Chapter 5: Newton s Laws: Force and Motion

Transcription

1 CHAPTER 5: NEWTON S LAWS: FORCE AND MOTION Chapter 5: Newton s Laws: Force and Motion Instructional Sequence Learning Goals National Science Standards Investigations and Materials Section 5.1: The First Law: Force and Inertia Two 45-minute class periods 1. Complete Chapter 5 Pretest. 2. Complete Investigation 5.1: The First Law: The Law of Inertia. 3. Read Section 5.1, pp. 100 to 102. Describe how the law of inertia affects the motion of an object. Give an example of a system or an invention designed to overcome inertia. INQ01.1 INQ01.2 INQ01.3 INQ01.4 INQ02.5 PS04.1 Investigation 5.1: The First Law: The Law of Inertia Materials (per group): SmartTrack, Energy Car, Steel marbles, Rubber band, Track feet (2), Bubble level, Velocity sensor, Data Collector, Electronic scale Section 5.2: The Second Law: Force, Mass, and Acceleration Two 45-minute class periods 1. Complete Investigation 5.2: The Second Law: Force, Mass, and Acceleration. 2. Read Section 5.2, pp. 103 to 108. Measure and describe force in newtons (N) and pounds (lbs). Calculate the net force for two or more forces acting along the same line. Calculate the acceleration of an object from the net force acting on it. INQ01.1 INQ01.2 INQ01.3 INQ01.4 INQ02.5 PS04.1 Investigation 5.2: The Second Law: Force, Mass, and Acceleration Materials (per group): Physics Stand, Double pulley, Red safety string, Mass hangers (2), Steel washers, Plastic washers, Measuring tape, Photogate, Data Collector, Electronic scale or triple beam balance Section 5.3: The Third Law: Action and Reaction Two 45-minute class periods 1. Complete Investigation 5.3: Newton s Third Law: Action and Reaction. 2. Read Section 5.3, pp. 109 to Complete Chapter 5 Assessment, pp. 115 to 116. Determine whether an object is in equilibrium by analyzing the forces acting on it. Draw a diagram showing an action-reaction pair of forces. Determine the reaction force when given an action force. INQ01.1 INQ01.2 INQ01.3 INQ01.4 INQ02.5 PS04.1 Investigation 5.3: Newton s Third Law: Action and Reaction Materials (per group): SmartTrack, 2 Energy Cars (1 blue, 1 orange), Energy Car link, Steel marbles, Rubber band, Track feet (2), Bubble level, Velocity sensor, Data Collector, Safety goggles 70 UNIT 2: MOTION AND FORCE IN ONE DIMENSION

2 CHAPTER 5 RESOURCES Assessment Tools Program Resources Technology Resources Chapter 5 Pretest Skill and Practice Worksheets 5.1 Isaac Newton Teaching Illustrations 5_1 Force Lesson Organizer CPO Web site Equipment Setup Videos Science Content Videos Simulations Presentation Slides Skill and Practice Worksheets 5.2 Newton s Second Law Section 5.2 Review Questions Teaching Illustrations 5_2 newtons second law Literature Selections Objects in Motion: Principles of Classical Mechanics by Paul Fleisher This book uses real-life examples to explain the universal laws of science in a reader-friendly language. Topics include Newton s laws of motion, universal gravitation, and falling objects. Chapter 5 Assessment ExamView Test Bank Multiple Choice Multi-format Skill and Practice Worksheets 5.3 Applications of Newton s Laws Section 5.3 Review Questions Teaching Illustrations 5_3 action reaction forces Connection Biomechanics Chapter 5 Problems Isaac Newton: The Scientist Who Changed Everything by Phillip Steele Recommended by NSTA, this book discusses the challenges Newton faced early in life and continues to delve into his accomplishments as an adult. Readers will find that Newton experienced situations such as bullying and problems at home just like many students do today. It is also an excellent resource for teaching about the process of science. 71

3 CHAPTER 5: NEWTON S LAWS: FORCE AND MOTION Investigation 5.1: The First Law: Force and Inertia Newton s first law states that all objects want to keep doing what they are doing. An object at rest will remain at rest, and an object in motion will stay in motion at a constant velocity as long as there are no unbalanced forces acting on it. In this investigation students use Newton s first law to explain the motion of a car as it rolls along a flat track. Next, students modify the experiment as they vary the mass of the car and observe the impact on its motion. From these observations, students are able to infer the relationship between an object s mass and its velocity when the force applied is constant. Key Question How does changing an object s inertia affect its motion? Objectives Students will: Change the Energy Car s inertia to see what affect it has on the Energy Car s motion. Apply Newton s first law to describe the Energy Car s motion. Setup 1. One class period is needed to complete the investigation. 2. Students work in small groups of two to three. Materials Each group should have the following: Newton s first law - states that an object at rest remains at rest until acted on by an unbalanced force. An object in motion continues with constant velocity in a straight line unless acted on by an unbalanced force. mass - a measure of an object s inertia; the amount of matter an object has. inertia - the resistance of a body to a change in motion. force - any action on a body that causes it to change motion. Force is a vector and always has a magnitude and a direction. constant velocity - maintained velocity that does not vary. net force - the amount of force that overcomes an opposing force to cause motion. The net force can be zero if the opposing forces are equal. Safety SmartTrack Energy Car Steel marbles Rubber band Track feet (2) Bubble level Velocity sensor Data Collector Electronic scale Students should observe general laboratory safety procedures while completing Investigation UNIT 2: MOTION AND FORCE IN ONE DIMENSION

