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A TIME for Physics First www.physicsfirstmo.org PROFESSIONAL DEVELOPMENT CURRICULUM Draft – September 2008 Summer Academy 2006-08 University of Missouri-Columbia, Columbia, MO UNIT 4: NEWTON’S LAWS Primary writers: DORINA KOSZTIN and MEERA CHANDRASEKHAR Department of Physics and Astronomy, University of Missouri, Columbia, MO Funded by the Missouri Department of Elementary and Secondary Education Mathematics and Science Partnership High School Science Reform Grant A TIME for Physics First Unit 4 –Newton’s Laws Page 1 Acknowledgements: Curriculum 2005-08 Curriculum Writing: Meera Chandrasekhar, Department of Physics, University of Missouri, Columbia Gabriel de la Paz, Clayton High School, St. Louis, MO Dorina Kosztin, Department of Physics, University of Missouri, Columbia (MU) Dennis Nickelson, William Woods University, Fulton, MO Curriculum Analysis: GLE analysis: Matthew Brouk, Morgan County R-II Schools, Versailles, MO and Kathy Phillips, Science Education Consultant, Fairfax, VA Modeling analysis: Kandiah Manivannan, Department of Physics, Astronomy and Materials Science, Missouri State University, Springfield, and James Roble, John Burroughs High School, St. Louis High tech/low tech labs: Jack Richens, Christian Fellowship School, Columbia Math connections: James Tarr, Learning, Teaching and Curriculum, MU Overall: Sara Torres and Marsha Tyson, Columbia Public Schools 5E analysis: Mark Volkmann, Learning, Teaching and Curriculum, MU Notebooking connections: Laura Zinszer, West Junior High School, Columbia \ Timelines: Gabriel de la Paz, Clayton High School, St. Louis Unit Objectives Analysis: Linda Kralina and Nancy Iannotti, Coach Mentors Astronomy: Lanika Ruzhitskaya, School of Information Sciences and Learning Technologies, University of Missouri, Columbia, MO Teacher Feedback: Ryan McCoy, Francis Howell Central HS; Doug Steinhoff, Jefferson Jr. High; Amy Campbell, Hazelwood East HS; Jason Bradley, Webb City HS; Dale Orr, Winnetonka HS. Sources Include: Arizona State University Modeling materials: http://modeling.asu.edu/ Thinking Physics, Lewis Caroll Epstein, Insight Press, San Francisco, 1985 Five Easy Lessons, Randall D. Knight, Pearson Education, San Francisco, 2004 Exploring Physics, Meera Chandrasekhar, Rebecca Litherland & Jennifer Geib, 2001 Deborah Rice and Rex Rice, St. Louis, MO, Consultants, 2006 M. Schober’s website, http://www.jburroughs.org/science/mschober/physics.html CAPER (Conceptual Astronomy and Physics Education Research), Univ. of Arizona Summer Academy Instructors 2006-08 Faculty Instructors: Meera Chandrasekhar, University of Missouri, Columbia Dorina Kosztin, University of Missouri, Columbia Kandiah Manivannan, Missouri State University, Springfield Peer Teachers: Gabriel de la Paz, Clayton High School, St. Louis Dennis Nickelson, William Woods University, Fulton James Roble, John Burroughs High School, St. Louis Science Education Instructors: Mark Volkmann, University of Missouri, Columbia Sara Torres, Columbia Public Schools Mathematics Education Instructor: James Tarr, University of Missouri, Columbia Physics Teaching Assistants: David Arrant (2006-07), Nicholas Criswell (2007), Justin Riffle (2006-08), Chelsea Brzuchalski (2008), Mason Prashek (2008), Department of Physics and Astronomy, University of Missouri Astronomy Observatory Facilitators: Ralph Dumas, Randall Durk, Val Germann, and Lanika Ruzhitskaya, Central Missouri Astronomical Association A TIME for Physics First Unit 4 –Newton’s Laws Page 2 Table of Contents Unit 4 Big Ideas ............................................................................................. 4 Unit 4 Objectives ........................................................................................... 5 Student Misconceptions .................................................................................. 7 Sequence of Concepts .................................................................................. 10 Newton's Third Law Lab ................................................................................ 13 Newton’s Third Law with Force Probes Lab ...................................................... 14 Reading Page – Newton’s Third Law ............................................................... 23 4.1. Practice: Identifying Pairs of Forces I ..................................................... 26 4.2. Practice: Identifying Pairs of Forces II .................................................... 28 4.3. Practice: Forces, Acceleration and Collisions ........................................... 33 4.4. Practice: Newton’s Third Law with Blocks................................................ 35 4.5. Practice: Newton’s Third Law Problems .................................................. 37 What Does It Take to Move? – Lab ................................................................. 40 Acceleration, Mass and Force: Pre-Lab Exercise ............................................... 42 Acceleration, Mass and Force Lab ................................................................... 45 Reading Page – Newton’s Second Law ............................................................ 47 4.6. Practice: Force Diagrams, Motion Diagrams and Newton’s Second Law ...... 52 Upward and Downward Ride Lab .................................................................... 61 4.7. Practice: Elevator Problems .................................................................. 64 4.8. Practice: Newton’s Second Law and Motion ............................................. 65 APPENDIX ................................................................................................... 66 Materials List for Unit 4 Labs ......................................................................... 67 Sample Data for Unit 4 Labs .......................................................................... 68 Newton’s Third Law with Force Probes Lab.................................................... 68 Sample Worksheet for What Does It Take to Move? – Lab ................................. 70 Unit 4 - Newton’s Laws: GLE and Process Standards by Activity ......................... 72 Unit 4 Recommended Timeline....................................................................... 74 4.9. Practice: Vertical Acceleration ............................................................... 75 A TIME for Physics First Unit 4 –Newton’s Laws Page 3 Unit 4 Big Ideas 1. Net force is proportional to mass and acceleration. 2. Forces come in pairs. A TIME for Physics First Unit 4 –Newton’s Laws Page 4 Unit 4 Objectives Core Concept: Newton’s Laws Newton’s laws describe the connection between forces and motion, and the interaction between objects. Learning Goals: By the end of this unit, the students should know and be able to: 1. Compare the forces on two objects that are interacting (Newton’s Third Law). (DOK3) a. Identify the forces acting on an object. b. Identify the action and reaction forces in an interaction between objects. c. Identify the objects upon which a given pair of forces acts. d. Construct a separate force diagram for each object in an interacting pair, labeling each force with its type, agent and receiver. e. Label all Newton’s Third Law pairs that occur in given force diagrams. f. Predict the relationship between action-reaction forces for interacting objects and then test the predictions, using force probes. g. Draw the action-reaction pair of forces as equal in magnitude and in opposite direction (FAB = - FBA) 2. Design and conduct an experiment to explain the relationship between, force, mass and acceleration. (DOK4) a. Predict the relationship between force, mass, and acceleration. b. Investigate the relationship between force, mass, and acceleration, (using technology, e.g., motion detectors, force probes). c. Show that force is related to acceleration (but not velocity). d. Identify the system for a given problem in which Newton’s Second Law is applied. e. Show that the directions of net force and acceleration are the same. f. Plot and interpret a graph of force vs. acceleration, a graph of force vs. mass and a graph of mass vs. acceleration. g. Develop the mathematical relationship between force, mass, and acceleration. h. Determine the net force in situations where acceleration is known (Newton’s Second Law). 