SCIENCE 1206 Unit 3. Physical Science Motion

Transcription

1 SCIENCE 1206 Unit 3 Physical Science Motion

2 Converting Base Units The Step Stair Method is a simple trick to converting these units. Kilo (k) Hecta (h) Deka (D) Larger unit as you go up the steps! Divide by a power of ten 10 Ex: To go from mg to Dg we move up 4 steps, so we divide by 4 10 Base unit (meters, grams) Deci (d) Centi (c) Milli (m) Smaller unit as you go down the steps! Multiply by a power of ten 10 Ex: To go from Km to cm we move down 5 steps, so we multiply by 5 10

3 You Try! Convert the following measurements: a) 125 cm => m Ans: 1.25m b) 2234 m => km Ans: km c) 23 mm => cm Ans: 2.3 cm d) 45 g => kg Ans: kg e) 300 ml => kl Ans: kl f) mm => km Ans: 1.2 km

4 Converting Units Converting units really just involves multiplying and dividing. However to convert units sometimes, we need to multiply the quantity we want to convert by a conversion factor. The conversion factor basically tells us how to convert one unit into another. i.e. 1ft =12 in; 1min = 60 sec; etc.

5 Converting Units (Derived Units) Ex: Convert 100 km/hr to m/s A Conversion like this must be done using multiple conversion factors! We need to convert hours into minutes and then minutes into seconds; then convert Km to m Converts Hr to min Converts Km to m 100 km hr 1hr x 60min x 1min 60sec x 1000m 1km 27.8 m/ s Converts min to sec In General: To change from km/hr to m/s we by 3.6 To change from m/s to Km/hr we X by 3.6

6 You Try! Convert the following measurements: a) 360m/s => km/hr Ans:1296 km/hr b) 50 km/hr => m/s Ans: 8.3 m/s c) 23 cm/s => m/s Ans: 0.23 m/s d) km/s => km/hr Ans: 4.32 km/hr

7 Accuracy & Precision Accuracy refers to the closeness of measurements to each other is how close a measured value is to the actual (true) value. Precision is how close the measured values are to each other.

8 Which ruler is more precise? Pencil A: Pencil B The smaller the unit you use to measure with, the more precise the measurement is.

9 MEASUREMENTS AND SIGNIFICANT DIGITS p What is the measurement of the Stick? The # of significant digits in a value includes all digits that are certain and one that is uncertain Therefore significant digits are digits that are statistically significant

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11 Learning Check What is the length of the wooden stick? 1) 4.5 cm 2) 4.54 cm 3) cm

12 What Time is it? Someone might say 1:30 or 1:28 or 1:27:55 Each is appropriate for a different situation In science we describe a value as having a certain number of significant digits 1:30 likely has 2, 1:28 has 3, 1:27:55 has 5 There are rules that dictate the # of significant digits in a value

13 Rules for Determining the Number of Significant Digits : 1. All non-zero digits (1-9) are to be counted as significant. Ex. 517, 51.7 and 5.17 all have 3 sig figs 2. For any decimal number, any zero that appears after the last non-zero digit( or between 2 nonzero digits) are significant. Ex , 5057 and all have 4 sig figs 3. For a whole numbers, only zeros between two non-zero digits are significant Ex, 47, 470, 4700 all have 2 sig fig

14 EXAMPLE All digits count Leading 0 s don t Trailing 0 s do 0 s count in decimal form 0 s don t count w/o decimal All digits count 0 s between digits count as well as trailing in decimal form

15 Rules to be used in Rounding #1. If the leftmost digit is 5 or greater, add 1 to the last digit to be kept and drop all other digits farther to the right. Ex: Rounding to 3 significant figures gives 1.22 #2. If the digit is less than 5, simply drop it and all digits farther to the right. Ex: Rounding to 3 significant figures gives 1.21

16 EXAMPLE 1 Make the following into a 3 Sig Fig number , X10 6 Your Final number must be of the same value as the number you started with, 129,000 and not 129

17 EXAMPLE 2 For example you want a 4 Sig Fig number is dropped, it is <5 Ans: ,582 8 is dropped, it is >5; Ans: 780,600 Note you must include the 0 s is dropped it is = 5; Ans: note you need a 4 Sig Fig