4 1 1 1 INVESTIGATION 5.1: THE FIRST LAW: FORCE AND INERTIA The First Law: The Law of Inertia Investigation 5.1 Investigation 5.1 The First Law: The Law of Inertia 5.1 The First Law: The Law of Inertia How does changing an object s inertia affect its motion? Newton s first law states that objects tend to keep doing what they are doing unless acted on by an unbalanced force. This law applies to both objects at rest and objects in motion. In this investigation, you will: change the Energy Car s inertia to see what affect it has on the Energy Car s motion. apply Newton s first law to describe the Energy Car s motion. A Making a prediction Newton s first law of motion applies to objects at rest and objects in motion. The first law can also be called the law of inertia. To understand why, consider what inertia is. Inertia is a property of matter that resists a change in motion. Inertia comes from an object s mass. Because of inertia, objects at rest remain at rest, and objects in motion remain in motion, unless acted upon by a net force. You will investigate the first law by launching the Energy Car on a flat track, and seeing what happens when you change the car s inertia (by changing its mass). a. You will launch an Energy Car several times on the flat track, and you will change the number of marbles in the car each time. Write a hypothesis to address the question How will changing the inertia of the car affect the car s motion on the flat track? Your hypothesis should follow this format: If inertia affects the car s motion on the flat track, then when I add more marbles to the car, the car. B Setting up the experiment Materials List SmartTrack Energy Car Steel marbles Rubber band Track feet (2) Bubble level Velocity sensor DataCollector a. Describe what happens to the Energy Car s velocity as it moves along the track. Explain why this happens. b. An object at rest remains at rest unless acted upon by an outside force. What is the outside force that acts on the car to disturb its state of rest at the start of the track? c. An object in motion remains in motion unless acted upon by an outside force. What outside force acts on the car to change its motion as it moves along the track? C Conducting the experiment and reporting back a. Design an experiment to test the hypothesis you stated in 1a. What is your procedure? b. Create a data table and a graph to communicate your results. c. Summarize your findings. Be sure to refer back to your hypothesis. D Reflecting on Newton s first law a. State Newton s first law in your own words. b. Place the energy in the center of the track so it stays at rest. What do you know about the forces on the Energy Car? Identify the forces acting on it. c. If the Energy Car is moving and there are no unbalanced forces acting on it, does its speed increase, decrease, or remain the same? Explain. d. Were any forces acting on the Energy Car as it rolled along the level track? Identify the forces. Explain how Newton s first law is applied to describe the motion you observed. e. What changes occur in the forces acting on the Energy Car when the track is tilted slightly up or down? Explain how the first law is applied to describe the observed motion in the case of uphill or downhill slope. 1. Attach a foot to each end of the SmartTrack so it sits level on the table. Check it with the bubble level and adjust the feet as necessary to make the track level. 2. Attach the velocity sensor to the end of the SmartTrack. 3. Fasten a rubber band on the launcher. 4. Plug the velocity sensor into the DataCollector. 5. Turn the DataCollector on. At the home window, select data collection mode. 6. At the Go window, choose setup at the bottom of the screen. 7. At the setup window, choose standard mode, 200 samples, and 0.02 Hz. This will allow the DataCollector to collect 50 samples of data from the velocity sensor each second. 8. Practice launching the Energy Car with no marbles. Once you have a consistent launch technique, get the car ready to launch, press the Go button on the DataCollector, and launch the car. 9. Switch from meter to table and graph view to study your data

5 CHAPTER 5: NEWTON S LAWS: FORCE AND MOTION Teaching Investigation 5.1 A Making a prediction In this investigation we will be studying Newton s first law. What does the first law say? Prompt a discussion on the different ways the first law can be stated. Some possibilities are an object at rest will tend to remain at rest, and an object in motion will tend to remain in motion; objects tend to keep doing what they are already doing; objects have inertia and resist changes in their motion. What is required for an object to change its state of motion or its state of having no motion? An unbalanced force is needed. If students simply answer force then discuss the difference between a force and an unbalanced force. Do all objects have the same ability to remain in their state of motion? No. This ability depends on an object s inertia. An object with more inertia has a greater tendency to remain in its state of motion. Mass is a measure of an object s inertia. Newton s first law is also known as the law of inertia, which refers to the fact that inertia is a property of matter that resists a change in motion. By resisting, we mean that if an object is at rest, it would resist changing its current state of rest unless something caused it to do so. Likewise, a moving object would continue to move unless something stopped it from moving. The something that causes a change in the object s motion is a net force. What do you think I mean when I say net force? Net force is the sum of all forces acting on a body. The concept of net force means that many different forces may be acting on an object. Consider what happens when you play tug of war with your friends. One group of friends is pulling the rope in one direction while the others are pulling in the opposite direction. If the net force is zero, does anyone win the competition? No one wins. That is correct. The force exerted by one team must be enough to overcome the effects of the other team s efforts in order for someone to win. You know this by observing the losing team being pulled across the neutral zone. In other words, the net force is no longer zero. Today you will investigate Newton s first law by launching the Energy Car on a flat track, and then observing what happens when you change the car s inertia. You will change the car s inertia by altering its mass. How do you think altering the mass of the car will influence its motion? Don t tell me what you think just yet. Instead, write your answer in the form of a hypothesis that will complete the statement in Part 1. Students complete question 1a. A Making a prediction Sample answer: a. If inertia affects the car s motion on a flat track, then when I add more marbles to the car (thus increasing the car s mass and inertia), the car s initial velocity after launch will decrease. 74 UNIT 2: MOTION AND FORCE IN ONE DIMENSION

6 INVESTIGATION 5.1: THE FIRST LAW: FORCE AND INERTIA B Setting up the experiment Set up the experiment exactly as directed in Part 1. It is important to have a level track, so use the level and adjust the feet as needed to get the track level. Students set up the experiment. Instruct students to stretch the rubber band a few times and show them how to position the rubber band to get good launches. Before you actually collect data, you will need to work on developing a consistent launch technique. Watch as I demonstrate. Do a few launches with emphasis on maintaining consistency in the deflection in the rubber band and the actual launch technique. Practice a few times until you feel confident about your method. The Energy Car should contain no marbles during your practice launches. Once you have a consistent technique then you should go forward with the experiment. Press the Go button and then launch the Energy Car. Students do the experiment. Let s talk about what the graph of your data suggests. What happened to the car s velocity as it moved along the track? It decreased. When we started this investigation, we established that a moving object continues to move unless some net force acts upon it. Did the car maintain its velocity all along the track or did it gradually decrease? The velocity should have decreased gradually. Why do you think the car s velocity decreased with time? Students may not readily identify the role of friction in slowing the car. Guide students in the discussion until they are able to see how the force of friction acts against the motion of the car along the track and causes it to slow down. Now think about the car before you started the experiment. Was it moving or at rest? The car was at rest. What net force initiated the car s change in motion from a position of rest? The rubber band initiates the motion. Imagine the car at rest once more, but this time when it is set into motion by the force of the rubber band, it moves along a frictionless track. How would the car s velocity be different from what you observed in the experiment? Without the force of friction acting to slow the car down as it moved along the track, the Energy Car would move at constant velocity indefinitely. Friction is discussed in greater detail in Lesson 6.2; but, this is a good opportunity to get students thinking about the different applications of the force of friction to humans daily lives. If time permits, have students generate a list of examples. B Setting up the experiment Sample answers: a. As the Energy Car moves along the track, the velocity is greatest right at the launch and then decreases over time. The car decelerates because the force of friction opposes its motion. The car would move at a constant velocity forever if all forces acting on it remained balanced, with no net force causing any changes in motion. b. At the start of the track, the rubber band supplies a net force to get the car moving. c. Friction is the outside force that changes the motion of the car after it is launched. 75