3. Analyze the forces acting on an object according to Newton’s Laws using multiple representations (i.e., motion diagrams, force diagrams, verbal descriptions, graphs, pictures, mathematical models, etc.). (DOK4) a. Draw force diagrams and motion diagrams of forces acting on objects. b. Give verbal description of force effects on objects. c. Draw a physical diagram from a verbal description of forces acting on an object. d. Determine algebraically the direction and strength of the net force acting on each object in an interacting pair. e. Contrast the paired forces when a large object and a small object interact. A TIME for Physics First Unit 4 –Newton’s Laws Page 5 f. Plot and interpret a graph of force vs. acceleration, a graph of force vs. mass and a graph of mass vs. acceleration. 4. Mathematically and graphically determine the force, mass and/or acceleration of an object. (DOK3) a. Determine the acceleration due to gravity from a force vs. mass graph. b. Resolve forces acting on interacting objects into their x- and ycomponents, then find the net (or resultant) force by taking the vector sum of the forces (by a graphical method). c. Solve quantitative problems involving forces, mass and acceleration using Newton’s Second Law, a = F/m. d. Determine the velocity or displacement of an object, given the net force and mass. 5. Analyze the motion of an object based on Newton’s Three Laws. (DOK4) a. Measure and analyze the forces that occur while riding in an elevator. b. Recognize that an accelerating object experiences a net force. c. Compare the forces involved when objects are stationary or moving at a constant speed. d. Compare and contrast the motion of two interacting objects, e.g., a small mass object interacting with a large mass object. e. Analyze applications of Newton’s Three Laws of Motion in everyday life. Learning Methods: The A TIME for Physics First classroom uses inquiry and modeling techniques and follows the 5E model to teach the curriculum. These methods are described in more detail in the documents*: 1. Conceptual Framework, Inquiry and Modeling of Physics First, by Mark Volkmann 2. A Modeling Method for High School Physics Instruction by Malcolm Wells, David Hestenes* & Gregg Swackhamer, Am. J. Phys. 63 (7), July 1995, 606-619. 3. Modeling Instruction in High School Physics by J. Mark Schober 4. Modeling Methodology for Physics Teachers by David Hestenes, Proceedings of the International Conference on Undergraduate Physics Education (College Park, August 1996). * included in the Resources folder of this CD A TIME for Physics First Unit 4 –Newton’s Laws Page 6 Student Misconceptions 1. Motion requires a force, or force causes motion or an object will slow down if there is no net force. Students hold the Aristotelian idea that an object's natural state is rest. Thus they believe that objects only move when a net force is exerted upon them. This stems from common everyday observations, e.g. students seeing that objects which have been pushed across the floor come to a stop (and not seeing friction as dissipative force acting on the object). 2. The motion will follow the path of the stronger force on the object. Rather than associating the direction of the net force with the direction of the acceleration, some students think that the object will accelerate in the direction of the force with the largest magnitude. 3. Passive forces don't exist (tables don't exert a normal force). Some students believe that inert objects cannot exert a force. They can alter an object's motion, but they don't exert a force. 4. Normal forces won't exceed the weight (active force) on an object. Many students hold that the normal force acting on an object is equal to the weight of the object, regardless of the physical situation. Thus the normal force has an upper (and lower) limit placed on it. 5. An object with a constant net force will have a constant speed. Some students believe that force is proportional to velocity. Thus if velocity isn't changing, the net force must be (a non-zero) constant. Furthermore, they associate an acceleration with an increasing force. 6. Faster moving objects have a larger force acting on them. Some students believe that force is proportional to velocity. Thus if velocity is larger, the net force must be larger. Furthermore, they associate acceleration with an increasing force. 7. A constant force accelerates a body, until the body uses up all the power of the force. From common everyday observations, e.g. students pushing on an object which is sliding across the floor, they find the force which will initially accelerate an object produces a constant velocity soon after (due to velocity dependent nature A TIME for Physics First Unit 4 –Newton’s Laws Page 7 of friction that we all ignore in F = N). Thus students conclude that the force has been used up by the body. 8. The net force must be in the direction of motion, so objects will travel along a line in that direction. Some students believe that force is proportional to velocity. Thus they assume that net force is in the same direction as velocity. Without seeing acceleration's role in changing the velocities' direction, they assume that the object will travel in a straight line. 9. Objects can be trained to follow a certain path by forces, and will continue along that path, even after the forces are removed. Some students believe that if an object repeats a motion, it will (inherently) learn that motion, and continue it regardless of changes in the forces acting on it. For example, a rock spun on a string is believed to continue on a curved path after the string is cut or released. 10. Heavier objects fall faster than light objects. Just like feathers fall more slowly than rocks, students believe that light objects simply fall slower than heavier objects. 11. Objects will point in the direction of their velocity. Like the trajectory of a football pass will have the point of the ball pointing in the direction of its velocity, students believe that objects will point in the direction of their velocity (regardless of the forces acting on them). The original motion of the object can define its "point" (which could be one side of a cube). 12. Force must be positive, plotted above the time axis. Many students have difficulty in associating the opposite direction with a change in sign. Some students will insist that forces, like their magnitudes, are always positive. 13. Strings transmit (unchanged) an external force acting on one object to another object. Some students believe that if two objects are tied together by a (continuously taught) string, while one object is pulled by an external force, the second object experiences a force equal in magnitude to the external force (regardless of its mass). A TIME for Physics First Unit 4 –Newton’s Laws Page 8 14. The tension in a string is the sum of the forces acting on each end. Students add the magnitudes of the each of the forces acting on strings/ropes and treat that as the tension in the string/rope. 15. The force of throw travels with the object Students believe that the force applied to a ball when throwing it travels with the ball (acts on the ball when the ball is airborne) until all the force is used up (impetus theory) A TIME for Physics First Unit 4 –Newton’s Laws Page 9 Sequence of Concepts 1: Newton’s Third Law Engage/Explore Framing Questions Activities: Newton’s Third Law Lab Develop a force law for two objects interacting with one another. Explain/Elaborate Activities: Newton’s Third Law with Force Probes Lab Investigate the similarities/differences between paired forces when a large and a small object interact Investigate the similarities/differences between paired forces when objects are stationary or moving at a constant speed Identifying action-reaction pairs Practice and Reading Pages (RP): Reading Page: Newton’s Third Law Evaluate Practice and Reading Pages (RP): 4.1 Practice: Identifying Pairs of Forces 4.2 Practice: Forces, Acceleration and Collisions 4.3 Practice: Newton’s Third Law with Blocks 4.4 Practice: Newton’s Third Law Problems 2: Newton’s Second Law Engage/Explore Activities: What does it take to move? – Lab Draws upon students’ prior knowledge of connections between force and motion; connects force diagrams and motion diagrams Makes students come to the qualitative conclusion that force is related to acceleration, not to velocity. A TIME for Physics First Unit 4 –Newton’s Laws Page 10 Explain Activities: Acceleration, Mass and Force – Pre-Lab Exercise Predictive exercise in finding the quantitative relationship between force, mass and acceleration. Acceleration, Mass and Force