Chapter 1 Lecture physics FOR SCIENTISTS AND ENGINEERS

Chapter 1 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight © 2013 Pearson Education, Inc.

Chapter 1 Concepts of Motion Pickup PSE 3 e Photo from page 2, snowboarder jump. Chapter Goal: To introduce the fundamental concepts of motion. © 2013 Pearson Education, Inc. Slide 1 -2

Chapter 1 Preview © 2013 Pearson Education, Inc. Slide 1 -3

Chapter 1 Preview © 2013 Pearson Education, Inc. Slide 1 -4

Chapter 1 Reading Quiz © 2013 Pearson Education, Inc. Slide 1 -5

Reading Question 1. 1 What is a “particle? ” A. Any part of an atom. B. An object that can be represented as a mass at a single point in space. C. A part of a whole. D. An object that can be represented as a single point in time. E. An object that has no top or bottom, no front or back. © 2013 Pearson Education, Inc. Slide 1 -6

Reading Question 1. 1 What is a “particle? ” A. Any part of an atom. B. An object that can be represented as a mass at a single point in space. C. A part of a whole. D. An object that can be represented as a single point in time. E. An object that has no top or bottom, no front or back. © 2013 Pearson Education, Inc. Slide 1 -7

Reading Question 1. 2 What quantities are shown on a complete motion diagram? A. The position of the object in each frame of the film, shown as a dot. B. The average velocity vectors (found by connecting each dot in the motion diagram to the next with a vector arrow). C. The average acceleration vectors (with one acceleration vector linking each two velocity vectors). D. All of the above. © 2013 Pearson Education, Inc. Slide 1 -8

Reading Question 1. 2 What quantities are shown on a complete motion diagram? A. The position of the object in each frame of the film, shown as a dot. B. The average velocity vectors (found by connecting each dot in the motion diagram to the next with a vector arrow). C. The average acceleration vectors (with one acceleration vector linking each two velocity vectors). D. All of the above. © 2013 Pearson Education, Inc. Slide 1 -9

Reading Question 1. 3 In physics, what is the difference between “speed” and “velocity”? A. Velocity is represented by an exact number, while speed is only an approximate number. B. Speed can be positive or negative, while velocity is always positive. C. Speed is a scalar, which is the magnitude of the velocity, which is a vector. D. Velocity is a scalar and speed is a vector. E. Speed and velocity mean the same thing. © 2013 Pearson Education, Inc. Slide 1 -10

Reading Question 1. 3 In physics, what is the difference between “speed” and “velocity”? A. Velocity is represented by an exact number, while speed is only an approximate number. B. Speed can be positive or negative, while velocity is always positive. C. Speed is a scalar, which is the magnitude of the velocity, which is a vector. D. Velocity is a scalar and speed is a vector. E. Speed and velocity mean the same thing. © 2013 Pearson Education, Inc. Slide 1 -11

Reading Question 1. 4 An acceleration vector A. B. C. D. E. Tells you how fast an object is going. Is constructed from two velocity vectors. Is the second derivative of the position. Is parallel or opposite to the velocity vector. Acceleration vectors weren’t discussed in this chapter. © 2013 Pearson Education, Inc. Slide 1 -12

Reading Question 1. 4 An acceleration vector A. B. C. D. E. Tells you how fast an object is going. Is constructed from two velocity vectors. Is the second derivative of the position. Is parallel or opposite to the velocity vector. Acceleration vectors weren’t discussed in this chapter. © 2013 Pearson Education, Inc. Slide 1 -13

Reading Question 1. 5 The pictorial representation of a physics problem consists of A. B. C. D. E. A sketch. A coordinate system. Symbols. A table of values. All of the above. © 2013 Pearson Education, Inc. Slide 1 -14

Reading Question 1. 5 The pictorial representation of a physics problem consists of A. B. C. D. E. A sketch. A coordinate system. Symbols. A table of values. All of the above. © 2013 Pearson Education, Inc. Slide 1 -15