7 CHAPTER 5: NEWTON S LAWS: FORCE AND MOTION C Conducting the experiment and reporting back In the initial experiment, you observed how the velocity of the car changed once it was set in motion by the rubber band and rolled along the track. Let s go back to the hypothesis you stated in Part 1. Students review their hypotheses. In this part of the investigation, your goal is to design an experiment to test your hypothesis. One key word in your hypothesis is inertia. When thinking about inertia, it is important to recall that inertia comes from an object s mass. Therefore, a change in inertia is accompanied by a change in mass. Do you have any materials that will allow you to change the mass of the car? Students should identify the presence of the steel marbles. Take a few moments to brainstorm with your group members and then devise your plan of action. Students develop a plan and share their experimental procedure. Allow students to execute their own plan, collect and analyze data, and summarize their findings before sharing your ideas. Here is a the dialogue to accompany the sample procedure mentioned in 3a (at right). You may do this as a demonstration if time or supplies are limited. Let s examine how motion is affected by changing mass. The force applied will remain constant. In my experiment, I will launch cars with four different masses. The first car will have no added mass. I will add one marble to the second car, two marbles to the third car, and then three marbles to the fourth car. Because mass is a factor in this experiment, I will record the mass of each car with or without marbles. This is where the data table comes in handy. Mass each car and say the measurement aloud as you record the data in the table. I have a consistent launch technique and I am using the same amount of force with each launch. Let s observe what happens to the velocity with each launch. Do the experiment with each car and have a student volunteer verify the data you collect and record in the table. Now we can analyze the graph of our data to better understand the results. How accurate were your hypotheses? Did your results confirm or refute your expectations? Students share findings. As the mass of the car increased, its velocity increased. In other words, the relationship between velocity and mass is inverse because as one variable increased the other decreased. C Conducting the experiment and reporting back a. Sample procedure: First, I set everything up just like I did in Part 2 of the investigation. Then, making sure I used the same launch force each time, I launched a car with no marbles, a car with 1 marble, then 2 marbles, and finally, 3 marbles. I recorded all data in the table below. b. Sample data table and graph: Table 1: Changing mass with constant force Mass of car Number of marbles added to car Velocity of car at launch (cm/s) (kg) The graph shows an inverse relationship. The greater the mass of the car, the lower the velocity. Speed (cm/s) Speed of the Car vs. Mass Mass of car (kg) c. My hypothesis was confirmed. Cars with greater inertia had less velocity at launch. Inertia resists changes in motion, and my results verify this first law of motion. 76 UNIT 2: MOTION AND FORCE IN ONE DIMENSION

8 INVESTIGATION 5.1: THE FIRST LAW: FORCE AND INERTIA D Reflecting on Newton s first law Newton s first law of motion is often called the law of inertia. Recall when you changed the mass of the car but kept the force constant. How can you explain your observations in terms of Newton s first law? Inertia comes from mass, and it is an object s resistance to a change in motion. The more massive the car, the more resistant it is to changing its motion. In the same manner, the least massive car would be the least resistant to changing its motion. Students can sometimes grasp this concept a little better when they are asked, Which is easier (or harder) to get moving: a very massive object or an object with a small mass? For example, is it easier to move a pebble or a boulder? The pebble, with its small mass does not offer much resistance to motion when a force is applied to it. However, if a person tried to move a boulder with the same amount of force applied to the pebble, the boulder would be much more resistant to motion. Consequently, the greater mass will experience slower speed because of this resistance, whereas the less massive object will experience faster speed. Place the Energy Car in the center of the track. The car should be at rest. Are any forces acting on the car? If so, identify the forces acting on the car. Since the car is at rest it is affected by the normal force and the force of the car s weight. Remind students that the if the car is at rest then the forces acting on it must be balanced. Otherwise, the car s motion would be changed in some way. What forces acted on the car as it moved along the track? Once the car was set in motion along the track, it encounter the force of friction. This explains why the car s velocity decreased over time. The car stopped when it reached the end of the track because it encountered a barrier. When considering Newton s first law, the car in motion remained in motion until it was acted upon by net forces of friction and the track s end. Suppose you altered the setup of the investigation so the track inclined upward or had a lightly downward tilt. How would the forces acting on the car and its motion be affected by these changes? Have students lead the discussion here. Students should consider the impact of friction and gravity here. If time permits, allow students to design an experiment to test their predictions. Direct students to use relevant vocabulary and to apply what they know about Newton s first law to explain their observations. Based on what you have observed in today s investigation, would you say that force causes velocity, or that force causes a change in velocity? Force causes a change in velocity, or acceleration. Remind students that acceleration is the change in velocity that occurs over a period of time and that acceleration may be positive or negative. This is a great lead in to discussion about Newton s second law, which is the topic of Lesson 5.2. D Reflecting on Newton s first law a. An object at rest remains at rest, and an object in motion remains in motion, unless acted upon by an unbalanced (net) force. b. The forces acting on the Energy Car when it is at rest are balanced. The weight of the car acts downward, and the normal force of the track acts upward. The forces are equal and opposite. c. If there are no unbalanced forces acting on the moving car, its velocity remains constant. I noticed that the car moved at a pretty constant speed for awhile on the track, but friction did slow it down a little. d. As the Energy Car rolled along the level track, friction provided a net force that opposed the forward motion of the car. Newton s first law applied, because an object in motion, like the moving car, would remain in motion, at a constant velocity, if it weren t for the outsides force of friction, and the end of the track. e. If the track is tilted slightly up, gravity and friction will oppose the motion of the car, and the car will decelerate more than when the track is flat. If the track is tilted slightly downward, gravity works with the car, and friction opposes the car. If you tilt the track downward just enough so that the help from gravity offsets the opposition from friction, you can create a balanced force that would allow the car to move at a very constant speed the whole way down the track. 77