Lab Find the quantitative relationship between force, mass and acceleration. Identify the system for which Newton’s 2nd law is applied Understand the that the directions of force and acceleration are the same Understand the source of the constant of proportionality that connects force, mass and acceleration. Practice and Reading Pages (RP): Reading Page: Newton’s Second Law 4.5 Practice: Force Diagrams, Motion Diagrams and Newton’s Second Law Elaborate Upward and Downward Ride Lab Experience and analyze forces felt in an elevator. Recognize that acceleration influences the actual forces felt by an object Evaluate Practice and Reading Pages (RP): 4.6 Practice: Elevator Problems 4.7 Practice: Newton’s Second Law and Motion A TIME for Physics First Unit 4 –Newton’s Laws Page 11 Framing Questions 1. Ben and Ronda pull on opposite ends of a rope in a game of tug-of-war. Ben is stronger than Ronda. Who exerts the larger force on the rope? a) Ben b) Ronda c) both exert the same amount 2. Now assume that Ben and Ronda have the same mass. They stand 4 meters apart and attempt playing tug-of-war on frictionless ice. First they pull on opposite ends of the rope with equal force, and observe that each one slides 2 meters to a point midway between them. Next, they start 4 m apart, Ronda has the rope fastened around her waist and only Ben pulls. How far does each person slide? 3. True or false? If a net force of 20 N oriented toward North acts on an object, the object moves North. Explain your answer. 4. A mall sports car collides head on with a heavy truck. The greater force of impact acts on (a) the car, (b) the truck, (c) neither, the force is the same on both. 5. Which vehicle undergoes the greatest magnitude acceleration? (a) the car, (b) the truck, (c) neither, the accelerations are the same for both. 6. A weight lifter stands on a bathroom scale. He pumps a barbell up and down. What happens to the reading on the scale? Is it changing, or is it the same? Explain your answer. Now the weight lifter decides to throw the barbell into the air. How does the reading on the scale change? 7. When you are rowing a boat, the paddles are pushed backwards. Why is the boat moving forward? A TIME for Physics First Unit 4 –Newton’s Laws Page 12 Newton's Third Law Lab (low tech version) Purpose: Is there a force law for two interacting objects? This is the low tech version of the lab. 5E: Engage/Explore Concepts addressed: Students develop a force law for two objects interacting with Materials one another. Low-tech: a pair of spring scales (newtons) platform or two bathroom scales String Directions: 5. Ask students to predict what would happen if they hooked their spring scales to each other and pulled on them. Have them predict their scale readings. 6. Have them try it - both students pull on their scales; have them record the force on each scale. 7. Ask students to predict: What would happen if one student pulled, while the other holds firm? What if they reversed their roles, each time comparing the force that one person exerts to the force that the second person exerts? Have them record their predictions and explain their reasoning. After student groups have discussed their predictions and reasoning, have them try it out. Have them discuss their observations and reasoning. Ask students about the directions of the forces they apply. Have them express the forces felt/applied by both students in a mathematical expression. Ask the students to draw a physical diagram for each case, as well as a force diagram for each object. 8. Next, ask students to predict what would happen (what the scales will read) if they pushed two bathroom scales against one another. Then have them predict what would happen if (a) both push, (b) the first one pushes and (c) the second student pushes. White boarding and discussion is recommended at this point. A TIME for Physics First Unit 4 –Newton’s Laws Page 13 Newton’s Third Law with Force Probes Lab (high tech version of Newton’s Third Law Lab) Purpose: Is there a force law for two interacting objects? 5E: Explain/Elaborate Concepts addressed: - investigate the similarities/differences Materials: between paired forces when a large and a small object interact Station 1: Two force probes with rubber - investigate the similarities/differences stoppers on each end between paired forces when objects are Station 2: Two force probes with a stationary or moving at a constant rubber band connecting them speed Station 3: Two force probes with blocks - identifying action-reaction pairs being pushed - one small and one large Station 4: Two force probes with blocks being towed - one small and one large Station 5: Two carts with repelling magnetic bumpers on a track, with attached force probes Teacher notes: When you demonstrate how to use the force probes, show students only one probe at a time (so you don’t give the experiment away!). You will have to set the logger pro settings to “reverse direction” for one of the force probes. Force vs. time curves for this experiment will show that, regardless of which person pulls, the forces measured by the probes are equal and opposite (example shown below). White boarding and discussion (with one station per group) is recommended at this point. A TIME for Physics First Unit 4 –Newton’s Laws Page 14 Station 1: Rubber stopper on the end of each force probe You and your partner will each hold a force probe. First predict how the force student 1 exerts on student 2 will compare to the force student 2 will exert on student 1. Explain the reasoning behind each prediction. Then try the activity. After you have performed the experiment, sketch the graph of force vs. time shown on the computer. Plot the reading from force probe 1 in red, and force probe 2 in blue. Assume that the force experienced by student 1 is indicated in force probe 1. Your predictions can take the form of F12 > F21, F12 < F21, or F12 = F21 if you wish, or some other form. Include a force diagram for each of the students in each situation. 1. Student 1 pushes the stopper while student 2 passively holds the force probe Prediction: Force Diagrams: Result: 2. Student 2 pushes the stopper while student 1 passively holds the force probe Prediction: Force Diagrams: Result: 3. Both students push on each other Prediction: Force Diagrams: Result: A TIME for Physics First Unit 4 –Newton’s Laws Page 15 Station 2: Rubber band connecting the hook of each force probe You and your partner will each hold a force probe. First predict how the force student 1 exerts on student 2 will compare to the force student 2 will exert on student 1. Explain the reasoning behind each prediction. Then try the activity. After you have performed the experiment, sketch the graph of force vs. time shown on the computer. Plot the reading from force probe 1 in red, and force probe 2 in blue. Assume that the force experienced by student 1 is indicated in force probe 1. Your predictions can take the form of F12 > F21, F12 < F21, or F12 = F21 if you wish, or some other form. Include a force diagram for each of the students in each situation. 1. Student 1 pulls on the rubber band; student 2 passively holds his/her force probe Prediction: Force Diagrams: Result: 2. Student 2 pulls on the rubber band; student 1 passively holds his/her force probe Prediction: Force Diagrams: Result: 3. Both students pull on each other Prediction: Force Diagrams: Result: A TIME for Physics First Unit 4 –Newton’s Laws Page 16 Station 3: Cars Pushing each other You and your partner will each hold a force probe. One of the cars should be imagined to be in neutral with its engine off. The other car has its engine on and pushes on the first one. Your hand will be like the engine, pushing the car. The cars are simulated by wooden blocks. First predict how the force student 1 exerts on student 2 will compare to the force student 2 will exert on student 1. Explain the reasoning behind each prediction. Then try the activity. After you have performed the experiment, sketch the graph of force vs. time shown on the computer. Plot the reading from force probe 1 in red, and force probe 2 in blue. Assume that the force experienced by student 1 is indicated in force probe 1. Your predictions can take the form of F12 > F21, F12 < F21, or F12 = F21 if you wish, or some other form. Include a force diagram for each of the students. 