18 ADDING OR SUBTRACTING SIGNIFICANT FIGURES Rule: When adding or subtracting sig fig, the answer should have the same number of decimal places as the smallest number of decimal places in the numbers that were added or subtracted. Answer is

19 MULTIPLYING OR DIVIDING SIGNIFICANT FIGURES When multiplying and dividing sig, fig. the answer will contain the same number of digits as in the original number with the least number of digits Ex: x 2.56 x m x 52.3m m 5.39x10 m

20 Using Scientific Notation (Page): There are at least two reasons for being familiar with scientific notation. 1) Method of writing numbers that are very big and very small. It works like this: a big number Speed of light => 300,000,000m/s = 3.0 x 10 8 a small number Charge on an electron => C => x 10-19

21 Using Scientific Notation (Page): 2) helpful for indicating how many significant figures are present in a number 100 cm as 1.00 x 10 2 ( 3 sig fig )cm 1.0 x 10 2 ( 2 sig fig )cm 1 x 10 2 ( 1 sig fig )cm

22 Sources of Error No measurement is exact; any scientific investigation will involve error. 1. Random error (uncertainty) An error that relates to reading a measuring device Ex. a person measuring the length of an object using a ruler must estimate the last digit; another person may not estimate to the same digit Can be reduced by taking many measurements and then averaging them (and having the same person take the measurement each time)

23 Sources of Error 2. Systematic error An error due to the use of an incorrectly calibrated measuring device. Ex. a clock that runs slow or a ruler with a rounded end Can be reduced by inspecting and recalibrating equipment regularly.

24 Introduction Motion is a common theme in our everyday lives: birds fly, babies crawl, and we, run, drive, and walk. Kinematics is the study oof how objects move.

25 Uniform motion Uniform motion occurs when an object is moving at a constant speed/ velocity in a straight line. Constant speed/velocity- means that the object is covering the same distance per unit of time. Scalar any quantity that is represented by a magnitude and a unit. Vector any quantity that is represented by a Magnitude, a unit and a direction.

26 Distance and Displacement Distance (d) is a scalar measure of the actual path between two locations. It has a magnitude and a unit. Ex: 50 m, 2.5 hrs. Displacement (d) is a vector measure of the change in position measured in a straight line from a starting reference point. Ex: 5 m [W]

27 Vectors are always added tip to tail. The resultant or net vector goes from the start of the first vector to the tip of the last vector. The black lines represents the distance traveled to get from the home base to the destination(path actually taken) The red line represents the displacement from the home base to the destination (the shortest distance from the start point to the end point)

28 Sign Convention In physics we will use a standard set of signs and directions. Up, right, east and north are positive directions. ( + ) Down, left, west, and south are negative directions. ( - )

29 Example 1 A person started from the zero position, moved 3.0 km East (or to the right), then moved backward 4.0 km West (or to the left). A)What is the distance 3.0 km km = 7.0 km B) What is the displacement 3.0 km East + 4.0km West = +3km km = -1.0 km Notice that the plus symbol right, and a negative symbol for left.

30 Example 2 Distance total trip d total = d 1 + d 2 + d 3 + d 4 d total = 2m + 4m + 2m + 4m d total = 20 m Displacement change in position d total = + d d d d 4 d total = + 2m + + 4m + - 2m + - 4m d total = 0 m

31 Speed Speed is a measure of the distance traveled in a given period of time; Change In d d Change in distance V t Time t

32 Instantaneous Speed Instantaneous speed is speed at any instant in time. A speedometer measures speed in real time (the instantaneous speed).

33 Average Speed Average speed is the average of all instantaneous speeds; found simply by a total distance/total time ratio The average speed of a trip: average V avg speed total distance elapsed time d d d t t t

34 Average Speed

35 Example 1: Suppose that during your trip to school, you traveled a distance of 1002 m and the trip lasted 300 seconds. The average speed of your car could be determined as.

36 Example 2: You go out for some exercise in which you run 12.0 km in 2 hours, and then bicycle another 20.0 km in 1 more hour. What was your average speed for the entire marathon?