9 CHAPTER 5: NEWTON S LAWS: FORCE AND MOTION Investigation 5.2: The Second Law: Force, Mass, and Acceleration It takes force to get an object moving and more force to make it stop. If you think about the words get moving or stop, you realize that force is linked to acceleration because both phrases imply changes in motion. Students will construct an Atwood s machine and use it to explore the relationship between force, mass, and acceleration. Key Question What is the relationship between force, mass, and acceleration? Objectives Students will: Measure the acceleration for an Atwood s machine of fixed total mass. Create a graph of force versus acceleration for the Atwood s machine. Determine the slope and y-intercept of the graph and then relate them to Newton s second law. Newton s second law - states that the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. newton (N) - the SI, or metric unit of force. net force - the amount of force that overcomes an opposing force to cause motion. The net force can be zero if the opposing forces are equal. line of best fit - a line drawn to show how two variables are related. A line of best fit comes closest to most points on a x-y scatterplot. mass - a measure of an object s inertia; the amount of matter an object has. Setup 1. One class period is needed to complete the investigation. 2. Students work in small groups of two to three. 3. Students should be familiar with the concept of acceleration as discussed in previous investigations. 4. Secure sponges or some other small cushions that can be used to protect the Physics Stand base from the impact of falling masses (Part 2). Each group will need one sponge or cushion. Materials Each group should have the following: Physics Stand Double pulley Red safety string Mass hangers (2) Electronic scale or triple beam balance Data Collector Steel washers (18) Plastic washers (6) Measuring tape Photogate Safety Students should observe general laboratory safety procedures while completing Investigation UNIT 2: MOTION AND FORCE IN ONE DIMENSION

10 INVESTIGATION 5.2: THE SECOND LAW: FORCE, MASS, AND ACCELERATION The Second Law: Force, Mass, and Acceleration Investigation The Second Law: Force, Mass, and Acceleration What is the relationship between force, mass, and acceleration? British scientist George Atwood ( ) used two masses on a light string running over a pulley to investigate the effect of gravity. You will build a similar device, aptly called an Atwood s machine, to explore the relationship between force, mass, and acceleration. In this investigation, you will: measure the acceleration for an Atwood s machine of fixed total mass. create a graph of force vs. acceleration for the Atwood s machine. determine the slope and y-intercept of your graph, and relate them to Newton s second law. A Analyzing the Atwood s machine To accelerate a mass, you need a net force. Newton s second law shows the relationship between force, mass, and acceleration: NEWTON S SECOND LAW Force (N) F = ma Mass (kg) Acceleration (m/s 2 ) The Atwood s machine is driven by an external force equal in magnitude to the weight difference between the two mass hangers. You will vary the two masses, m 1 and m 2, but you will keep the total mass constant. As you move plastic washers from m 2 to m 1, you will use a photogate to measure the acceleration of the system. If you know the acceleration and the total mass of the system, you will be able to calculate the force that is responsible for accelerating the system. The equation for the system s motion is a variation of the basic second law formula: F ext (m 1+ m 2)a An ideal pulley would be frictionless and massless, and would just redirect the one-dimensional motion of the string and attached masses, without interfering with the motion. However, the pulley you will use has mass and there will be some friction involved. For the purpose of this investigation, we will neglect the mass of the pulley, but we will be able to analyze the friction involved with our Atwood s machine. To represent the friction present in the system, you must subtract it from the external force, since the friction opposes the external force. F friction (m + m )a ext 1 2 It is easiest to move the friction force (f) to the other side of the equation, so you get: F (m + m )a + f ext 1 2 Materials List Physics stand Double pulley Red safety string 2 mass hangers Steel washers Plastic washers Measuring tape Photogate DataCollector 29 Investigation 5.2 The Second Law: Force, Mass, and Acceleration B Setting up the Atwood s machine 1. Set up the Atwood s machine as shown in the photo at right. Attach the double pulley to the top of the physics stand. You will only use the striped pulley. 2. Attach the mass hangers to the red safety string. Place 8 steel washers and 6 plastic washers on one mass hanger. This will be m 2. Place 10 steel washers on the other mass hanger. This will be m 1. Place the string over the dynamic pulley. 3. Pull m 2 down to the stand base. Place a sponge or some other small cushion on the base to protect it from the falling m 1. Let go of m 2 and observe the motion of the Atwood s machine. a. Which mass moves downward, and why? b. What would happen if m 1 and m 2 were equal masses? Why? c. Do the masses accelerate when they move? Explain. d. How does the acceleration of m 1 compare to the acceleration of m 2? e. The machine s external force equals the weight difference of the mass hangers. Write a simple formula that will allow you to use the mass difference and g, the acceleration due to gravity, to calculate the weight difference of the mass hangers (the external force). C Collecting data 1. Find the total mass of m 1 and m 2 and record in Table Attach a photogate to the double pulley as shown at right. Plug the photogate into the DataCollector (input A). The striped pattern on the pulley will break the light beam of the photogate as the pulley rotates. 3. Turn on the DataCollector. At the home window, select data collection mode. 4. At the Go window, tap on the setup option at the bottom of the screen. 5. In the setup window, choose standard mode. 6. For photogate A (PG A ), select acceleration in m/s 2. Set the PG B option to none. 7. Pull m 2 to the base. Tap Go at the bottom of the setup window. 8. When the experiment has started, release m 2. When the hanger falls onto the cushion, press the button on the DataCollector enclosure to stop the experiment. 9. Select the table and/or graph option at the bottom of the screen, and study the acceleration data. The acceleration should be constant. Record the acceleration in Table 1. Calculate the net force (see your answer to 2e) and record it in Table Transfer one of the plastic washers from m 2 to m Press the button on the DataCollector enclosure to resume data collection. Repeat steps 7-10 until you have transferred all of the plastic washers to m 1. D Analyzing the data The Second Law: Force, Mass, and Acceleration Investigation 5.2 Table 1: Acceleration and force data Acceleration (m/s 2 ) a. Make a graph of net force vs. acceleration (force on the y-axis and acceleration on the x-axis). Draw a best-fit line through the data points. b. What kind of relationship does the graph show? Is this consistent with Newton s second law? Explain. c. Determine the slope of your line. What is the significance of the slope in your experiment? d. Compare your slope and the known total mass of the system. What is the percent difference? What could account for any difference? e. Determine the y-intercept of your line. The equation for a line is y = mx + b (m is the slope and b is the y-intercept). Substitute your variables in for y, m, and x. Compare this equation to the one presented in part 1: F (m + m )a + f ext 1 2 Calculated net force (N) f. Based on your answer to the previous question (4f), what does the y-intercept represent? Does this value make sense? Explain