Reading Question 1. 6 The basic SI units are A. B. C. D. E. Second, meter, gram. Second, meter, kilogram. Second, centimeter, gram. Meter, meter/second 2. Yard, span, cubit. © 2013 Pearson Education, Inc. Slide 1 -16

Reading Question 1. 6 The basic SI units are A. B. C. D. E. Second, meter, gram. Second, meter, kilogram. Second, centimeter, gram. Meter, meter/second 2. Yard, span, cubit. © 2013 Pearson Education, Inc. Slide 1 -17

Chapter 1 Content, Examples, and Quick. Check Questions © 2013 Pearson Education, Inc. Slide 1 -18

Four basic types of motion © 2013 Pearson Education, Inc. Slide 1 -19

Making a Motion Diagram § Consider a movie of a moving object. § A movie camera takes photographs at a fixed rate (i. e. , 30 photographs every second). § Each separate photo is called a frame. § The car is in a different position in each frame. § Shown are four frames in a filmstrip. © 2013 Pearson Education, Inc. Slide 1 -20

Making a Motion Diagram § Cut individual frames of the filmstrip apart. § Stack them on top of each other. § This composite photo shows an object’s position at several equally spaced instants of time. § This is called a motion diagram. © 2013 Pearson Education, Inc. Slide 1 -21

Examples of Motion Diagrams § An object that has a single position in a motion diagram is at rest. § Example: A stationary ball on the ground. § An object with images that are equally spaced is moving with constant speed. § Example: A skateboarder rolling down the sidewalk. © 2013 Pearson Education, Inc. Slide 1 -22

Examples of Motion Diagrams § An object with images that have increasing distance between them is speeding up. § Example: A sprinter starting the 100 meter dash. § An object with images that have decreasing distance between them is slowing down. § Example: A car stopping for a red light. © 2013 Pearson Education, Inc. Slide 1 -23

Examples of Motion Diagrams § A motion diagram can show more complex motion in two dimensions. § Example: A jump shot from center court. § In this case the ball is slowing down as it rises, and speeding up as it falls. © 2013 Pearson Education, Inc. Slide 1 -24

Quick. Check 1. 1 Car A Car B Motion diagrams are made of two cars. Both have the same time interval between photos. Which car, A or B, is going slower? © 2013 Pearson Education, Inc. Slide 1 -25

Quick. Check 1. 1 Car A Car B Motion diagrams are made of two cars. Both have the same time interval between photos. Which car, A or B, is going slower? © 2013 Pearson Education, Inc. Slide 1 -26

The Particle Model § Often motion of the object as a whole is not influenced by details of the object’s size and shape. § We only need to keep track of a single point on the object. § So we can treat the object as if all its mass were concentrated into a single point. § A mass at a single point in space is called a particle. § Particles have no size, no shape and no top, bottom, front or back. § Below is a motion diagram of a car stopping, using the particle model. © 2013 Pearson Education, Inc. Slide 1 -27

The Particle Model Motion Diagram in which the object is represented as a particle Motion diagram of a rocket launch © 2013 Pearson Education, Inc. Slide 1 -26

Quick. Check 1. 2 Three motion diagrams are shown. Which is a dust particle settling to the floor at constant speed, which is a ball dropped from the roof of a building, and which is a descending rocket slowing to make a soft landing on Mars? A. B. C. D. E. (a) is dust, (b) is ball, (c) is rocket. (a) is ball, (b) is dust, (c) is rocket. (a) is rocket, (b) is dust, (c) is ball. (a) is rocket, (b) is ball, (c) is dust. (a) is ball, (b) is rocket, (c) is dust. © 2013 Pearson Education, Inc. Slide 1 -29