1. Large car pushes small car at constant speed on a level road Prediction: Force Diagrams: Large car Small Car Force Diagrams: Large car Small Car Force Diagrams: Large car Small Car Result: 2. Small car pushes large car at constant speed on a level road Prediction: Result: 3. Small car pushes large car while speeding up Prediction: Result: A TIME for Physics First Unit 4 –Newton’s Laws Page 17 4. Small car pushes large car up a hill at constant speed (make a ramp) Prediction: Force Diagrams: Large car Small Car Force Diagrams: Large car Small Car Force Diagrams: Large car Small Car Result: 5. Large car pushes the small car up a hill at constant speed Prediction: Result: 6. Large car pushes small car down the hill at constant speed Prediction: Result: A TIME for Physics First Unit 4 –Newton’s Laws Page 18 Station 4: Cars Towing each other You and your partner will each hold a force probe. One of the cars should be imagined to be in neutral with its engine off. The other car has its engine on and pulls on the other one. Your hand will be like the engine, pulling the car. The cars are simulated by wooden blocks. First predict how the force student 1 exerts on student 2 will compare to the force student 2 will exert on student 1. Explain the reasoning behind each prediction. Then try the activity. After you have performed the experiment, sketch the graph of force vs. time shown on the computer. Plot the reading from force probe 1 in red, and force probe 2 in blue. Assume that the force experienced by student 1 is indicated in force probe 1. Your predictions can take the form of F 12 > F21, F12 < F21, or F12 = F21 if you wish, or some other form. Include a force diagram for each of the students. 1. Large car tows small car at constant speed on a level road Prediction: Force Diagrams: Large car Small Car Force Diagrams: Large car Small Car Force Diagrams: Large car Small Car Result: 2. Large car tows small car while speeding up Prediction: Result: 3. Small car tows large car while speeding up Prediction: Result: A TIME for Physics First Unit 4 –Newton’s Laws Page 19 4. Small car pulls large car up a hill at constant speed (make a ramp) Prediction: Force Diagrams: Large car Small Car Force Diagrams: Large car Small Car Force Diagrams: Large car Small Car Force Diagrams: Large car Small Car Result: 5. Large car tows small car up a hill at constant speed Prediction: Result: 6. Small car tows large car down the hill at constant speed Prediction: Result: 7. Large car tows small car down the hill at constant speed Prediction: Result: A TIME for Physics First Unit 4 –Newton’s Laws Page 20 Station 5: Carts colliding Two carts, of equal or different masses, will collide as described below. The magnetic bumpers will extend the time of collision. Be sure to keep the cars on the track. You and your partner will each hold a force probe. First predict how the force student 1 exerts on student 2 will compare to the force student 2 will exert on student 1. Explain the reasoning behind each prediction. Then try the activity. After you have performed the experiment, sketch the graph of force vs. time shown on the computer. Plot the reading from force probe 1 in red, and force probe 2 in blue. Assume that the force experienced by student 1 is indicated in force probe 1. Your predictions can take the form of F12 > F21, F12 < F21, or F12 = F21 if you wish, or some other form. Include a force diagram for each of the students in each situation. 1. Cart 1 collides with an identical cart which is initially at rest Prediction: Force Diagrams: Result: 2. Two identical carts with equal speeds have a head-on collision. Prediction: Force Diagrams: Result: 3. Slow cart collides with fast cart. Prediction: Force Diagrams: Result: A TIME for Physics First Unit 4 –Newton’s Laws Page 21 4. Large-mass cart collides with a small-mass cart which is initially at rest Prediction: Force Diagrams: Result: 5. Large-mass cart collides with small-mass cart that is initially at rest. Prediction: Force Diagrams: Result: 6. Large-mass cart collides with small-mass cart, both of which are moving toward each other with equal speeds. Prediction: Force Diagrams: Result: White boarding and discussions may continue at this point. Sample data for this lab can be found in the Appendix. A TIME for Physics First Unit 4 –Newton’s Laws Page 22 Reading Page – Newton’s Third Law What is the connection between forces acting on two objects interacting with each other? Let’s consider the simple interaction between a hammer and a nail. The hammer exerts a force on the nail as it drives it into the wall. At the same time, the nail exerts a force on the hammer. If you are not sure that it does, imagine hitting the nail with a banana or a glass hammer. It is the force of the nail on the banana that pokes holes into it or shatters the glass. Let’s look now at the picture on left: a mom is pulling on her son, trying to get him away from his computer. The mom interacts with her son, and her son interacts with the computer. We have already learned how to identify all the forces acting on the boy, or on the mom or on the computer. But how do we deal with objects that interact with each other, such as the mom and the boy, or the boy and the computer? Newton’s Third Law explains how two objects/systems interact with each other. Every time an object A pushes or pulls on an object B, object B pushes or pulls back on object A. When the mom pulls on the boy, the boy pulls back (and she feels this in her arms). The two objects, mom and boy, are interacting. An interaction is the mutual influence of two systems on each other. The boy and mom are also interacting with the ground/earth. Let’s analyze all forces acting on the boy: And now let’s analyze all forces acting on the mom: The pulling force applied by the mom on the boy is the action force, and the pulling force applied by boy on his mom’s arms is the reaction force. Although we name one force the action and the other force the reaction for convenience, these two forces occur simultaneously and one cannot strictly specify which one is the “action” and which one is the “reaction”. An action/reaction pair of forces exists as a pair, or A TIME for Physics First Unit 4 –Newton’s Laws Page 23 not at all. Also, paired action and reaction forces have (a) the same magnitude, (b) act in opposite directions and (c) act on different objects. But how about the rest of the forces acting on the boy and mom? Are they part of an action/reaction pair? Yes, all forces in the universe are part of action/reaction pairs – there are no forces that act alone. If you look only at the forces acting on the boy it may seem that these forces are isolated but that is because we have chosen our system to be one single object: the boy. All forces acting on the boy arise from his interaction with the environment (which is outside for the chosen system). To be able to identify all the action reaction forces we must consider the expanded system which consists of boy, his mom and the ground. Let’s now identify all the action reaction pairs that act in the system. In the diagram below the action reaction forces are connected through a dotted line. For each force applied on the boy, there is a force the boy applies to another object. The same holds true for the mom. All interaction forces between boy and mom, boy and ground, and mom and ground are contact forces. The exception is the weight applied by earth, which is a long range force. How do action reaction pairs work for long range forces? If you let a ball fall, it will move down toward the earth because the earth pulls on it with a force called weight, the action force. But does the ball pull on the earth? Is there a “reaction” force acting on the earth? Indeed there is. The ball also attracts the earth with the same amount of force – the weight of the object. Does the earth then fall toward the ball? Yes, it does. But since the earth is huge and the ball is A TIME for Physics First Unit 4 –Newton’s Laws Page 24 very small what one observes is a larger effect on the small ball. A similar effect occurs with two magnets: two magnets attract or repel each other through a long range force that can act at a distance. If you hold a magnet in each hand, you can feel the force acting on each magnet because long range forces come in pairs too. There is only one force in the boy + mom + ground diagram for which a force pair is not drawn: the friction force applied by the keyboard on the boy’s fingers. Is there no pair for this force? Yes, there is: the force with which the boy’s fingers act on the keyboard. We have not drawn the reaction for that force intentionally. Whenever we deal with Newton’s Third Law we must define the system of interacting object. In our case the system was boy + mom + ground/earth. The computer was an external object to our system and thus the force applied by the computer to the boy’s fingers is considered an external force. Newton’s Third Law states that: Every force occurs as one member of an action/reaction pair of forces. The two members of an action/reaction pair act on two different objects. The two members of an action/reaction pair point in opposite directions, and are equal in magnitude. Rules to follow when identifying action/reaction pairs: 1. Identify the objects that are systems of interest. Other objects whose motion you don’t care about are part of the environment. 