11 CHAPTER 5: NEWTON S LAWS: FORCE AND MOTION Teaching Investigation 5.2 A Analyzing the Atwood s machine Newton s second law is one of the most useful relationships in all of physics. The second law tells you how an object s motion will change if you know its mass and the forces acting on it. The second law also tells you how much force you need to apply to an object to create a specific change in its motion. Today s investigation will use a clever device called an Atwood s machine to explore an application of the second law. An Atwood s machine is a pulley with a string over it. Each end of the string has a different mass attached. When you let the string go, one mass rises and the other mass falls. Set up an Atwood s machine with the pulley in front of the class and demonstrate. Why does one mass rise while the other mass falls? Start a discussion. The system is not in equilibrium because one mass is larger than the other and therefore there is a net force acting. Recall from Investigation 5.1 that we talked about how force causes a change in velocity over time. This change is acceleration. In order to accelerate a mass, there must be a net force. So when you look at the form of Newton second law shown in Part 1, the F in the equation is really the net force. Use the Newton s second law teaching illustration to reinforce this point. The Atwood s machine is driven by an external force, F ext that is equal in magnitude to the weight different between the two mass hangers. Although you will vary the two masses, which we will call m 1 and m 2, the total mass will remain constant. As you move the plastic washers from m 2 to m 1, you will use a photogate to measure the acceleration. You can use the acceleration and the known mass to calculate the force that caused the system to accelerate. Prepare a model setup that you can use as a visual aid to the discussion. It will also come in handy in Part 2 as students setup their own Atwood s machine. Write the equation on the board (as shown in Part 1). Point to each variable as you describe its relationship to what students will do in the investigation. A perfect pulley would be massless, have no friction, and it would simply redirect the onedimensional motion of the string and the attached masses without affecting the motion. However, the effects of mass and friction will be a factor in the pulley you will use. You will neglect the mass of the pulley, but you will be able to analyze the effects of friction. Let s look at how you will do this. Reproduce the equations shown in Part 1 on the board. Show students how the equation can be manipulated to include the effects of friction. A Analyzing the Atwood s machine There are no questions to answer in Part 1. A challenge Many devices use acceleration to measure the mass of an object. Often the technique used is to cause something to vibrate. A vibration is a rapid back-andforth motion that results in similarly rapid acceleration. If the mass of an object changes, its acceleration changes and the frequency of vibration changes. Electronic devices can easily be made that are very responsive to small changes in frequency. As a result, this technique is used to measure very small amounts of mass quickly, such as the mass of a single drop of water. Challenge students to measure the mass of a single steel washer by making acceleration measurements. To do this they will first have to calibrate the apparatus for the effects of friction. This means measuring the acceleration for a known mass of washers on both sides of the pulley. Once the system is calibrated, a single washer added to one of the hangers will result in a measurable change in acceleration. The change in acceleration can be used to determine the mass. The sensitivity of the technique depends on the accuracy with which acceleration can be measured. Two factors are important: the repeatability of triggering the stopwatch with a finger, and the resolution of the stopwatch (0.01 s). Have the students measure the repeatability of their timing measurements. If the timing is repeatable to within 5 percent, then the acceleration may also be accurate to 5 percent if there are no other significant sources of error. To determine the effect of limited time resolution, have the students estimate the difference in acceleration that would result from a time measurement being +/- 0.1 second from its nominal value. 80 UNIT 2: MOTION AND FORCE IN ONE DIMENSION

12 INVESTIGATION 5.2: THE SECOND LAW: FORCE, MASS, AND ACCELERATION B Setting up the Atwood s machine Follow steps 1 and 2 exactly as stated in Part 2 to set up the Atwood s machine. Place the model setup you prepared earlier in a very visible location. Modify it to the specifications discussed in Part 2 as students prepare their own version. Be prepared to assist students with the setup. Pull the m 2 mass down to the base of the Physics Stand. Place your sponge on the base to protect it from the impact of the falling m 1. Let go of m 2. What happens? Students share observations. Suppose the masses m 1 and m 2 were equal. How might this change what you observed? The difference in masses caused an unbalanced force and was responsible for the motion students observed. If the masses are equal, then the forces are balanced. Balanced forces mean there is a net force of zero and the objects remain in place. In previous discussions about acceleration, we established that a net force causes a change in motion. Consider the motion of the masses. Do the masses accelerate when they move? The masses do accelerate. Remind students that acceleration is defined as the change in velocity over time. This change in motion is caused by the net force. Acceleration is caused by unbalanced force. According to Newton s second law, the acceleration of an object is equal to the net force acting on the object divided by the mass of the object. In fact, the metric definition of force is based on mass and acceleration. A force of 1 newton is exactly the force required to create an acceleration of 1 meter per second squared for a 1 kilogram object. Write the definition of force on the board: 1 N = 1 kg-m/s 2, or F = ma. Point out that this is a different, but equivalent arrangement of the same relationship, a = F m. Acceleration may be positive or negative. This is because acceleration is a vector quantity that considers both the magnitude and direction of motion. Did both masses accelerate in the same way? The masses had equal magnitude but accelerated in opposite directions. The external force of the Atwood s machine is equal to the weight difference of the mass hangers. Newton s second law is represented as F net = ma. How do you think you can use Newton s second law to calculate the weight difference of the mass hangers? Walk students through the explanation if needed. The weight difference of the mass hangers implies subtraction, so students should substitute (m 1 -m 2 ) for m. The acceleration due to gravity is defined as g and should replace the variable a in the equation. Therefore, the external force should be expressed as F net = (m 1 -m 2 )g. B Setting up the Atwood s machine a. The m 1 mass hanger has more mass than m 2, resulting in an unbalanced force. The external force is in the downward direction on the more massive side of the machine, which is the m 1 side. b. If m 1 and m 2 were equal masses, the Atwood s machine would be in equilibrium, and there would be no motion. c. Yes, the masses accelerate, because there is a net force created by the difference between the two masses. d. The accelerations are equal in magnitude and opposite in direction. e. Formula: C Collecting data Sample data: Table 1: Acceleration and force data Acceleration (m/s 2 ) Force net = ma Force = (m -m ) g net 1 2 Calculated force (N)