Quick. Check 1. 2 Three motion diagrams are shown. Which is a dust particle settling to the floor at constant speed, which is a ball dropped from the roof of a building, and which is a descending rocket slowing to make a soft landing on Mars? A. B. C. D. E. (a) is dust, (b) is ball, (c) is rocket. (a) is ball, (b) is dust, (c) is rocket. (a) is rocket, (b) is dust, (c) is ball. (a) is rocket, (b) is ball, (c) is dust. (a) is ball, (b) is rocket, (c) is dust. © 2013 Pearson Education, Inc. Slide 1 -30

Position and Time § In a motion diagram it is useful to add numbers to specify where the object is and when the object was at that position. § Shown is the motion diagram of a basketball, with 0. 5 s intervals between frames. § A coordinate system has been added to show (x, y). § The frame at t 0 is frame 0, when the ball is at the origin. § The ball’s position in frame 4 can be specified with coordinates (x 4, y 4) (12 m, 9 m) at time t 4 2. 0 s. © 2013 Pearson Education, Inc. Slide 1 -31

Position as a Vector § Another way to locate the ball is to draw an arrow from the origin to the point representing the ball. § You can then specify the length and direction of the arrow. § This arrow is called the position vector of the object. § The position vector is an alternative form of specifying position. § It does not tell us anything different than the coordinates (x, y). © 2013 Pearson Education, Inc. Slide 1 -32

Tactics: Vector Addition © 2013 Pearson Education, Inc. Slide 1 -33

Vector Addition Example: Displacement Sam is standing 50 ft east of the corner of 12 th Street and Vine. He then walks northeast for 100 ft to a second point. What is Sam’s change of position? § Sam’s initial position is the vector. § Vector is his position after he finishes walking. § Sam has changed position, and a change in position is called a displacement. § His displacement is the vector labeled. © 2013 Pearson Education, Inc. Slide 1 -34

Definition of Displacement § The displacement of an object as it moves from an initial position to a final position is § The definition of involves vector subtraction. § With numbers, subtraction is the same as the addition of a negative number. The negative of a vector. § Similarly, with vectors � © 2013 Pearson Education, Inc. Slide 1 -35

Tactics: Vector Subtraction © 2013 Pearson Education, Inc. Slide 1 -36

Quick. Check 1. 3 Given vectors © 2013 Pearson Education, Inc. and , what is ? Slide 1 -37

Quick. Check 1. 3 Given vectors © 2013 Pearson Education, Inc. and , what is ? Slide 1 -38

Quick. Check 1. 4 Given vectors © 2013 Pearson Education, Inc. and , what is ? Slide 1 -39

Quick. Check 1. 4 Given vectors © 2013 Pearson Education, Inc. and , what is ? Slide 1 -40

Time Interval § It’s useful to consider a change in time. § An object may move from an initial position at time ti to a final position at time tf. A stopwatch is used to measure a time interval. § Different observers may choose different coordinate systems and different clocks, however, all observers find the same values for the displacement and the time interval t. © 2013 Pearson Education, Inc. Slide 1 -41

Average Speed, Average Velocity To quantify an object’s fastness or slowness, we define a ratio: The victory goes to the runner with the highest average speed. © 2013 Pearson Education, Inc. § Average speed does not include information about direction of motion. § The average velocity of an object during a time interval t, in which the object undergoes a displacement , is the vector: Slide 1 -42

Motion Diagrams with Velocity Vectors § The velocity vector is in the same direction as the displacement . § The length of is directly proportional to the length of . § Consequently, we may label the vectors connecting the dots on a motion diagram as velocity vectors. § Below is a motion diagram for a tortoise racing a hare. § The arrows are average velocity vectors. § The length of each arrow represents the average speed. © 2013 Pearson Education, Inc. Slide 1 -43

EXAMPLE 1. 2 Accelerating Up a Hill Motion diagram of a car accelerating up a hill. © 2013 Pearson Education, Inc. Slide 1 -44