2. Draw each object separately. Place them in the correct position relative to other objects. Don’t forget to include objects like the earth that may not be mentioned in the problem. 3. Identify every force. Draw the force vector on the object on which it acts. Label each with a subscripted label. The usual force symbols can be used. 4. Identify the action/reaction pairs. A force goes with a force. Connect the two force vectors of each action/reaction pair with a dotted line. When you’re done, there should be no unpaired forces. 5. Draw a free-body diagram for each object within the system. Include only the forces acting on the objects in your system, not forces that the objects in your system exert on other objects. Newton’s third law is one of the fundamental symmetry principles of the universe. Since we have no examples of it being violated in nature, it is a useful tool for analyzing situations which are somewhat counter-intuitive. For example, when a small truck collides head-on with a large truck, your intuition might tell you that the force on the small truck is larger. Not so! Both cars experience the same force. But why does the small car sustain much more damage than the truck? That has to do with Newton’s Second Law! A TIME for Physics First Unit 4 –Newton’s Laws Page 25 4.1. Practice: Identifying Pairs of Forces I Identify one pair of actionreaction forces acting on the objects in the pictures below: A. Draw a force diagram of all forces acting on each one of the objects interacting and write explicitly which forces make up a pair. Force from plate pushing up on cake = Force from cake pushing down on plate B. C. A TIME for Physics First Unit 4 –Newton’s Laws Page 26 D. E. F. G. A TIME for Physics First Unit 4 –Newton’s Laws Page 27 4.2. Practice: Identifying Pairs of Forces II Recommended: = class, whiteboard; = homework; = challenge problems For each of the following problems, draw a physical diagram; construct a separate force diagram for each object, labeling each force with its type, agent and receiver. Label any Newton’s 3rd law pairs that occur in your force diagrams. 1. One book lies on top of another book, which rests on a table. System: the two books. Physical Diagram Force Diagrams: Force Diagrams: 2. A person exerts an upward force of 40N to hold a sack of groceries. System: person’s hand and sack of groceries. Physical Diagram Force Diagrams: A TIME for Physics First Unit 4 –Newton’s Laws Force Diagrams: Page 28 3. A magnet is suspended from the ceiling by a string. A second magnet is held up by the first magnet. System: the two magnets (they don’t touch each other). Physical Diagram Force Diagrams: Force Diagrams: 4. (a) Eric holds a ball in his hand, and is in the process of throwing the ball upward. System: hand and ball. Physical Diagram Force Diagrams: Force Diagrams: (b) The ball just left Eric’s hand. System: ball and hand. Physical Diagram Force Diagrams: A TIME for Physics First Unit 4 –Newton’s Laws Force Diagrams: Page 29 (c) The ball is on its way down. System: ball and hand. Physical Diagram Force Diagrams: Force Diagrams: (d) The ball has just hit the ground, and is slowing down. System: ball and ground. Physical Diagram Force Diagrams: Force Diagrams: 5. You are pushing a box across a very rough floor with a constant speed. System: you and the box. Physical Diagram Force Diagrams: A TIME for Physics First Unit 4 –Newton’s Laws Force Diagrams: Page 30 6. You are sitting on a chair on the ground. Draw well-separated diagrams for your body, the chair and the whole earth. Show the relative sizes of the forces via the lengths of the force arrows. Physical Diagram Force Diagrams: Force Diagrams: Force Diagrams: 7. You are standing on the ground in a shed. You are pulling vertically downward on a string that is attached to the bottom of a block. The block is attached to the ceiling by a rope. Draw well-separated diagrams for your body, the string, the block, the rope, the shed and the earth. Physical Diagram Force Diagrams: Force Diagrams: Force Diagrams: Force Diagrams: Force Diagrams: Force Diagrams: A TIME for Physics First Unit 4 –Newton’s Laws Page 31 8. A mass of 250 g is hung from springs in the following configurations. What do you think the spring scales will read in each case? Each spring scale reads forces, not masses. Draw force diagrams and explain your reasoning. A. A TIME for Physics First B. C. Unit 4 –Newton’s Laws Page 32 4.3. Practice: Forces, Acceleration and Collisions Recommended: = class, whiteboard; = homework; = challenge problems 1. A large truck and a small car collide. For each situation below (1 and 2) choose one answer (A though G) that best describes the forces between the car and the truck. A. The truck exerts a greater amount of force on the car than the car exerts on the truck. B. The car exerts a greater amount of force on the truck than the truck exerts on the car. C. Neither exerts a force on the other; the car gets smashed simply because it is in the way of the truck. D. The truck exerts a force on the car but the car doesn't exert a force on the truck. E. The truck exerts the same amount of force on the car as the car exerts on the truck. F. Not enough information is given to pick one of the answers above. G. None of the answers above describes the situation correctly. Case 1: the truck is much heavier than the car. 1. They are both moving at the same speed when they collide. Which choice describes the forces?_______________ 2. The car is moving much faster than the heavier truck when they collide. Which choice describes the forces? _______________ 3. The truck is moving much faster than the car when they collide. Which choice describes the forces? _______________ 4. The car is standing still when the truck hits it. Which choice describes the forces? _______________ 5. The heavier truck is standing still when the car hits it. Which choice describes the forces? _______________ Case 2: the truck is a small pickup truck and has the same mass as the car. 1. They are both moving at the same speed when they collide. Which choice describes the forces? _______________ 2. The car is moving much faster than the truck when they collide. Which choice describes the forces? _______________ 3. The truck is moving much faster than the car when they collide. Which choice describes the forces? _______________ 4. The car is standing still when the truck hits it. Which choice describes the forces? _______________ 5. The truck is standing still when the car hits it. Which choice describes the forces? _______________ A TIME for Physics First Unit 4 –Newton’s Laws Page 33 2. A large truck breaks down and receives a push back to town from a small compact car. For each situation below (1 through 4) choose one of the choices A through F that correctly describes the forces between the car and the truck. A. The force of the car pushing against the truck is equal to that of the truck pushing back against the car. B. The force of the car pushing against the truck is less than that of the truck pushing back against the car. C. The force of the car pushing against the truck is greater than that of the truck pushing back against the car. D. The car's engine is running so it applies a force as it pushes against the truck, but the truck's engine isn't running so it can't push back with a force against the car. E. Neither the car nor the truck exerts any force on each other. The truck is pushed forward simply because it is in the way of the car. F. None of these descriptions is correct. 