13 CHAPTER 5: NEWTON S LAWS: FORCE AND MOTION C Collecting data In Part 3, you will use a photogate attached to the double pulley to collect force and acceleration data. Keep everything else from the setup you used in Part 2 the same. First you need to determine the total of masses 1 and 2. Write this measurement down on your handout or in your notebook. Then attach the photogate to the double pulley and use a knob to secure everything in place. Students set up the equipment. Plug the photogate into Input A on the backside of the Data Collector. With the Data Collector in Data Collection mode, select the setup option and choose standard mode. You are only using one photogate A which is denoted as PG A. Set the PG B option to none. You want to measure acceleration in meters per second squared. Students should still have the sponge in place to cushion the falling mass. One person in your group should pull the mass, m 2 to the base of the stand. Lightly tap the Go button and then release m 2. When the hanger falls onto the sponge, stop the experiment. Demonstrate the process if needed. Review the acceleration data you collected. What do you observe? Write the value from the Data Collector in your notebook. Students should observe constant acceleration data. In Part 2e, you figured out a way to determine the force if mass and acceleration data is known. Use the formula and the mass and acceleration data you recorded to calculate the net force. Now you will consider how changes in mass, caused by moving the plastic washers from m 2 to m 1 one at a time changes your observations of force and acceleration. Start by transferring the first plastic washer from m 2 to m 1. Resume data collection and then repeat the steps you took (steps 7 10) until the six plastic washers have been transferred over. D Analyzing the data Use the data you recorded in Table 1 to make a force versus acceleration graph. Does your graph coincide with Newton s second law? Student graphs should show that force and acceleration are directly proportional. This is in line with Newton s second law. Draw students attention to Table 5.1 on page 105 of the text which shows three forms of Newton s second law. Focus on the third row to emphasize how to find the mass of an object if acceleration and force are known. The graphs generated from the experiment should reflect that the slope of the line is equal to the mass of the system. D Analyzing the data a. Sample graph: b. The graph shows a direct relationship between force and acceleration, just as Newton s law states. c. The slope of the line is d. Force divided by acceleration equals the mass of the system. In my experiment, the total mass was kg. Rise over run is force over acceleration. According to Newton s second law, force divided by acceleration equals mass. The slope of the line equals the mass of the system. The percent difference is 20%. I was not careful with acceleration measurements! e. The y-intercept of the line is The equation is: y = mx+ b force = mass( acceleration) + friction force f = ma+ f f. The y-intercept represents the force of friction. I know there is some friction in the system, but it is so small that it doesn t show up in the data we collected. Friction is truly negligible in this Atwood s machine. 82 UNIT 2: MOTION AND FORCE IN ONE DIMENSION

14 INVESTIGATION 5.3: NEWTON S THIRD LAW: ACTION AND REACTION Investigation 5.3: Newton s Third Law: Action and Reaction Newton s third law deals with action-reaction pairs. We rely on this law when we walk, place an item on a table, push a shopping cart, or travel in a car. Examples and demonstrations of Newton s third law are everywhere in our lives yet the subtle way it affects us can often be overlooked without careful analysis of what is actually taking place. For example, when you apply a force to throw a ball, you also feel the force of the ball against your hand. This is because all forces exist in pairs called action and reaction. There can never be a single force (action) without its opposite (reaction) partner. Action and reaction forces always act in opposite directions on two different objects. In this investigation students use the Energy Cars to study Newton s third law. Key Question What happens when equal and opposite forces act on a pair of Energy Cars? force - any action on a body that causes it to change motion. Force is a vector and always has a magnitude and a direction. Newton s third law - states that whenever one object exerts a force on another, the second object exerts an equal and opposite force on the first. action, reaction - the equal and opposite forces which comprise the action-reaction pair according to Newton s third law. Objectives Link two Energy Cars to create an action/reaction force pair. Use different numbers of marbles in each car to see how motion is affected. Relate the cars motion to Newton s third law. Setup 1. One class period is needed to complete the investigation. 2. Students work in small groups of two to three. 3. It is important that the track remains level throughout the experiment. Prepare a setup in advance so you will be able to demonstrate proper procedure in Part 1. Materials Each group should have the following: SmartTrack 2 Energy Cars (one blue, one orange) Energy Car link Steel marbles Rubber band Track feet (2) Bubble level Velocity sensor Data Collector Safety goggles Safety Students should wear safety goggles for the duration of the investigation. This is necessary to protect eyes from the car-connector accessory, as it may fly off. 83

15 CHAPTER 5: NEWTON S LAWS: FORCE AND MOTION Investigation 5.3 Newton s Third Law: Action and Reaction 5.3 Newton s Third Law: Action and Reaction What happens when equal and opposite forces act on a pair of Energy Cars? When you apply a force to throw a ball you also feel the force of the ball against your hand. That is because all forces come in pairs called action and reaction. Newton s third law of motion states that there can never be a single force (action) without its opposite (reaction) partner. Action and reaction forces always act in opposite directions on two different objects. You can set up two Energy Cars to study Newton s third law. In this investigation, you will: link two Energy Cars to create an action/reaction force pair. use different numbers of marbles in each car to see how motion is affected. relate the cars motion to Newton s third law. A 32 Setting up and action/reaction force pair Materials List SmartTrack 2 Energy Cars (blue and orange) Energy Car link Steel marbles Rubber band Track feet (2) Bubble level Velocity sensor DataCollector 1. Attach a foot to each end of the Smart track so it sits level on the table. Check it with the bubble level and adjust the feet as necessary to make the track level. 2. Attach the velocity sensor to the end of the Smart track. 3. Place one steel marble in each car, and wrap one car with a rubber band. 4. Place the 2 cars, nose to notch in the middle of the track. 5. Squeeze the cars together and attach them with the car link. 6. Position the attached car pair in the middle of the track so the blue car is closest to the velocity sensor. Make sure all 4 wheels of both cars are on the track. 7. With a very quick upward motion, pull the link straight up and out from the cars. CAUTION: Wear eyeglasses or safety glasses to avoid injury. a. Describe how the cars move when you remove the car link. b. How does Newton s third law of motion explain the motion of the cars when you remove the car link? c. You will use different numbers of marbles in each car to see how that affects the cars motion. Write a hypothesis to address the question What happens when equal and opposite forces act on objects that have different masses? Your hypothesis should follow this format: If equal and opposite forces act on objects of different masses, then. Finish the statement to create your hypothesis. B C Collecting data Newton s Third Law: Action and Reaction Investigation Place one steel marble in each car, and wrap one car with a rubber band. 2. Place the 2 cars, nose to notch in the middle of the track. 3. Squeeze the cars together and attach them with the Energy Car link. 4. Position the attached car pair in the middle of the track so the blue car is closest to the velocity sensor. Make sure all 4 wheels of both cars are on the track. 5. Plug the velocity sensor into input 1 on the DataCollector. 6. Turn the DataCollector on. At the home window, select data collection mode. 7. At the Go window, choose setup at the bottom of the screen. 8. At the setup window, choose standard mode, 200 samples, and 0.02 Hz. This will allow the DataCollector to collect 50 samples of data from the velocity sensor each second. 9. Press Go on the DataCollector. 10. With a very quick upward motion, pull the link straight up and out from the cars. CAUTION: Wear eyeglasses or safety glasses to avoid injury. 11. When the cars stop moving, press the button on the DataCollector enclosure to stop the experiment. 12. Switch from meter to table and graph view to study your data. Go to setup to note the name of the experiment in case you want to go back and look at the data later. Record the maximum velocity of the blue car in Table 1. You can only record the blue car s data, because it was the car the motion detector could see. 13. Attach the cars with the energy link again, and position them so the orange car is closest to the velocity sensor. Each car should still have one marble. Set up a new experiment on the DataCollector and repeat steps Change the marble configuration as listed in Table 1 and repeat the experiment. Continue until you have completed Table 1. For each trial, you will have to collect two sets of data one with the blue car facing the velocity sensor, and one with the orange car facing the velocity sensor. Table 1: Action/reaction pair data Trial Marble pairings for connected cars Maximum Velocity (cm/s) Experiment file name Blue Orange Blue Orange Blue Orange 1 1 marble 1 marble 2 0 marbles 2 marbles 3 2 marbles 2 marbles 4 0 marbles 3 marbles Analyzing the data a. How does the velocity of each car compare when masses are equal? b. How does the velocity of each car compare when one car has 2 or 3 times the mass of the other car? c. Explain how your velocity data supports the idea that equal and opposite action and reaction forces acted on the once-linked car pairs. Investigation 5.3 Newton s Third Law: Action and Reaction d. If the action/reaction forces are equal in strength when the cars separate, why does one car move at a different velocity than the other car when the masses are unequal, as in trials 2 and 4? e. Which of Newton s laws of motion best explains the answer to the previous question (3d)? f. Compare and contrast the velocity/time graphs for the blue car from trial 1 and trial 3. g. Compare and contrast the velocity/time graphs for the orange car from trial 2 and trial 3. h. What is one common characteristic from all of the velocity/time graphs for each car at every trial? Explain why this characteristic is true about all of the motion scenarios. D Why don t equal and opposite forces cancel each other out? It is easy to get confused about action-reaction forces. People often ask, Why don t they cancel each other out? The reason is that the action and reaction forces act on different objects. Prove that action-reaction forces never act on the same object by doing the following: a. Create a sketch showing your calculator sitting on top of your textbook which is sitting on top of your desk which is standing on the tile floor. b. Identify the forces that serve as the action-reaction forces and draw them in your sketch. c. Now draw a free body diagram that shows each object by itself (the calculator, the textbook, the table, the tile floor, and Earth) and uses arrows to represent the forces acting on each particular object. d. Look at the forces on any one object. Does that one object have both forces from any single actionreaction pair acting on it? Is this true for all of the objects? (This is the key to Newton s third law: The action-reaction forces are equal in size and opposite in direction but since they act on different objects, they do not cancel each other out.) UNIT 2: MOTION AND FORCE IN ONE DIMENSION

16 INVESTIGATION 5.3: NEWTON S THIRD LAW: ACTION AND REACTION Teaching Investigation 5.3 Newton s first and second laws of motion deal with single objects and the motion that results from forces that act on them. Newton s third law of motion pertains to pairs of objects and the interactions between them. The important thing to remember about Newton s third law is that it always applies to two objects. In fact, an isolated force can never be created without its twin. If I throw this eraser, I apply a force to it. Call that the action force. I feel the eraser against my hand, resisting my action force through its inertia. That means the eraser exerts a force back against my hand, which is what I feel. This is the reaction force. The action is me acting on the eraser. The reaction is the eraser acting back against my hand. Suppose Joe is pulling a heavy wagon. What is the action-reaction pair in this scenario? Joe exerts a force on the wagon, and the wagon exerts an equal and opposite force on Joe. He feels the handle of the wagon against his hand, that is the reaction force. It is obvious that Joe exerts a force on the wagon, but why is it true that the wagon exerts an equal and opposite force on Joe? It is one of the rules of the universe. If object A exerts a force on object B, object B exerts an equal and opposite force on object A. The pair of forces occur in unison as part of an interaction. Which one we call the action and which one we define as the reaction makes no difference. Practically speaking, you know that the wagon must exert a force on Joe, because imagine how it feels on your arm to pull a heavy wagon. It sometimes feels as though the wagon is pulling on you, and it is, because it is automatically part of a force pair that is created as soon as you grab the handle and start pulling. A Setting up an action/reaction force pair Set up the SmartTrack with a foot attached to each end. Use the bubble level to set the track level. A level track is essential to this experiment. Emphasize this fact to students. Attach the velocity sensor to the end of the SmartTrack. Place one steel marble in each car, and wrap the blue car with a thick rubber band as shown in Part 1. Place the cars nose to notch, squeeze the cars together, and then attach them with the car-connector. Center the attached car pair on the track, with the blue car closer to the velocity sensor. Make sure all four wheels of both cars are on the track. A Setting up an action/reaction force pair Sample answers: a. When you remove the car link, the cars move apart, in opposite directions. b. The compressed rubber band applies a force to the cars when they are unlinked; the force exerted on the blue car is equal and opposite to the force exerted on the orange car. c. If equal and opposite forces act on objects of different mass, then the object with the most mass will experience less change in motion than the object with the least mass. In other words, the more massive car will take off with less velocity than the less massive car. Ensure that students are wearing their safety glasses before proceeding. With a very quick upward motion, pull the connector straight up and out from the cars. Use the prepared setup to demonstrate the procedure. Students should wear safety glasses to avoid injury from the flying connector. Students who wear prescription eyeglasses do not need to wear goggles over them. What happened when you removed the car connector? Students should observe that the cars moved away from the each other, in opposite directions. 85