Acceleration § § Sometimes an object’s velocity is constant as it moves. More often, an object’s velocity changes as it moves. Acceleration describes a change in velocity. Consider an object whose velocity changes from to during the time interval ∆t. § The quantity is the change in velocity. § The rate of change of velocity is called the average acceleration: The Audi TT accelerates from 0 to 60 mph in 6 s. © 2013 Pearson Education, Inc. Slide 1 -45

Tactics: Finding the Acceleration Vector © 2013 Pearson Education, Inc. Slide 1 -46

Tactics: Finding the Acceleration Vector § Notice that the acceleration vectors goes beside the dots, not beside the velocity vectors. § That is because each acceleration vector is the difference between two velocity vectors on either side of a dot. © 2013 Pearson Education, Inc. Slide 1 -47

Quick. Check 1. 5 A particle has velocity as it accelerates from 1 to 2. What is its velocity vector as it moves away from point 2 on its way to point 3? © 2013 Pearson Education, Inc. Slide 1 -48

Quick. Check 1. 5 A particle has velocity as it accelerates from 1 to 2. What is its velocity vector as it moves away from point 2 on its way to point 3? © 2013 Pearson Education, Inc. Slide 1 -49

The Complete Motion Diagram © 2013 Pearson Education, Inc. Slide 1 -50

Example 1. 5 Skiing Through the Woods © 2013 Pearson Education, Inc. Slide 1 -51

Example 1. 5 Skiing Through the Woods © 2013 Pearson Education, Inc. Slide 1 -52

Speeding Up or Slowing Down? § When an object is speeding up, the acceleration and velocity vectors point in the same direction. § When an object is slowing down, the acceleration and velocity vectors point in opposite directions. § An object’s velocity is constant if and only if its acceleration is zero. § In the motion diagrams to the right, one object is speeding up and the other is slowing down, but they both have acceleration vectors toward the right. © 2013 Pearson Education, Inc. Slide 1 -53

Quick. Check 1. 6 A cyclist riding at 20 mph sees a stop sign and actually comes to a complete stop in 4 s. He then, in 6 s, returns to a speed of 15 mph. Which is his motion diagram? © 2013 Pearson Education, Inc. Slide 1 -54

Quick. Check 1. 6 A cyclist riding at 20 mph sees a stop sign and actually comes to a complete stop in 4 s. He then, in 6 s, returns to a speed of 15 mph. Which is his motion diagram? © 2013 Pearson Education, Inc. Slide 1 -55

Tactics: Determining the Sign of the Position, Velocity, and Acceleration © 2013 Pearson Education, Inc. Slide 1 -56

Tactics: Determining the Sign of the Position, Velocity, and Acceleration © 2013 Pearson Education, Inc. Slide 1 -57

Tactics: Determining the Sign of the Position, Velocity, and Acceleration © 2013 Pearson Education, Inc. Slide 1 -58

Quick. Check 1. 7 A ball is tossed straight up in the air. At its very highest point, the ball’s acceleration vector A. Points up. B. Is zero. C. Points down. © 2013 Pearson Education, Inc. Slide 1 -59

Quick. Check 1. 7 A ball is tossed straight up in the air. At its very highest point, the ball’s acceleration vector A. Points up. B. Is zero. C. Points down. In fact, the acceleration vector points down as the ball rises, at the highest point, and as it falls. © 2013 Pearson Education, Inc. Slide 1 -60

Quick. Check 1. 8 The motion diagram shows a particle that is slowing down. The sign of the position x and the sign of the velocity vx are: A. B. C. D. Position is positive, velocity is positive. Position is positive, velocity is negative. Position is negative, velocity is positive. Position is negative, velocity is negative. © 2013 Pearson Education, Inc. Slide 1 -61

Quick. Check 1. 8 The motion diagram shows a particle that is slowing down. The sign of the position x and the sign of the velocity vx are: A. B. C. D. Position is positive, velocity is positive. Position is positive, velocity is negative. Position is negative, velocity is positive. Position is negative, velocity is negative. © 2013 Pearson Education, Inc. Slide 1 -62