1. The car is pushing on the truck, but not hard enough to make the truck move. _______________ 2. The car, still pushing the truck, is speeding up to get to cruising speed. _______________ 3. The car, still pushing the truck, is at cruising speed and continues to travel at the same speed. _______________ 4. The car, still pushing the truck, is at cruising speed when the truck puts on its brakes and causes the car to slow down. _______________ 3. Farmer Brown hitches Old Dobbin to his wagon one day, then says, "OK, Old Dobbin, let's go!" Old Dobbin turns to Farmer Brown and says "Do you remember how Newton's Third Law says that every action force has an equal and opposite reaction force?,” says Old Dobbin. Ignoring Farmer Brown's impatience, he continues, "If the wagon's pull is always equal and opposite of my pull, then the net force will always be zero, so the wagon can never move! Since it is at rest, it must always remain at rest! Get over here and unhitch me, since I have just proven that Newton's Laws say that it is impossible for a horse to pull a wagon!" At this point, Farmer Brown throws up his hands in dismay and turns to you. "Please help me!" he says, "I really should have paid more attention in physics class! I know that Newton's Laws are correct, and I know that horses really can pull wagons.” Help Farmer Brown by drawing separate force diagrams for the wagon, the horse, and the horse and the cart together. Then explain in words the flaw in the horse’s reasoning. A TIME for Physics First Unit 4 –Newton’s Laws Page 34 4.4. Practice: Newton’s Third Law with Blocks Recommended: = class, whiteboard; = homework; = challenge problems For each of the situations below compare the forces exerted by the blocks on each other as they move on a table with some friction. Note: the 100 g block experiences twice as much frictional force as the 50 g block. For each of the problems A through F, select from the following choices: a) block A exerts a greater force b) block B exerts a greater force c) the forces are equal Also draw separate force diagrams for block A, for block B, and for a system that includes both blocks. A. B. A TIME for Physics First Unit 4 –Newton’s Laws Page 35 C. D. E. F. A TIME for Physics First Unit 4 –Newton’s Laws Page 36 4.5. Practice: Newton’s Third Law Problems Recommended: = class, whiteboard; = homework; = challenge problems 1. While driving down the road, an unfortunate butterfly strikes the windshield of your car. You are thinking: this is a case of Newton's third law of motion! The butterfly hit the car windshield and the car windshield hit the butterfly. Which of the two forces is greater: the force on the butterfly or the force on the car’s windshield? Explain. 2. Andy goes hunting for the first time. He has just learned Newton’s Third Law and is now ready to explain to his dad why the gun recoils when it is fired. He tells his dad that the recoil is the result of action-reaction force pairs. As the gases from the gunpowder explosion expand, the gun pushes the bullet forwards and the bullet pushes the gun backwards. His dad has two questions for Andy (and you must answer them): a) How are the forces that act on the gun and on the bullet related and why? b) Are the accelerations of the gun and the bullet the same? Explain your answer. 3. Wherever there is an action force, there must be a reaction force which A) always acts in the same direction. B) is slightly smaller in magnitude than the action force. C) is slightly larger in magnitude than the action force. D) is exactly equal in magnitude. 4. An archer shoots an arrow. Consider the action force to be exerted by the bowstring against the arrow. The reaction to this force is the A) combined weight of the arrow and bowstring. B) air resistance against the bow. C) friction of the ground against the archer's feet. D) grip of the archer's hand on the bow. E) arrow's push against the bowstring. 5. A player catches a ball. Consider the action force to be the impact force of the ball against the player's glove. The reaction to this force is the A) player's grip on the glove. B) force the glove exerts on the ball. C) friction of the ground against the player's shoes. D) muscular effort in the player's arms. E) none of these A TIME for Physics First Unit 4 –Newton’s Laws Page 37 6. A player hits a ball with a bat. The action force is the impact force of the bat against the ball. The reaction to this force is the A) air resistance on the ball. B) weight of the ball. C) force that the ball exerts on the bat. D) grip of the player's hand against the ball. E) weight of the bat. 7. A karate chop delivers a blow of 3000 N to a board that breaks. The force that acts on the hand during this event is A) zero. B) 1500 N. C) 3000 N. D) 6000 N. 8. Arnold Strongman and Suzie Small each pull very hard on opposite ends of a massless rope in a tug-of-war. The greater force on the rope is exerted by A) Arnold, of course. B) Suzie, surprisingly. C) both the same, interestingly enough. 9. An automobile and a small empty wagon traveling at the same speed collide head-on. The impact force is A) greater on the automobile. B) greater on the small empty wagon. C) the same for both. 10. A Mack truck and a Volkswagen traveling at the same speed have a head-on collision. The vehicle that undergoes the greatest change in velocity will be the A) Volkswagen car. B) Mack truck. C) same for both. 11. A 10.0 N force is pulling vertically up on the ring of spring scale that weighs 2.0 N. If an 8.0 N mass is attached to the bottom hook of the scale, the scale reading would be A) 0 N. B) 2.0 N. C) 8.0 N. D) 10.0 N E) 12.0 N A TIME for Physics First Unit 4 –Newton’s Laws Page 38 12. A horse exerts 500 N of force on a heavy wagon. The wagon pulls back on the horse with an equal force. A) The wagon still accelerates because these forces are not an action-reaction pair. B) The wagon still accelerates because there is an unbalanced force on the wagon. C) The wagon still accelerates because the horse pulls on the wagon a brief time before the wagon reacts. D) The wagon does not accelerate because these forces are equal and opposite. E) The wagon does not accelerate the wagon is not alive. A TIME for Physics First Unit 4 –Newton’s Laws Page 39 What Does It Take to Move? – Lab Purpose: What is the connection between force and motion–related factors such as time, displacement, velocity and acceleration? Materials: Cart and spring scale on low-friction floor Or large spring scale and a skateboard Or car, spring scale and track 5E: Engage/Explore Concepts addressed: - Draws upon students’ prior knowledge of connections between force and motion; connects force diagrams and motion diagrams - Makes students come to the qualitative conclusion that force is related to acceleration, not to velocity. Pre-lab discussion: In this activity, students will pull a cart (or car) with a spring scale, and note the connection between force and the motion as they tune specific factors. Students make several predictions and then try the experiments. Make sure that the prediction-trial steps are not short-circuited, and have students explain their reasoning at each step. Students are known to have strong preconceptions of the relationship between force and motion. Their ideas must be discussed in detail. Note: this lab can be used as a low tech version of the Newton’s second law lab. Directions: 1. Have students discuss and then predict the forces on a car(t) when it is stationary. Questioning strategies: What forces act on a cart that is sitting motionless on a frictionless surface? Draw a force diagram and a motion diagram. 2. Next, students predict what must happen to make the cart start moving. Questioning strategies: If you want to make the car(t) move, what must you do? Suppose you were to attach a spring scale to the cart and pull on it to make it move. What do you think the spring scale will read? Will the reading change once the cart is moving? Now try it. As the car(t) just begins to move, note what the spring scale does, and describe it. Draw a force diagram and a motion diagram. 3. Next, we want students to start the cart in motion, and keep it moving, with zero net force. Predict: Is this possible? Explain your reasoning. Now try it. Describe what happens. Draw a force diagram and a motion diagram. What conclusion can you draw about the connection between force and velocity? 