Physics for Scientists and Engineers PDF Chapter 1

9/10/2024 Physics for Scientists and Engineers Fifth Edition, Global Edition Chapter 1 Concepts of Motion Copyright © 2023 Pearson Education Ltd. All Rights Reserved....

9/10/2024 Physics for Scientists and Engineers Fifth Edition, Global Edition Chapter 1 Concepts of Motion Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-1 Chapter 1 Concepts of Motion IN THIS CHAPTER, you will learn the fundamental concepts of motion. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-2  9/10/2024 Chapter 1 Preview (1 of 4) What is motion? Before solving motion problems, we must learn to describe motion. We will use motion diagrams graphs pictures Motion concepts introduced in this chapter include position, velocity, and acceleration. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-3 Chapter 1 Preview (2 of 4) Why do we need vectors? Many of the quantities used to describe motion, such as velocity, have both a size and a direction. We use vectors to represent these quantities. This chapter introduces graphical techniques to add and subtract vectors. Chapter 3 will explore vectors in more detail. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-4  9/10/2024 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. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-5 Reading Question 1.1 Answer 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. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-6  9/10/2024 Reading Question 1.2 Which 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. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-7 Reading Question 1.2 Answer Which 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. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-8  9/10/2024 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. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-9 Reading Question 1.3 Answer 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. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 10  9/10/2024 Reading Question 1.4 An acceleration vector A. tells you how fast an object is going. B. is constructed from two velocity vectors. C. is the second derivative of the position. D. is parallel or opposite to the velocity vector. E. Acceleration vectors weren’t discussed in this chapter. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 11 Reading Question 1.4 Answer An acceleration vector A. tells you how fast an object is going. B. is constructed from two velocity vectors. C. is the second derivative of the position. D. is parallel or opposite to the velocity vector. E. Acceleration vectors weren’t discussed in this chapter. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 12  9/10/2024 Reading Question 1.5 The pictorial representation of a physics problem consists of A. a sketch. B. a coordinate system. C. symbols. D. a table of values. E. All of the above. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 13 Reading Question 1.5 Answer The pictorial representation of a physics problem consists of A. a sketch. B. a coordinate system. C. symbols. D. a table of values. E. All of the above. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 14  9/10/2024 Reading Question 1.6 The basic SI units are A. second, meter, and gram. B. second, meter, and kilogram. C. second, centimeter, and gram. D. meter, meter/second, and meter/second2. E. yard, span, and cubit. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 15 Reading Question 1.6 Answer The basic SI units are A. second, meter, and gram. B. second, meter, and kilogram. C. second, centimeter, and gram. D. meter, meter/second, and meter/second2. E. yard, span, and cubit. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 16  9/10/2024 Four Basic Types of Motion Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 17 Making a Motion Diagram (1 of 2) An easy way to study motion is to make a video of a moving object. A video camera takes images at a fixed rate, typically 30 every second. Each separate image is called a frame. Shown are four frames from a video of a car going past. The car is located at a different position in each frame. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 18  9/10/2024 Making a Motion Diagram (2 of 2) Suppose we edit the video by layering the frames on top of each other, creating the composite image shown below. This edited image, showing an object’s position at several equally spaced instants of time, is called a motion diagram. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 19 Examples of Motion Diagrams (1 of 2) Images that are equally spaced indicate an object moving with constant speed. An increasing distance between the images shows that the object is speeding up. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 20  9/10/2024 Examples of Motion Diagrams (2 of 2) A decreasing distance between the images shows that the object is slowing down. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 21 QuickCheck 1.1 Motion diagrams are made of two cars. Both have the same time interval between photos. Which car, A or B, is moving slower? Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 22  9/10/2024 QuickCheck 1.1 Answer Motion diagrams are made of two cars. Both have the same time interval between photos. Which car, A or B, is moving slower? Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 23 The Particle Model (1 of 2) For many types of motion, we can treat the object as if all its mass were concentrated in a single point in space. An object that can be represented as a mass at a single point in space is called a particle. If we model an object as a particle, we can represent the object in each frame of a motion diagram as a single dot rather than having to draw the entire object. Below is a motion diagram of a car slowing down. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 24  9/10/2024 The Particle Model (2 of 2) Motion diagram of a rocket launch Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 25 QuickCheck 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. (a) dust, (b) ball, (c) rocket. B. (a) ball, (b) dust, (c) rocket. C. (a) rocket, (b) dust, (c) ball. D. (a) rocket, (b) ball, (c) dust. E. (a) ball, (b) rocket, (c) dust. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 26  9/10/2024 QuickCheck 1.2 Answer 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. (a) dust, (b) ball, (c) rocket. B. (a) ball, (b) dust, (c) rocket. C. (a) rocket, (b) dust, (c) ball. D. (a) rocket, (b) ball, (c) dust. E. (a) ball, (b) rocket, (c) dust. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 27 Position and Time To use a motion diagram, you would like to know where the object is and when the object was at that position. Position measurements can be made by laying a coordinate- system grid over a motion diagram. To illustrate, the figure shows a sled sliding down a snow-covered hill. (b) shows a motion diagram for the sled, over which we’ve drawn an xy-coordinate system. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 28  9/10/2024 Displacement We said that motion is the change in an object’s position with time, but how do we show a change in position? Shown is the motion diagram of a sled sliding down a snow-covered hill. To show how the sled’s position changes between t3 = 3 s and t4 = 4 s, we b u s se l a u q b u s se l a u q draw a vector arrow between the two dots of the motion diagram. This vector is the sled’s displacement, which is given the symbol Δ𝑟⃗. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 29 Tactics: Vector Addition Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 30  9/10/2024 QuickCheck 1.3 Given vectors 𝑃 and 𝑄, what is 𝑃 𝑄? A. B. C. D. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 31 QuickCheck 1.3 Answer Given vectors 𝑃 and 𝑄, what is 𝑃 𝑄? A. B. C. D. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 32  9/10/2024 Tactics: Vector Subtraction Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 33 QuickCheck 1.4 Given vectors 𝑃 and 𝑄, what is 𝑃 𝑄? A. B. C. D. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 34  9/10/2024 QuickCheck 1.4 Answer Given vectors 𝑃 and 𝑄, what is 𝑃 𝑄? A. B. C. D. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 35 Time Interval It’s useful to consider a change in time. An object may move from an initial position 𝑟 at time 𝑡 to a final position 𝑟⃗ at time 𝑡. The time interval is Δ𝑡 𝑡 𝑡. 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 Δ𝑟⃗ and the time interval Δ𝑡. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 36  9/10/2024 Average Speed, Average Velocity To quantify an object’s fastness or slowness, we define a ratio: distancetraveled 𝑑 averagespeed timeinterval spent traveling Δ𝑡 Average speed does not include information about direction of motion. The victory goes to the runner The average velocity of an with the highest average speed. object during a time interval Δ𝑡, in which the object undergoes a displacement Δ𝑟⃗, is the vector: Δ𝑟⃗ 𝑣⃗ Δ𝑡 Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 37 Motion Diagrams with Velocity Vectors The velocity vector is in the same direction as the displacement Δ𝑟⃗. The length of 𝑣⃗ is directly proportional to the length of Δ𝑟⃗. Consequently, we may label the vectors connecting the dots on a motion diagram as velocity vectors 𝑣⃗. Below is a motion diagram for a tortoise racing a hare. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 38  9/10/2024 Example 1.2 Accelerating Up a Hill The light turns green and a car accelerates, starting from rest, up a 20° hill. Draw a motion diagram showing the car’s velocity. MODEL Use the particle model to represent the car as a dot. VISUALIZE The car’s motion takes place along a straight line, but the line is neither horizontal nor vertical. A motion diagram should show the object moving with the correct orientation—in this case, at an angle of 20°. FIGURE 1.11 shows several frames of the motion diagram, where we see the car speeding up. The car starts from rest, so the first arrow is drawn as short as possible and the first dot is labeled “Start.” The displacement vectors have been drawn from each dot to the next, but then they are identified and labeled as average velocity vectors 𝑣⃗. Figure 1.11 Motion diagram of a car accelerating up a hill Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 39 Linear 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 𝑣⃗ to 𝑣⃗ during the time interval Δ𝑡. The quantity Δ𝑣⃗ 𝑣⃗ 𝑣⃗ is the change in velocity. The rate of change of velocity is called the average acceleration: Δ𝑣⃗ 𝑎 Δ𝑡 The Audi TT accelerates from 0 to 60 mph in 6 s. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 40  9/10/2024 Tactics: Finding the Acceleration Vector (1 of 2) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 41 Tactics: Finding the Acceleration Vector (2 of 2) Notice that the acceleration vector 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. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 42  9/10/2024 QuickCheck 1.5 A particle has velocity 𝑣⃗ as it accelerates from 1 to 2. What is its velocity vector 𝑣⃗ as it moves away from point 2 on its way to point 3? A. B. C. D. E. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 43 QuickCheck 1.5 A particle has velocity 𝑣⃗ as it accelerates from 1 to 2. What is its velocity vector 𝑣⃗ as it moves away from point 2 on its way to point 3? A. B. C. D. E. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 44  9/10/2024 The Complete Motion Diagram Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 45 Example 1.5 Skiing Through the Woods (1 of 2) A skier glides along smooth, horizontal snow at constant speed, then speeds up going down a hill. Draw the skier’s motion diagram. MODEL Model the skier as a particle. It’s reasonable to assume that the downhill slope is a straight line. Although the motion as a whole is not linear, we can treat the skier’s motion as two separate linear motions. Figure 1.14 Motion diagram of a skier. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 46  9/10/2024 Example 1.5 Skiing Through the Woods (2 of 2) VISUALIZE FIGURE 1.14 shows a complete motion diagram of the skier. The dots are equally spaced for the horizontal motion, indicating constant speed; then the dots get farther apart as the skier speeds up going down the hill. The insets show how the average acceleration vector 𝑎⃗ is determined for the horizontal motion and along the slope. All the other acceleration vectors along the slope will be similar to the one shown because each velocity vector is longer than the preceding one. Notice that we’ve explicitly written 0 for the acceleration beside the dots where the velocity is constant. The acceleration at the point where the direction changes will be considered in Chapter 4. Figure 1.14 Motion diagram of a skier. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 47 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. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 48  9/10/2024 QuickCheck 1.6 A cyclist riding at 20 mph sees a stop sign and 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? A. B. C. D. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 49 QuickCheck 1.6 Answer A cyclist riding at 20 mph sees a stop sign and 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? A. B. C. D. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 50  9/10/2024 Tactics: Determining the Sign of the Position, Velocity, and Acceleration (1 of 3) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 51 Tactics: Determining the Sign of the Position, Velocity, and Acceleration (2 of 3) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 52  9/10/2024 Tactics: Determining the Sign of the Position, Velocity, and Acceleration (3 of 3) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 53 QuickCheck 1.7 A ball is tossed straight up in the air. At its very highest point, the ball’s acceleration vector 𝑎⃗. A. points up. B. is zero. C. points down. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 54  9/10/2024 QuickCheck 1.7 Answer A ball is tossed straight up in the air. At its very highest point, the ball’s acceleration vector 𝑎⃗. 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. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 55 QuickCheck 1.8 The motion diagram shows a particle that is slowing down. What are the signs of the position x and the velocity 𝑣 ? A. Position is positive, and velocity is positive. B. Position is positive, and velocity is negative. C. Position is negative, and velocity is positive. D. Position is negative, and velocity is negative. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 56  9/10/2024 QuickCheck 1.8 Answer The motion diagram shows a particle that is slowing down. 𝑣 ? What are the signs of the position x and the velocity A. Position is positive, and velocity is positive. B. Position is positive, and velocity is negative. C. Position is negative, and velocity is positive. D. Position is negative, and velocity is negative. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 57 QuickCheck 1.9 The motion diagram shows a particle that is slowing down. The sign of the acceleration ax is b u s A. positive. B. negative. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 58  9/10/2024 QuickCheck 1.9 Answer The motion diagram shows a particle that is slowing down. The sign of the acceleration ax is b u s A. positive. B. negative. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 59 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: Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 60  9/10/2024 Example 1.7 Interpreting a Position Graph (1 of 2) The graph in FIGURE 1.19a represents the motion of a car along a straight road. Describe the motion of the car. MODEL We’ll model the car as a particle with a precise position at each instant. FIGURE 1.19 Position-versus-time graph of a car. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 61 Example 1.7 Interpreting a Position Graph (2 of 2) VISUALIZE As FIGURE 1.19b shows, the graph represents a car that travels to the left for 30 minutes, stops for 10 minutes, then travels back to the right for 40 minutes. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 62  9/10/2024 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 A new building requires careful planning. The statement or re-statement using words. architect’s visualization and A pictorial representation includes motion drawings have to be diagrams, coordinate systems, simple complete before the detailed drawings, and symbols. procedures of construction get under way. The same is A graphical representation uses graphs true for solving problems in when appropriate. physics. A mathematical representation uses specific equations which must be solved. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 63 Tactics: Drawing a Pictorial Representation (1 of 2) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 64  9/10/2024 Tactics: Drawing a Pictorial Representation (2 of 2) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 65 Chapter 1 Summary Slides Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 66  9/10/2024 General Strategy (1 of 2) Problem Solving MODEL Make simplifying assumptions. VISUALIZE Use: Pictorial representation Graphical representation SOLVE Use a mathematical representation to find numerical answers. REVIEW Does the answer have the proper units and correct significant figures? Does it make sense? Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 67 General Strategy (2 of 2) Motion Diagrams Help visualize motion. Provide a tool for finding acceleration vectors. These are the average velocity and acceleration vectors. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 68  9/10/2024 Important Concepts (1 of 2) The particle model represents a moving object as if all its mass were concentrated at a single point. Position locates an object with respect to a chosen coordinate system. Change in position is called displacement. Velocity is the rate of change of the position vector 𝑟⃗. Acceleration is the rate of change of the velocity vector v. An object has an acceleration if it changes speed and/or changes direction. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 69 Important Concepts (2 of 2) Pictorial Representation 1. Draw a motion diagram. 2. Establish coordinates. 3. Sketch the situation. 4. Define symbols. 5. List knowns. 6. Identify desired unknown Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1 - 70