Quick. Check 1. 9 The motion diagram shows a particle that is slowing down. The sign of the acceleration ax is: A. Acceleration is positive. B. Acceleration is negative. © 2013 Pearson Education, Inc. Slide 1 -63

Quick. Check 1. 9 The motion diagram shows a particle that is slowing down. The sign of the acceleration ax is: A. Acceleration is positive. B. Acceleration is negative. © 2013 Pearson Education, Inc. Slide 1 -64

Position-versus-Time Graphs § Below is a motion diagram, made at 1 frame per minute, of a student walking to school. § A motion diagram is one way to represent the student’s motion. § Another way is to make a graph of x versus t for the student: © 2013 Pearson Education, Inc. Slide 1 -65

Example 1. 7 Interpreting a Position Graph © 2013 Pearson Education, Inc. Slide 1 -66

Example 1. 7 Interpreting a Position Graph © 2013 Pearson Education, Inc. Slide 1 -67

Quick. Check 1. 10 This is a graph of an object moving along a straight line. The most likely interpretation is: A. A person walking down a steep mountain. B. A car that drives and stops and drives and stops. C. An elevator descending. D. A rock that falls, bounces, and falls some more. E. A ball that is hit, caught, and thrown to someone else. © 2013 Pearson Education, Inc. Slide 1 -68

Quick. Check 1. 10 This is a graph of an object moving along a straight line. The most likely interpretation is: A. A person walking down a steep mountain. B. A car that drives and stops and drives and stops. C. An elevator descending. D. A rock that falls, bounces, and falls some more. E. A ball that is hit, caught, and thrown to someone else. © 2013 Pearson Education, Inc. Vertical motion About 150 feet in 50 s Slide 1 -69

Solving Problems in Physics § Physics problems are often presented using words, which can be imprecise or ambiguous. § Part of problem-solving involves using symbols and drawings to create a representation, which is clear and precise. § A verbal representation is a problem statement or re-statement using words. A new building requires careful planning. The architect’s visualization and drawings have to be complete before the detailed procedures of construction get under way. The same is true for solving problems in physics. § A pictorial representation includes motion diagrams, coordinate systems, simple drawings, and symbols. § A graphical representation uses graphs when appropriate. § A mathematical representation uses specific equations which must be solved. © 2013 Pearson Education, Inc. Slide 1 -70

Tactics: Drawing a Pictorial Representation © 2013 Pearson Education, Inc. Slide 1 -71

Tactics: Drawing a Pictorial Representation © 2013 Pearson Education, Inc. Slide 1 -72

General Problem-Solving Strategy © 2013 Pearson Education, Inc. Slide 1 -73

Example 1. 9 Launching a Weather Rocket © 2013 Pearson Education, Inc. Slide 1 -74

Example 1. 9 Launching a Weather Rocket © 2013 Pearson Education, Inc. Slide 1 -75

Example 1. 9 Launching a Weather Rocket © 2013 Pearson Education, Inc. Slide 1 -76

Example 1. 9 Launching a Weather Rocket © 2013 Pearson Education, Inc. Slide 1 -77

Units § Science is based on experimental measurements, and measurements require units. § The system of units in science is called le Système Internationale d’unités or SI units. § The SI unit of time is the second, abbreviated s. § 1 s is defined as the time required for 9, 192, 631, 770 oscillations of the radio wave An atomic clock at the National Institute of Standards and Technology is the primary absorbed by a cesium-133 atom. standard of time. § The SI unit of length is the meter, abbreviated m. § 1 m is defined as the distance traveled by light in a vacuum during 1/299, 292, 458 of a second. © 2013 Pearson Education, Inc. Slide 1 -78

Units § The SI unit of mass is the kilogram, abbreviated kg. § 1 kg is defined as the mass of the international standard kilogram, a polished platinumiridium cylinder stored in Paris. § Many lengths, times, and masses are either much less or much greater than the standards of 1 m, 1 s, and 1 kg. § We use prefixes to denote various powers of 10, which make it easier to talk about quantities. © 2013 Pearson Education, Inc. Slide 1 -79