4. In this step we want students to start the cart in motion, and keep it moving, but with a constant force of 2 N. First predict: What do you think the motion will look like? Explain your reasoning. Now try it. Describe what happens. Draw a force diagram, and a motion A TIME for Physics First Unit 4 –Newton’s Laws Page 40 diagram. What conclusion can you draw between force and acceleration? White boarding and discussion is recommended at this point. Post-lab discussion- Conclusions Questioning strategies: If an object is moving at a steady speed, what force must be exerted on it? What if it were moving at twice the speed? (Make sure that students’ answers are consistent with step 3.) If an object is accelerating, what can one conclude about the force on the object? (Make sure that students’ answers are consistent with step 4.) From students’ observations above, have them write four things they learned about how force is related to the motion factors of speed and acceleration. These statements should be clearly stated, with evidence from their lab. Have them return to these conclusions and add to them after the next lab. A TIME for Physics First Unit 4 –Newton’s Laws Page 41 Acceleration, Mass and Force: Pre-Lab Exercise Purpose: What is the quantitative relationship between force, mass and acceleration? 5E: Explain Concepts addressed: Predictive exercise in finding the quantitative relationship between force, mass and acceleration The picture on the right is a sketch of a car or cart attached to a mass hanger with a light string. The car(t) sits on a frictionless track, and the pulley is frictionless too. The car(t) is held in place by the experimenter’s hand. 1. If the car(t) is released, what type of motion do you expect it to have? Explain your reasoning. 2. When the car(t) is released, what kind of motion will the mass hanger have? Explain your reasoning. 3. Draw force diagrams below for: A system that consists A system that consists only of the mass hanger only of the car(t) The net force for this system is: The net force for this system is: A system which consists of the car(t), the string, and the mass hanger The net force for this system is: 4. Discuss whether the force diagrams you just drew are consistent with the predictions you made in steps 1 and 2. A TIME for Physics First Unit 4 –Newton’s Laws Page 42 5. Design an experiment where you can use the motion detector to test your predictions in step 1. What factors can you measure? What factors need to be kept constant? Be sure to address this question: “What kind of motion occurs when a system of constant mass experiences a constant net force?” What specific motion factor do you think will be affected by the force? In order to measure this motion factor, explain what graphs you have to produce, and how you would use these graphs to test your predictions. For the next few questions, assume that you have the system pictured previously, plus anything you choose to add to the car and/or the mass hanger. 6. Question: What effect does changing the net force on a system have on the acceleration of the system when the mass of the system is held constant? Write a hypothesis that describes your prediction: 7. Design an experiment that would allow you to test the effect of changing the net force on the system on the acceleration of the system. Include a description of the variables you would keep constant in the experiment, and how you would keep those variables constant. A TIME for Physics First Unit 4 –Newton’s Laws Page 43 Question: What effect does changing the mass of a system have on the acceleration of the system when the mass of the system is held a constant? Write a hypothesis that describes your prediction: 8. Design an experiment that would allow you to test the effect of changing the mass of the system on the acceleration of the system. Include a description of what variables you would keep constant in the experiment, and how you would keep those variables constant. White boarding and discussion is recommended at this point. A TIME for Physics First Unit 4 –Newton’s Laws Page 44 Acceleration, Mass and Force Lab Purpose: What is the quantitative relationship between force, mass and acceleration? 5E: Explain Concepts addressed: - find the quantitative relationship between force, mass and acceleration. - identify the system for which Newton’s 2nd law is applied - understand net force and acceleration have the same direction - understand the source of the constant of proportionality that connects force, mass and acceleration. Materials: Car(t) and track Mass hanger and masses Pulley and string Motion detector or smart pulley Pre-lab discussion: As a result of the pre-lab exercise, you should know that: The system is the car(t), the mass hanger, string plus anything you add to the cart or hanger The total mass of the system is the sum of the masses of all components described above. For a given run, the total mass of the system (hanger + cart) needs to be kept a constant. When you remove a mass from the hanger, put it on the cart. The net force acting on the system is the gravitational force due to the hanger + any added masses. Allow a suspended mass to tow a cart (glider) across the track; ask students to observe its motion. We’ve already established that a force is required to produce acceleration. We just haven’t quantified the relationship. Rather than brainstorming general observations, ask them to identify other factors that might affect the acceleration of the cart. To proceed, the list must include mass, amount of friction, and amount of force used to tow the cart. Ask them for ideas on how to minimize the effect of friction. After some discussion, they will hopefully come to the idea of inclining the ramp slightly to compensate for friction. Ask them how to measure the acceleration of the cart. While they cannot measure it directly, there are at least two ways to determine the acceleration. One can calculate it from rearrangement of the kinematical model 12 a t 1 x vi t a t 2 2 2 since vi 0 (Note: The use of this model requires the assumption that acceleration is constant. The rationale for such an assumption could be based on an "extra credit" lab.) Another method is to use a motion detector. The slope of the velocity vs time graph yields the acceleration. The dependent variable is the acceleration of the cart. The independent variables are the mass of the cart/hanger system and the force used to pull the cart. Make sure to stress that the mass that is being accelerated is the total mass of A TIME for Physics First Unit 4 –Newton’s Laws Page 45 the system (the cart and hanging mass are connected, so both must accelerate at the same rate). Directions: NOTE: The experimental parameters may vary with your equipment 1. Experimental Notes: Use small mass hangers (e.g. 5g) and change by 10 to 20 g increments. Increase cart mass by 10-20 g at a time (from the car to the hanger). Adjust the angle of incline so that the cart can move at a constant speed with a very small initial push. Convince students that they must transfer mass from the cart to the hanger in order to keep the total mass constant when they vary the force. Convert the hanging mass to newtons. 2. As before, students’ documentation should contain: The Experimental Question, Constants of the experiment, Hypothesis, IV, DV, Materials List, Procedure, Data table, and a Graph with a smooth line through data points. 3. Conclusions: Questioning strategies: What slope did you get for the graph? What are its units? What is the intercept, and what does the intercept mean? White boarding and discussion is recommended at this point. Post-lab discussion Since the units of slope are not intuitive, focus on proportionalities. Discuss the combination of two proportionalities into one: a Fnet a 1 m a Fnet m Turn the proportionality into an equation; rearrange to solve for k. ak Fnet ma k m Fnet Substitute values from regression line to solve for k. With luck, students’ values should cluster around 1.0. Now is the time to point out that the slope of force of gravity vs mass (9.8 N/kg) and the slope of velocity vs time (9.8 m/s2) have the same numerical value due to the way the newton was defined. Describe whether and if yes, how the directions of net force and acceleration are related to one another (since both force and acceleration are vectors and therefore have associated directions). What does this relationship mean? Describe whether and if yes, how the directions of the net force and velocity are related to one another. Have students write four things they learned from this lab. Have students return to the conclusions you wrote after the “What does it take to move?” lab and add the conclusions from this lab. A TIME for Physics First Unit 4 –Newton’s Laws Page 46 Reading Page – Newton’s Second Law Newton’s first law told us what happens when no net external force acts: Things that are sitting still will not move on their own, they need an outside force to make them move. Things that are moving in a straight line will not stop, slow down or speed up on their own, they need an external force to change their motion. Things that are moving in a straight line will not change direction unless a force makes them do so. So it is pretty clear that if a net external force does act, Things that are sitting still can begin to move. Things that are moving can be made to slow down, speed up or even stop. Things that are moving in one direction can be made to change direction. In the previous activity we saw that a net external force changes the motion of an object by making it accelerate. How does that go along with the statements above? Things that are sitting still can begin to move: the object had a velocity of zero to begin with, and after a force is applied, it accelerates to a higher velocity. Things that are moving can be made to slow down (force is applied to change a high velocity to low velocity) speed up or even stop. Things that are moving in one direction can be made to change direction – this is also a change in velocity, namely, the amount of velocity may not have changed, but the direction has, so there is a net acceleration. We also saw in the previous activity that the amount of mass affects the force applied. In other words, for two masses to have the same acceleration, the larger mass needs a larger force. In equation form, uuur r Force = mass x acceleration, or Fnet ma or ur uuur r F F ma net A lot of the applications of Newton’s second law deal with the fact that several forces can act on an object, but if the forces don’t all balance out and there is a net external force. This net force causes acceleration – and the acceleration will be along the direction of that net force. Teacher Notes: Force anduracceleration are both vectors, as indicated by the arrow above the r symbolur( F and r a ). uuur r F ma Since F and a are related through the equation net the directions of the force ur and r acceleration are the same (if a force F is along the south-west, the acceleration a that it causes is also along the south-west direction). A TIME for Physics First Unit 4 –Newton’s Laws Page 47 A TIME for Physics First Unit 4 –Newton’s Laws Page 48 4.1. Practice: Newton’s Second Law Recommended: = class, whiteboard; = homework; = challenge problems For each of the problems below, explain the reasoning behind your answer!! 1. A 10-kg brick and a 1-kg book are dropped in a vacuum. The force of gravity on the 10-kg brick is A) the same as the force on the 1-kg book. B) 10 times as much C) one-tenth as much. D) zero. 2. If an object's mass is decreasing while a constant force is applied to the object, would its acceleration decrease, increase, or remain the same? Explain. 3. An object is propelled along a straight-line path in space by a force. If the object sweeps up extra particles and its mass becomes twice as much, its acceleration A) quadruples. B) doubles. C) stays the same. D) halves. E) none of these 4. The force of friction on a sliding object is 10 newtons. Would the applied force needed to maintain a constant velocity be more than 10 N, less than 10 N or 10 N? Explain. 5. A 10-N falling object encounters 4 N of air resistance. The net force on the object is A) 6 N upwards. B) 4 N upwards. C) 6 N downwards. D) 10 N downwards. E) none of these. 6. A 10-N falling object encounters 10 N of air resistance. The net force on the object is A) 0 N. B) 4 N. C) 6 N. D) 10 N. E) none of these 7. An apple weighs 1 N. When held at rest above your head, what is the net force on the apple? A TIME for Physics First Unit 4 –Newton’s Laws Page 49 8. An apple weighs 1 N. If Tammy throws it up in the air, what is the force on it while it is on its way up? What is its acceleration on the way up? What is the direction of the acceleration? 9. An apple at rest weighs 1 N. What is the net force on the apple when it is in free fall? What is its acceleration? What is the direction of the acceleration? 10. A 1-kg rock that weighs 9.8 N is thrown straight upward at 20 m/s. Neglecting air resistance, would the net force that acts on it when it is half way to the top of its path be less than 9.8 N, 9.8 N, or more than 9.8 N? 11. Which has zero acceleration? An object A) at rest. B) moving at constant velocity. C) in mechanical equilibrium. D) all of these E) none of these 12. Whenever the net force on an object is zero, would its acceleration be less than zero, zero, or more than zero? Explain. 13. Your car is coasting on level ground at 60 km/h and you apply the brakes until the car slows to 40 km/h. If you suddenly release the brakes now, would the car tend to momentarily regain its higher initial speed, continue moving at 40 km/h, or decrease in speed if no other forces act? Explain. 14. When you hang from a pair of gym rings, the upward support forces of the rings will always A) each be half your weight. B) each be equal to your weight. C) add up to equal your weight. 15. A car has a mass of 2000 kg and accelerates at 2 meters per second per second. What is the magnitude of the net force exerted on the car? 16. A tow truck exerts a force of 3000 N on a car, accelerating it at 2 meters per second per second. What is the mass of the car? 17. A girl pulls on a 10-kg wagon with a constant horizontal force of 30 N. If there are no other horizontal forces, what is the wagon's acceleration in meters per second per second? A) 0.3 B) 3.0 C) 10 D) 30 E) 300 18. A force of 1 N accelerates a mass of 1 kg at the rate of 1 m/s2. The acceleration of a mass of 2 kg acted upon by a net force of 2 N is A) half as much. B) twice as much. C) the same. D) none of these. A TIME for Physics First Unit 4 –Newton’s Laws Page 50 19. An object following a straight-line path at constant speed A) has a net force acting upon it in the direction of motion. B) has zero acceleration. C) has no forces acting on it D) none of these 20. A man weighing 800 N stands at rest on two bathroom scales so that his weight is distributed evenly over both scales. The reading on each scale is A) 200 N. B) 400 N. C) 800 N. D) 1600 N. E) none of these 21. When a woman stands at rest with both feet on a scale, it reads 500 N. When she gently lifts one foot, the scale reads A) less than 500 N. B) more than 500 N. C) 500 N. 22. A 10-N block and a 1-N block lie on a horizontal frictionless table. To provide them with equal horizontal acceleration, we would have to push with A) equal forces on each block. B) 10 times as much force on the heavier block. C) 10 squared or 100 times as much force on the heavier block. D) 1/10 as much force on the heavier block. E) none of these 23. A block is dragged without acceleration in a straight-line path across a level surface by a force of 6 N. What is the force of friction between the block and the surface? A) less than 6 N B) more than 6 N C) 6 N D) need more information to say 24. Suppose a particle is being accelerated through space by a 10-N force. Suddenly the particle encounters a second force of 10 N in the opposite direction from the first force. The particle with both forces acting on it A) is brought to a rapid halt. B) decelerates gradually to a halt. C) continues at the speed it had when it encountered the second force. D) theoretically tends to accelerate toward the speed of light. E) none of these A TIME for Physics First Unit 4 –Newton’s Laws Page 51 4.6. Practice: Force Diagrams, Motion Diagrams and Newton’s Second Law Recommended: = class, whiteboard; = homework; = challenge problems 1. For each of the situations below, draw a picture and then the force diagram. A. A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book. B. A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration. Diagram the forces acting upon the sled. C. A football is moving upwards towards its peak after having been booted by the punter. Diagram the forces acting upon the football as it rises upward towards its peak. D. A car is coasting to the right and slowing down. Diagram the forces acting upon the car. A TIME for Physics First Unit 4 –Newton’s Laws Page 52 E. An egg falls from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it falls. 2. In the following problems you are given a representation of the motion that occurs. Fill in the rest of the table. A. