Physics CFU 2 Material PDF

EXPLORATION 1 Representing Motion Imagine that you and a friend are planning to meet at the library. You want to meet at the library’s door, but you will travel to the library from different locations in the city....

EXPLORATION 1 Representing Motion Imagine that you and a friend are planning to meet at the library. You want to meet at the library’s door, but you will travel to the library from different locations in the city. FIGURE 1: A and B are starting positions of two friends on their way to the library. town hall door library A B Motion: Movement Displacement: CollaborateChange in distance Write a description of the pathand to thedirection. door of the library starting from Velocity: Change Position A in Figurein1 speed andwrites while a partner direction. a description of the path starting from Position B. Trade descriptions, Magnitude: Value and follow your partner’s directions from your starting point. How does Scalar:theMagnitude. starting position Ex. affect Speed where you end up? & Direction. Vector: Magnitude and Direction. Ex. Velocity & Displacement. INFER Use evidence from your experience to infer what information scientists FIGURE 2: Two frames of need to include when communicating about position and motion. reference used to describe Note: When you write the speed you only write (Number) motion m/s, but when you write the velocity you write (number) m/ y-axis s Left/right/up/down. Same works fro the distance and + displacement x-axis – + Frame of Reference Representations of motion, such as a multiple-exposure photo or a graph of © Houghton Mifflin Harcourt Publishing Company – position over time, enable scientists to quantify motion and look for patterns. a Cartesian Descriptions of motion should be accurate, and the usage of units should be consistent. Lack of precision can cause confusion. For example, the position North description “5 m” might mean a position “5 m above the floor” or a position “5 m left of the door.” Motion is a change in position relative to something else. Motion is described West East within a frame of reference, which is a system of coordinates that has a fixed origin. Figure 2 shows two common frames of reference that you might use to describe motion and position in science class or in everyday life. Examples South of origins might include things such as oneself, the steps in front of the local library, or the bottom left corner of a desk. The observed position and motion b Cardinal of an object depend on the frame of reference of the observer. 28 Unit 1 Physics and Engineering  Hands-On Lab Frame of Reference in Motion When police officers investigate car accidents, they may interview several FIGURE 3: Different witnesses. People watching from nearby sidewalks or other cars will make perspectives of the same car different observations of the motion of the cars in the accident. The officers must interpret each description based on frame of reference of that witness. In this activity, you will record the same event from various frames of reference, like the example in Figure 3. RESEARCH QUESTION How does frame of reference change the description of a moving object? a Car filmed from the side MAKE A CLAIM How does the location of a camera affect the way motion is captured? b Car filmed from behind POSSIBLE MATERIALS · meterstick · video-recording device, such · wind-up or remote- · tape as a cell phone control car SAFETY INFORMATION © Houghton Mifflin Harcourt Publishing Company Image Credits: ©HMH (both images) Wear safety goggles during the setup, hands-on, and takedown segments of the activity. If recording the car from above, make sure to attach the camera securely to its support. It should not be placed above shoulder height, and one student in the group should be on-hand to catch the assembly should it begin to fall. Immediately pick up any items dropped on the floor so they do not become a slip/fall hazard. PLAN THE INVESTIGATION In your Evidence Notebook, develop a procedure to investigate how frames of reference change how you describe the motion of the car. Make sure your teacher approves your procedure and safety plan before proceeding. When developing your procedure, consider the following: To compare the same event from different frames of reference, you will need to be able to recreate the car’s motion exactly in repeated trials. In some trials, the camera will be stationary. Adjust the car’s path and the camera’s position so that the path fits in the frame of the camera. In your plan, include a list of the camera shots that describes the position of the camera and the motion of the car. Also include a description of the camera’s motion if it moves during a shot. Plan to perform multiple trials of each shot. Lesson 2 Modeling Motion 29  ANALYZE 1. In your Evidence Notebook, draw the experimental setup for at least two of your trials. Label key components, and define your coordinate system. 