Unit Conversions § It is important to be able to convert back and forth between SI units and other units. § One effective method is to write the conversion factor as a ratio equal to one. § Because multiplying by 1 does not change a value, these ratios are easily used for unit conversions. § For example, to convert the length 2. 00 feet to meters, use the ratio: § So that: © 2013 Pearson Education, Inc. Slide 1 -80

Assessment § When problem solving, it is important to decide whether or not your final answer “makes sense. ” § For example, if you are working a problem about automobile speeds and reach an answer of 35 m/s, is this a realistic speed? § The table shows some approximate conversion factors that can be used to assess answers. § Using 1 m/s ≈ 2 mph, you find that 35 m/s is roughly 20 mph, a reasonable speed for a car. § If you reached an answer of 350 m/s, this would correspond to an unreasonable 700 mph, indicating that perhaps you made a calculation error. © 2013 Pearson Education, Inc. Slide 1 -81

Significant Figures § It’s important in science and engineering to state clearly what you know about a situation—no less, and no more. § For example, if you report a length as 6. 2 m, you imply that the actual value is between 6. 15 m and 6. 25 m and has been rounded to 6. 2. § The number 6. 2 has two significant figures. § More precise measurement could give more significant figures. § The appropriate number of significant figures is determined by the data provided. § Calculations follow the “weakest link” rule: The input value with the smallest number of significant figures determines the number of significant figures to use in reporting the output value. © 2013 Pearson Education, Inc. Slide 1 -82

Determining significant figures. © 2013 Pearson Education, Inc. Slide 1 -83

Tactics: Using Significant Figures © 2013 Pearson Education, Inc. Slide 1 -84

EXAMPLE 1. 10 Using significant figures © 2013 Pearson Education, Inc. Slide 1 -85

Orders of Magnitude and Estimating Some approximate lengths and masses Distance you can drive in 1 hour ~105 m Distance across a college campus ~1000 m Length of your arm ~1 m Length of your little fingernail ~0. 01 m Thickness of a sheet of paper ~10– 4 m Small car ~1000 kg Large human ~100 kg Science textbook ~1 kg Apple ~0. 1 kg Raisin ~10– 3 kg © 2013 Pearson Education, Inc. § In many cases a very rough estimate of a number is sufficient. § A one-significant-figure estimate or calculation is called an order-ofmagnitude estimate. § An order-of-magnitude estimate is indicated by the symbol ~, which indicates even less precision than ≈. Slide 1 -86

Quick. Check 1. 11 Rank in order, from the most to the least, the number of significant figures in the following numbers. For example, if b has more than c, c has the same number as a, and a has more than d, you would give your answer as b > c = a > d. a. 8200 A. B. C. D. E. b. 0. 0052 c. 0. 430 d. 4. 321 × 10 – 10 d>c>b=a a=b=d>c>a d>c>a>b a=d>c>b © 2013 Pearson Education, Inc. Slide 1 -87

Quick. Check 1. 11 Rank in order, from the most to the least, the number of significant figures in the following numbers. For example, if b has more than c, c has the same number as a, and a has more than d, you would give your answer as b > c = a > d. a. 8200 2? Ambiguous A. B. C. D. E. b. 0. 0052 2 c. 0. 430 3 d. 4. 321 × 10 – 10 4 d>c>b=a a=b=d>c>a d>c>a>b a=d>c>b © 2013 Pearson Education, Inc. Slide 1 -88

Chapter 1 Summary Slides © 2013 Pearson Education, Inc. Slide 1 -89

General Strategy © 2013 Pearson Education, Inc. Slide 1 -90

General Strategy © 2013 Pearson Education, Inc. Slide 1 -91

Important Concepts © 2013 Pearson Education, Inc. Slide 1 -92

Important Concepts © 2013 Pearson Education, Inc. Slide 1 -93