Solving Problems In Physics

Transcription

1 Solving Problems In Physics 1. Read the problem carefully. 2. Identify what is given. 3. Identify the unknown. 4. Find a useable equation and solve for the unknown quantity.

2 5. Substitute the given quantities. 6. Check Units. 7. Does the answer make sense??? 8. Organization will be a key to your success.

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4 Physics - Chapter 2 REPRESENTING MOTION

5 Perceiving motion is instinctive your eyes pay more attention to moving objects than to stationary ones. Movement can be in many directions, such as the straight-line path of a bowling ball in a lane s gutter, the circular path of a merry-go-round horse, the arc of a thrown ball

6 Motion An object is in motion if it changes positions relative to a frame of reference. A frame of reference is a point or object from which motion is determined. oa frame of reference is assumed to be fixed. othe surface of the Earth is the most common frame of reference.

7 Using the earth as your frame of reference, describe your motion. Using the sun as your frame of reference, describe your motion.

8 It is said that all motion is relative because it depends on your frame of reference. The motion of objects can be described by words - distance time Comparison Yields Speed or Velocity

9 Velocity Time Comparison Yields Acceleration Understanding Physics is understanding motion.

10 Picturing Motion/ Motion Diagrams Keeping track of the motion of the runner is easier if we disregard the movements of the arms and the legs, and instead concentrate on a single point at the center of the body.

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12 Scalar and Vector Quantities

13 Scalars quantities which are described by a magnitude alone. General 5 kg, 50 gal, 3 hrs, 25 grapes Eat 25 grapes and then eat 12 more You ate grapes.

14 Scalar quantities add algebraically. Scalar quantities are typically represented by simple letters. m = mass t = time T = temperature

15 Drive 45 km from school and then drive 30 km more. How far did you drive? 45 km + 30 km = 75 km Drove 75 km but where are you? Need more information...

16 Vectors quantities which are fully described by both a magnitude and a direction. Specific Drove 15 km N --Far end of town Vectors do not add algebraically. Must take direction into account.

17 Vector Addition - Graphical Method Vectors are represented by an Drawn to scale and points in the direction of motion.

18 N + W - + E - S

19 15 O 15 O E of N Or 75 O N of E 35 O More Later 35 O S of W Or 55 O W of S

20 Adding Vectors Walk 50 m E and then 100 m E. What is the net outcome? 50 m 100 m 150 m E Net Outcome = Resultant (Result after adding vectors)

21 100 m 50 m 150 m E Vectors can be added in any order. Vectors are added head to tail.

22 Walk 50 m E and then 100 m W. What is the resultant? Resultant - Vector Quantity 50 m W 50 m 100 m

23 How far did you walk? 50 m m = 150 m Scalar Quantity

24 Distance vs Displacement Distance Displacement Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion.

25 Displacement is a vector quantity which refers to "how far out of place an object is. It is an object's change in position. It is a resultant vector.

26 Walk 4 km E and then 3 km W. What distance was covered and what was the displacement? 4 km Resultant 3 km Distance (Scalar) = 7 km Displacement (Vector) = 1 km E

27 Suppose a person moves in a straight line from the lockers (at a position x = 1.0 m) toward the physics lab (at a position x = 9.0 m), as shown below. m d = 9.0 m 1.0 m = 8.0 m The answer is positive so the person must have been traveling horizontally to the right.

28 Suppose the person turns around and returns to where they started! d = 1.0 m 9.0 m = m The answer is negative so the person must have been traveling horizontally to the left What is the DISPLACEMENT for the entire trip? d = 1.0 m 1.0 m = 0.0 m What is the total DISTANCE for the entire trip? 8 m + 8m = 16m

29 Walk 5 km N and 5 km E. 5 km Resultant 5 km Ө R Distance = 10 km Displacement =? A 2 + B 2 = C 2 R = 7.07 km Resultant Need Direction

30 R = 7.07 km at 45 o of. 5 km 5 km R Ө R = 7.07 km at 45 o E of N.

31 What is displacement? A. The vector drawn from the initial position to the final position of the motion in a coordinate system. B. The length of the distance between the initial position and the final position of the motion in a coordinate system. C. The amount by which the object is displaced from the initial position. D. The amount by which the object moved from the initial position.

32 Answer: A Reason: Options B, C, and D are all defining the distance of the motion and not the displacement. Displacement is a vector drawn from the starting position to the final position.

33 Time Intervals and Displacement The difference between the initial and the final times is called the time interval.

34 The time interval is defined mathematically as follows: The common symbol for a time interval is t, where the Greek letter delta,, is used to represent a change in a quantity. Although i and f are used to represent the initial and final times, they can be initial and final times of any time interval you choose. t = t t f i

35 Using a Graph to Find Out Where and When Graphs of an object s position and time contain information about an object s position at various times and can be used to determine the displacement of an object during various time intervals.

36 The data can be plotted with the time data on a horizontal axis and the position data on a vertical axis.

37 Draw a line that best fits the recorded points. This line represents the most likely positions of the runner at the times between the recorded data points.

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40 In the graph, when and where does runner B pass runner A? B passes A about 190 m beyond the origin, 45.0 s after A has passed the origin.