2. When the camera is stationary, what determines the perceived direction of the car’s motion? 3. Suppose you film the car from the side. In one trial, the camera is moving at the same speed in the same direction as the car. In another trial, the camera is moving at the same speed in the opposite direction. If the car’s speed is 0.3 meters per second (m/s) relative to its surroundings, what will its apparent speed relative to the camera be in each trial? 4. How does the frame of reference affect how an observer perceives motion? In this lab, the camera is the observer, and the video recording is what an observer would perceive. DRAW CONCLUSIONS Write a conclusion that addresses each of the points below. Claim How does the location of the camera affect the way motion is captured? Was your initial claim correct? Evidence What evidence from your investigation supports your claim? © Houghton Mifflin Harcourt Publishing Company Reasoning Explain how the evidence you gave supports your claim. Describe in detail the connections between the evidence you cited and the argument you are making. Evidence Notebook How might viewing the beam prototypes in your unit project from different frames of reference yield information to help you improve the design? 30 Unit 1 Physics and Engineering  Position and Changes in Position If you were to describe your position, you may say “at my desk” or “by the teacher.” You would describe your position compared to some other point in space, like the desk or the teacher. In science, the point in space you refer to is the origin in a frame of reference. Modeling Changes in Position When something moves or is in motion, how it moves can be described with distance, direction, and time. Displacement is a change in position in a frame of reference that Is the change in distance and direction describes the distance and direction of an object’s final position from its initial position. Examples of displacement include moving right 5 units on graph paper or walking 8 blocks north on a city grid. Quantities used to describe motion and other quantities in science are either scalars or vectors. A scalar is a quantity that has magnitude (duration or size) but no direction, such as 15 minutes (min) or 8.3 meters (m). A vector is a quantity that has both magnitude and direction, such as 14 centimeters (cm) forward, 0.09 millimeters per second (mm/s) left, or –15 m, where the negative sign indicates direction in a frame of reference. Vector variables are given in bold, for example v. A FIGURE 4: Vector representation of displacement, ∆x scalar that gives the magnitude of a vector but not the direction is indicated using absolute value notation as |v| or using scalar notation as v. Position is a vector 10 m 10 m 20 m 25 m 35 m because it has magnitude and direction from the origin in a frame of reference. Displacement, ∆x, is a vector that represents a change in the position vector x, as shown in Figure 4. The symbol ∆ is the Greek letter Delta, and it means change in. Distance is a scalar quantity. If an object travels in a straight path, the distance, how far it traveled, is the magnitude of its displacement, how much its position changed. For example, the displacement ∆x = –8 m corresponds to the distance of 8 m. In a 100 m race, runners travel a distance of 100 m, and the displacement is 100 m forward from the starting line. Vector quantities can be modeled with arrows. The length of the arrow corresponds to the magnitude of the vector, and the orientation of the arrow corresponds to its direction. FIGURE 5: Vector addition and subtraction in one dimension Vector Addition Vector Subtraction © Houghton Mifflin Harcourt Publishing Company A A B B A+B A + (–B) A+B=C A–B=C a  Vector addition for motion along b  Vector subtraction for motion along a straight line a straight line Arrow models of vectors can be helpful when adding and subtracting vectors, as shown in Figure 5. To add two vectors, align the head (triangle end) of the first arrow with the tail (flat end) of the second arrow. Draw a new arrow from the tail of the first arrow to the head of the second arrow. This new arrow represents the magnitude and direction of the resultant vector. Subtracting vectors is similar, except that you would align the subtracted arrow –B in the opposite direction as the original vector B. From there, subtraction is the addition of a negative term, so the head-tail method of vector addition can be applied. Lesson 2 Modeling Motion 31  Distance Hands-On Activity Distance : The total length of the path Modelingof traveled, regardless Displacement direction. Start The magnitude of displacement is sometimes but not always equal to the distance