17 CHAPTER 5: NEWTON S LAWS: FORCE AND MOTION Newton s third law states that whenever one object exerts a force on another, the second object exerts an equal and opposite force on the first. How can you use this statement to explain what you observed when the car connector was removed? Lead a brief discussion to describe what happened when the connector was removed. Use your students existing understanding of potential energy and what it means if something is elastic to describe the transfer of energy from the rubber band to the cars. In the next part of the investigation you will use different numbers of marbles in each car to test the effect on the motion of the cars. What do you think will happen when equal and opposite forces act on objects with different masses? Write a hypothesis to express your answer. Your hypothesis should be in the form of an if-then statement, as shown in Part 1c. Students make predictions. B Collecting data Let s move on from the prediction stage to actually testing your hypothesis. Repeat the setup from Part 1, but this time you will place one steel marble in each Energy Car. Have students verify that the track is still level. The cars should be connected nose to notch in the center of the track. The rubber band should be wrapped around the blue car, which is positioned closer to the velocity sensor. Plug the velocity sensor into Input 1 on the Data Collector and turn the Data Collector on. Place it in Data Collection mode. Setup the Data Collector as described in Part 2, steps 7 9. Ensure that students are wearing their safety glasses before proceeding. With a very quick upward motion, pull the connector straight up and out from the cars. When the cars are no longer moving, press the button on the Data Collector to stop the experiment. Go to the table and graph view to see the data you collected. You can obtain the name of the experiment if you go to the setup. Write it in Table 1 or in your notebook in case you need to go back to it later. Record only the blue car data because it was this car s motion that was detected by the velocity sensor. Students record data. You now need to collect data for the orange car with only one marble. Use the Energy Car connector to reattach the cars. This time place the orange car closer to the velocity sensor. Set up a new experiment on the Data Collector and repeat steps Students repeat this procedure for each of the marble pairings described in Table 1. C Analyzing the data Look at the data you recorded in Table 1. When the masses are equal how do the velocities of the cars compare? The velocities are nearly the same when the masses are equal. B Collecting data Sample data: C Trial Table 1: Action/reaction pair data Marble pairings for connected cars Analyzing the data Sample answers: a. When the masses are equal the velocities are very close. b. The car that has twice the mass has half the velocity. c. The forces were equal and opposite in all cases. The only case when the velocities were also equal was in the case of equal mass. d. With the same force on both objects, the object with more mass will have less of a change in motion. e. Newton s second law of motion. Maximum velocity (cm/s) Blue Orange Blue Orange 1 0 marbles 2 marbles marbles 0 marbles marbles 0 marbles marbles 2 marbles f. Both graphs show a very gradually decreasing velocity; the blue car velocity in trial 1 starts higher than the blue car velocity in trial 3. g. The graphs for the orange car in trial 2 and 3 are nearly identical, as would be expected. h. For each car at every trial, the velocity/time graph shows a gradually decreasing velocity. In all cases, friction opposes the motion of the car and it gradually slows down. 86 UNIT 2: MOTION AND FORCE IN ONE DIMENSION

18 INVESTIGATION 5.3: NEWTON S THIRD LAW: ACTION AND REACTION What happens to the velocity of each car when the mass of one car is doubled? The velocity is reduced by about half when the mass is doubled. Considering what you have already learned about the first and second laws, is this what you would have expected to happen? Students should recall that the mass of an object is inversely proportional to its velocity. You observed that the velocities of the car were the same or almost the same when the masses were equal. How does this observation explain the idea that the forces acting on the cars were equal and opposite? At equal masses, the cars experience similar motion (closely related velocities), but travel in opposite directions. This is an indication that the forces must be action-reaction (equal and opposite) forces. Action-reaction forces are equal in strength, but when the cars separate one car moves at a different velocity than the other when their masses are unequal. Why does this happen? When one car is twice as massive as another, its resistance to motion will be greater than the less massive car. Consequently, there will be differences in acceleration. Even though the forces are equal and opposite, the resulting motion (net force) will be different. Review the concept of net force and Newton s second law with students. How do the velocity versus time graphs compare in the different trials. Generate the graphs and then we can talk about what they tell us. Have different groups lead the discussions to compare and contrast the graphs. Direct them to tell whether their observations support what the graphs indicate about the motion of the cars. D Why don t equal and opposite forces cancel each other out? We have consistently stated that action/reaction pairs do not cancel each other out. Do you agree with this statement? Students share opinions. In this part of the investigation, we will draw a series of free body diagrams to prove this fact. A free body diagram is a sketch showing all the forces acting on an object. Let s begin with 4a. At this point in the study of Newton s third law, students may or may not be very comfortable with drawing action-reaction force pair diagrams. However, the visuals may enhance their understanding of what is meant by action/reaction. This activity will further drive home the key to Newton s third law: action-reaction forces are equal in size and opposite in direction, but since they act on different objects, they do not cancel each other out. Students will see this clearly when they study each object in their diagram. None of the objects have both members of any force pair acting on it. D Why don t equal and opposite forces cancel each other out? a. Sample sketch: b. See 4a. c. Free body diagram: d. None of the objects have both forces from actionreaction pairs acting on it. 87