37 Average Speed When we are dealing with uniform motion that has different speeds at different times, you cannot determine the overall average speed by averaging the speeds of the different parts

38 Example 3: A traveler journeys by plane at km/hr for 5.0 hours, then drives by car for 180 km in 2.0 hours and finally takes a 45 minute ferry ride the last 12 km to his home. What is her average speed for the entire trip?

39 Velocity Speed in a given direction is velocity (vector). What is the velocity of a car that travels from Labrador City to Churchill Falls (283Km) in 3h?

40 Difference Between Speed and Velocity Scalar Quantities (Number and unit) Vector Quantities (Number, unit and direction) Volume liters Distance Voltage Speed (KM/h) Speed is a Scalar Quantity 10 Km West 50 Km/hr south 100 newtons right Velocity (Speed and Direction) Velocity is a Vector Quantity

41 Practice Examples Question #1 An ant on a picnic table walks 130 cm to the right and then 290 cm to the left in a total of 40.0 s. Determine the ant s distance covered, displacement from original point, average speed, average velocity.

42 Solution distance = d = total path of the ant = l30 cm cm = 420 cm displacement = d = change in position of the ant =130cm+ ( 290) cm = 160 cm = 160 cm [left] of the starting point

43 Question #3 Vectors at 90 degrees. A crow flies 30.0 km west, then 40.0 km south. The entire trek took 3.0 h. Determine the crow s: (a) total distance traveled (b) average speed (c) displacement (actual distance and direction from where he started) (d) average velocity

44 Solution(c&d) 30.0 km West 40.0 km South Ɵ Resultant or net Right triangle so we can use: Pythagorean Theorem To get the angle of direction we use Tan Ɵ tan(theta) = (40/30) = Theta = tan -1 (1.333) Theta = 53.1 degrees Then; V R 2 = (30) 2 + (40) 2 R 2 = 2500 R = SQRT (2500) R = 50 km d 50km 16.7 km / h t 3hr The crow has a velocity of 16.7 km/h [ W S ]

45 Uniform Motion Rolling ball is an example of uniform motion. 1)Speed of the ball is constant (with no friction). 2) In a straight line

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47 Distance-time graphs On your paper, graph the following: D(m) T(sec)

48 Distance Time Graphs Distance (m) Time (s)

49 Was your graph a straight line? A distance-time graph which is a straight line indicates constant speed. In constant speed, the object does not speed up or slow down. The acceleration is zero.

50 The Steeper the slope the faster the object is moving. In this graph Object A is moving fastest and Object C is moving slowest

51 On a distance time graph for uniform motion the slope equals the average speed. V avg d t

52 What is the V avg for this graph? y y Vavg Slope 2 m / s x2 x

53 Displacement Time Graphs Like distance time graphs only displacement can be either positive or negative, therefore we need two quadrants. d t d t d t d t Moving left away from origin Moving right toward origin from left Stopped right of origin Stopped left of origin

54 ACCELERATION Acceleration is a vector quantity which is defined as "the rate at which an object changes its velocity." An object is accelerating if it is changing its velocity

55 CONSTANT ACCELERATION Sometimes an accelerating object will change its velocity by the same amount each second. This is known as a constant acceleration since the velocity is changing by the same amount each second.

56 Calculating Acceleration Acceleration can be found using the following formula: a v v v 2 1 t t a 2 v1 = acceleration = initial velocity v t = final velocity = change in time Note: The units for acceleration is m/s/s or m/s 2

57 Example 1: A skier is moving at 1.8 m/s (down) near the top of a hill. 4.2 s later she is travelling at 8.3 m/s (down). What is her average acceleration?

58 Example 2: A rabbit, eating in a field, scents a fox nearby and races off. It takes only 1.8 s to reach a top velocity of 7.5 m/s [N]. What is the rabbit s acceleration during this time?

59 Example 3: Canadian Myriam Bedard won two gold medals in the biathlon in the 1994 Winter Olympics. If she accelerates at an average of 2.5 m/s 2 (E) for 1.5 s, what is her final velocity at the end of 1.5 s?