41 A position-time graph of an athlete winning the 100-m run is shown. Estimate the time taken by the athlete to reach 65 m.

42 Slope red = d t 2 2 d t 1 1 = 6.0 m 2.0 m 3.0 s 1.0 s = 2.0 m/s Slope blue d t 3.0 m 2.0 m 3.0 s 2.0 s 2 1 = = = 1.0 m/s 2 d t 1

43 The slope of a position-time graph for an object is the object s average velocity the ratio of the change of position to the time interval during which the change occurred. Average Velocity v d d d = f t t t f i i

44 Examine the graph. Describe what is taking place. V = 0m 20 m 4s 0s -5 m s or 5 m/s in the negative direction

45 It is a common misconception to say that the slope of a position-time graph gives the speed of the object.

46 The slope, 5.0 m/s, indicates the average velocity of the object and not its speed. The object moves in the negative direction at a rate of 5.0 m/s.

47 The absolute value of the slope of a position-time graph tells you the average speed of the object. The sign of the slope tells you in what direction the object is moving. The combination of an object s average speed, and the direction in which it is moving is the average velocity.

48 If an object moves in the negative direction, displacement is negative. The object s velocity will always have the same sign as the object s displacement.

49 The graph describes the motion of a student riding his skateboard along a smooth, pedestrian-free sidewalk. What is his average velocity?

50 Find the average velocity using two points on the line. d d d Average Velocity v = f t t t f i i V = 12 m 6.0 m 7.0 s 3.5 s V = 1.7 m/s in the + direction

51 What is his average speed? S = 1.7 m/s

52 Is this object moving at a constant velocity? If the slope of a straight line position time graph yields the average velocity, how is the velocity of the object determined on this graph?

53 Use the tangent line to determine the instantaneous velocity of the object at the time of 1.2 seconds. Need to. use two points that are ON the line..

54 DESCRIBE THE MOTION REPRESENTED BY EACH LINE P O S I T I O N m TIME s

55 Speed and Velocity Speed: scalar quantity Speed = distance per unit of time 25 km hr 25 m s Small distance unit Small time unit Large distance unit Large time unit

56 Velocity: Vector quantity Velocity = displacement per unit of time 25 km E 25 m at 35 O S of E hr s Must include a direction.

57 Average Speed and Velocity A biker rides 15 km in 30 minutes. What was the bikers average speed? 15 km 0.5 hr = 30 km hr Biker could have gone 45 km/hr for 15 minutes and 15 km/hr for 15 minutes.

58 Average Speed = Distance Time Average S = d t d = d f - d i

59 SPEED is simply the RATE at which DISTANCE changes. A rate is any quantity divided by time. There are three (3) types of speed: 1. Constant Speed: Speed that does not change; Speed that stays the same. 2. Average Speed: Total distance divided by total time. 3. Instantaneous Speed: Speedometer Speed at any given point in time.

60 Maximum instantaneous speed allowable. Constant Speed Average Speed Instantaneous Speed

61 Velocity is SPEED in a given DIRECTION Average Velocity = Displacement Time V = d t d = d f - d i

62 A man runs 5 minutes at an average velocity of 4 m/s E. What was his displacement? V = d = 4 m/s E? V = d t t = 5 minutes d = V t

63 d = V t Units!!! d = 4 x 5 = 20 meters d = 4 m X 5 min s X 60 s 1 min 1200 meters E

64 Walk 10 km W and then 3 km S. What was the distance and displacement? d = 13 km 10 km 3 km θ R = displacement = 10.4 km R = 10.4 km at O S of W θ

65 Instantaneous Velocity A motion diagram shows the position of a moving object at the beginning and end of a time interval. During that time interval, the speed of the object could have remained the same, increased, or decreased. All that can be determined from the motion diagram is the average velocity.

66 The speed and direction of an object at a particular instant is called the instantaneous velocity. The term velocity refers to instantaneous velocity and is represented by the symbol v.

67 An object s position is equal to the average velocity multiplied by time plus the initial position. Equation of Motion for Average Velocity d = v t + d i y = mx + b

68 d = V t d = d f - d i d f d i = V t d f = V t + d i Note: Many times the value of d i will be 0 m. d = V t

69 Which of the following statement defines the velocity of the object s motion? A. The ratio of the distance covered by an object to the respective time interval. B. The rate at which distance is covered. C. The distance moved by a moving body in unit time. D. The ratio of the displacement of an object to the respective time interval.

70 Answer: D Reason: Options A, B, and C define the speed of the object s motion. Velocity of a moving object is defined as the ratio of the displacement ( d ) to the time interval ( t).

71 The position-time graph of a car moving on a street is as given here. What is the average velocity of the car?

72 Same speed, velocity, acceleration, displacement?

73 Is this object moving at a constant velocity? If the slope of a straight line position time graph yields the average velocity, how is the velocity of the object determined on this graph?

74 Use the tangent line to determine the instantaneous velocity of the object at the time of 1.2 seconds. Need to. use two points that are ON the line..

75 DESCRIBE THE MOTION REPRESENTED BY EACH LINE P O S I T I O N m TIME s

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81 Which line of dots represents constant velocity?

82 The End