Unit: Meter an object travels. In this activity, you will model a random path with a number line, a marker, and a coin. You will move the marker one unit with each coin flip, with the direction determined by the coin flip result. Scalar or Vector: Scalar Displacement MATERIALS Distance · safety goggles · coin · marker · number line Finish SAFETY INFORMATION Wear safety goggles during the setup, hands-on, and takedown segments of Displacementthe : The activity. shortest straight-line distance from the starting Immediately pick up any items dropped on the floor so they do not become a point to the ending point, along with the direction slip/fall hazard. CARRY OUT THE INVESTIGATION Unit: Meter Start the marker at zero on the number line, and flip the coin. For heads, move the marker one unit right; for tails, move one unit left. Scalar or Vector: Vector Conduct ten rounds of coin flips. In your Evidence Notebook, use vector arrow models to determine the displacement of your marker after ten coin flips. Velocity: Displacement ANALYZE / Time Interval How does the distance traveled by the coin compare to its displacement after ten flips? Compare your results with those of other groups. The relation between velocity and displacement is directly propotional. Changes in Position over Time © Houghton Mifflin Harcourt Publishing Company Image Credits: ©HMH Change in speed The velocity of an object is a vector giving its speed in a particular direction. The average and direction velocity over a time interval is the displacement of the object divided by that time interval. ANNOTATE A sprinter is photographed at equal time intervals. Draw vectors arrows to indicate the displacement between adjacent images of the sprinter. What happens to the sprinter’s displacement between images? What happens to the sprinter’s velocity? 32 Unit 1 Physics and Engineering  Math Connection Average and Instantaneous Velocity A dog runs across a field in a straight line, and its motion can be analyzed with a position-time graph (Figure 6). The x-axis shows time, t; the y-axis shows position, x. The change in the y-value between any two points gives the dog’s displacement over that time interval. Dividing the change in y (position) by the change in x (time) will give the average velocity in that interval. Place a straight edge between the points for t = 0 s and t = 4 s in Figure 6. The slope of the line (rise ÷ run) is equal to the runner’s average velocity during that segment. displacement ​x​  final​–​x​  initial​ ∆x average velocity = ​​ __    ​​  =  ​​ _     ​​ = ​​ _ ​​ change in time t​ ​  final​–​t​  initial​ ∆t To find the average velocity in the first 4 s, and over the whole graph: 20 m − 0 m v = ​​  _  ​​  = 5 m/s forward 4s−0s 100 m − 0 m v = ​​  __  ​​  = 10 m/s forward 10 s − 0 s Over the entire 100 m, the average velocity was 10 m/s forward, but this number does not capture Position-Time Graph of a Running Dog the velocity at each point in the dog’s path. The FIGURE 6: The position of a dog at 2 s intervals average velocity in the first 2 s was slower, and 100 the average velocity in the last 2 s was faster. The average velocity only conveys the total motion over 80 that interval, not the precise velocity at any single Position (m) moment. The dog’s momentary velocity at one 60 point in time is called the instantaneous velocity. 40 If the graph were a straight line, it would indicate that displacement changed linearly over time, and 20 so velocity was constant. That velocity would be 0 equal to the slope of the line. A curved line on a 0 2 4 6 8 10 position-time graph indicates that the velocity is Time (s) changing over time. EVALUATE Determine whether the question asks © Houghton Mifflin Harcourt Publishing Company Average Instantaneous about an average or instantaneous velocity. velocity velocity How fast must you bike to get there in half an hour? What is the fastest she can run? What is the minimum speed for takeoff? How fast did he run the first 5 miles of the marathon? Evidence Notebook Look back at the multiple-exposure photo of the sprinter as well as the position versus time graph for the dog in Figure 6. If the sprinter and dog were instead slowing down, how would the photo and graph look different? Lesson 2 Modeling Motion 33  What is the distance traveled? The distance traveled is 12m + 15m + 18m = 45m. What is the displacement? The displacement is 0 meters. (∆x) (m) (∆t) (s) To find on graphs: = ∆𝑥 𝑥2 −𝑥1 m/s ∆𝑡 = 𝑡2 − 𝑡1 What is the displacement? The displacement is 270 meters. What is the time? The time is 60 seconds. What is the average speed? 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 270𝑚 Average Speed = = = 4.5 m/s 𝑇𝑖𝑚𝑒 60𝑠 What is the average velocity? 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 270𝑚 Average Speed = = = 4.5 m/s 𝑇𝑖𝑚𝑒 60𝑠