60 Acceleration Note: The direction of velocity and acceleration will determine the size of the velocity (ie. If an object is speeding up or slowing down) Velocity Moving Forward, Speeding up Moving Forward, Slowing down - Moving backward, slowing down Moving backward, speeding up

61 Example 4: An air puck on an air table is attached to a spring. The puck is fired across the table at an initial velocity of 0.45 m/s right and the spring accelerates the air puck at an average acceleration of 1.0 m/s 2 left. What is the velocity of the air puck after 0.60s?

62 Example 5: A person throws a ball straight up from the ground. The ball leaves the person s hand at an initial velocity of 10.0 m/s up. The acceleration of the ball is 9.81m/s 2 down. Assume up is positive and down is negative. What is the velocity of the ball after 0.50s and after 1.5s?

63 Over the next few slides we will summarize some facts about graphs and motion. Velocity-time Graphs: The basics

64 Slope is zero therefore the acceleration is zero.

65 Describe the motion:

66 Explanation

67 Describe the motion depicted by the v-t graph below

68 Explanation Answer The object is moving at a fixed speed to the left. As time goes on, the speed remains constant. All v values are in the negative, fourth quadrant, meaning the object is traveling to the left.

69 The slope of the line on a velocity time graph equals the average acceleration. y x y x a Slope 2 m / s

70 Describe the motion depicted by the v-t graph below

71 Explanation Answer The object starts from rest and accelerates to the right. As time goes on, the speed increases from zero. All v values are positive meaning the object is traveling to the right.

72 Describe the motion depicted by the v-t graph below

73 Explanation Answer At time zero the object is already moving to the right. It continues to accelerate to the right. At time zero, there is already a positive value for the speed. As time goes on, the positive speeds increase. That is, the object picks up speed to the right.

74 Describe the motion depicted by the v-t graph below

75 Explanation Answer The object is moving to the right but accelerating to the left. It therefore slows down and stops. At time zero, there is already a positive value for the speed. As time goes on, the positive speeds decrease. The object keeps moving to the right but slows down and stops.

76 Describe the motion depicted by the v-t graph below

77 Explanation Answer The object starts from rest and accelerates to the left. At time zero, the object is not moving. Then, as time goes on there is an increase in negative speeds as the object picks up speed to the left.

78 Describe the motion depicted by the v-t graph below

79 Explanation Answer The object starts with an initial speed to the left but slows down and stops. At time zero, the object has a maximum speed to the left. However, as time increases, speed decreases, and the object stops.

80 Describe the motion depicted by the v-t graph below

81 Explanation Answer The object starts with an initial speed to the left and accelerates to the right. At time zero, the object has a maximum speed to the left. However, as time increases, speed decreases, and the object stops. But it continues to accelerate to the right, meaning that after its brief stop, it took off to the right.

82 On a velocity - time graph the area between the graphed line and the x-axis equals the displacement Area = l x w = 6 s x 30 m/s = 180 m

83 Object is moving at a constant speed for 5.0 s then it speeds up for the next 5.0 sec. Displacement is equal to the area between the drawn line and the x-axis d A A Rec tan gle Triangle bh lw 2 (10.0 s)(5.0 m / s) 50m 25m 75m (10.0 m / s)(5.0 s) 2

84 Displacement-time Graphs (Accelerated Motion)

85 d Tangent Lines t On a position vs. time graph: The slope of a tangent line will give the velocity at that point in time. ( instantaneous velocity ) SLOPE Positive Negative Zero VELOCITY Positive Negative Zero

86 Describe the motion depicted by the d-t graph below

87 Explanation Answer The object is accelerating to the right. As time goes on, the tangents acquire larger and larger positive slopes, i.e. larger speeds to the right.

88 Describe the motion depicted by the d-t graph below

89 Explanation Answer The object heads left but with ever decreasing speed. At half-time it stops very briefly and then speeds up to the right. Tangents 1, 2, and 3 have negative slopes that are getting smaller. This means the object is moving to the left and slowing down. At 4 it is stopped. Then it picks up speed to the right as indicated by the positive slopes of 5 & 6.

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94 A. Describe what is happening in each leg of the trip. B. During which parts of the trip is the object stopped? C. During which part of the trip is the object moving the fastest? What is its Velocity?

95 Motion Graphs Position vs. Time constant, rightward (+) velocity of +10 m/s a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

96 Motion Graphs Velocity vs. Time constant, rightward (+) velocity of +10 m/s a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating