit are not significant [trailing zeros] ie 15000

6. Significant Digits 3. All other digits are significant 4. When measurement is written in scientific notation, all digits are significant 5. Counted and defined values have infinite significant digits

7. Significant Digits • Certainty of measurements

8. Calculation Rules • Rounding rule: if the digit to be retained as significant is a 5 or greater, round up • Eg 9.147 cm rounded up to 3 digits – 9.15cm • 7.23 g rounded to two digits – 7.2 g • When rounding in a many step question, round at the end

9. Percentage Error • Percentage error = absolute error x 100% accepted value • = measured value – accepted value ------------------------------------ x 100% accepted value

10. Percentage Difference • PD = difference in measurement ----------------------------- x 100% average measurement

11. Dimensional Analysis • Is a method of calculation, where the dimensions or units of the measurement are analyzed in the calculations. If the final units make sense, then the problem has been solved correctly

12. Dimensional Analysis • Examples of conversion: 1 min ; 1 km ; 24 hrs ; 1000 mg 60 sec 1000m 1day 1 g • Another example: 360 s x 1 min = 6 min 60 s

13. Are you ready? • Read Chapter 1 from pages 1 – 49 • Complete the following questions: • Page 2 – are you ready? • Page 6 - # 1, 2, 3 pages 21 - # 4, 5 • Page 8 - # 6, 7, 8 pages 23 - # 6 - 8 • Page 11 - # 1 – 8 pages 24 - # 1 - 5 • Page 12/13 - # 1-4 Page 14 # 5 – 9 • Page 17/18 - # 1 – 6, 7 a,c • Page 19 # 1 • Page 20 # 2, 3a, b

14. Are you ready? • pages 26 # 1 - 2 • pages 28 # 3 - 8 • pages 30 # 10 • pages 33 # 13 • pages 36 # 1 – 8 • Pages 38 # 1 -2 • pages 42 # 1 – 5 • Pages 46 # 1 – 7 • Chapter Review – know the key terms like the back of your hand • Pages 49 – 51 - # 1 – 21 • Quizzes here and there

17. Motion • Everything is in a state of motion • Examples : the Earth revolves around the sun • You walk, ride your bike, drive to school • Some of your mouths are in constant motion • KINEMATICS – is the study of motion

18. Motion contd • Uniform Motion – Linear motion:- is the movement at a constant speed in a straight line • Example – walking in a straight line • Non – uniform motion: the movement that involves change in speed or direction or both. Eg roller coaster

19. Scalar Quantities • A scalar quantity is defined as a quantity that has  magnitude only.  Typical examples of scalar quantities are time, speed, temperature, and volume • Additional examples of scalar quantities are density, mass, and energy.

20. Vector Quantities • A vector quantity is defined as a quantity that has both magnitude and direction.  To work with vector quantities, one must know the method for representing these quantities. • Examples include position, displacement, velocity, acceleration, momentum, force

21. Position, Distance, & Displacement • Position is defined as the exact location of an object in regards to its origin, so 3m [S], 7m [S], 10m [S] • Distance is a measure of the interval between two locations regardless of its direction • Displacement is the change in position, so d2 – d1 = ∆d

22. Motion contd • Average Speed: The total distance travelled divided by the total time of travel • Vav = d / t • Avg. Velocity: the displacement (or the position from the origin) divided by the total time of travel

23. Motion contd. • Example : Donovan Bailey – (gold medal winner ) ran 100 m in 9.70 secs • Given: Time = 9.70 secs, distance = 100 m Formula: v = d/t V = 100m / 9.70 s V = 10.3 m/s

24. Motion • Instantaneous speed: the speed at a particular instant • Uniform Motion • Movement at a constant speed in a straight line • Position: the distance and direction of an object from a reference point • Displacement: The change in position of an object in a given direction. {d2 – d1}

25. Distance – Time Graphs • Average Velocity: the rate of change of position divided by the time interval for that change --> --> • Vavg. = ∆ d / ∆t • Velocity -  -> -> Vave. = d2 - d1 t2 - t1

26. Vectors - Addition • Vectors can be added for many reasons • Position vectors can be added to calculate displacement • Velocity vectors can be added for relative velocity • walking in wind • Planes • Boating

27. Vectors • Force vectors can be added to determine the net force acting on an object • Rules: add vectors head to tail (tip to tail) either add the vectors by scale or algebraically Either add the vectors by scale or algebraically

28. 2D – Motion • The sum of the individual displacements, or the sum of the vectors. (adding tip to tail) • Use the Pythagorean Theorem to solve for the magnitude and the direction of the vector. • Please check out the following page:

31. Adding and Subtracting Vectors

33. Relative Motion • Any motion observed depends on the frame of reference chosen. • The Frame of Reference is a coordinate system relative to which motion can be observed. • The velocity of a body relative to a particular frame of reference is called relative velocity • In all previous examples in regards to velocity, we have assumed that Earth or ground is the frame of reference

34. Relative Motion • When we analyze motion with more than one frame of reference, we put two subscripts after the velocity symbol. • The first subscript represents the object whose velocity is stated relative to the object represented by the second subscript. • The second subscript is the frame of reference. See example on page 22 of text

35. Relative Motion • When two motions are involved, the relative velocity equation is: __> __> __> VAC = VAB + VBC Vector Addition The following diagram is an example of relative motion

37. Check out the following example

38. Solution to the problem – graphically and mathematically

40. A pictorial example of relative motion

41. Relative Motion problems

43. Uniform Acceleration • Definition: Uniformly accelerated motion is a motion that occurs when an object travelling in a straight line changes its speed uniformly with time. • Accelerated motion is a non-uniform motion as it involves a change in speed and or direction of an object • How can we measure this experimentally?

44. Uniform Acceleration • Well, we use graphs, by plotting the data on a displmnt/time graph or a velocity / time graph • The slope of the line, or the tangent of a point on the line would give us average velocity or acceleration and the tangent would give us instantaneous velocity or acceleration respectively

45. Uniform Acceleration • Uniform Acceleration: motion that occurs when an object travelling in a straight line changes its speed uniformly with time • Example: a dragster accelerating down a straight track (moving in a straight line) starting from rest and increases its speed by 5.0m/s in an easterly direction

46. Accelerated Motion • This can also occur when an object slowsdown travelling in a straight line called deceleration. • Example: slowing down 5.0m/s moving in a straight line in a westerly direction • Is non-uniform motion that involves a change in an objects speed or direction or both. • Example: a car ride in a city during rush hour or a roller coaster ride

47. Acceleration of a Motorcycle and a Car • ∆V = 9.0 m/s • ∆t = 2.0 s • aav = ? • aav = ∆V / ∆t --- 9.0 m/s / 2.0s = 4.5 m/s/s • aav = 4.5 m/s2 -- average acceleration ________________________________

48. Calculating Acceleration • For uniform accelerated motion, the inst. Acceleration has the same value as the avg. acceleration • Avg. acceleration = change in velocity / time interval • aav = ∆V / ∆t - aav = Vf – Vi / tf – ti

49. Using Velocity-Time Graphs to Find the acceleration: Slope of a velocity time graph gives the acceleration WS # 3,5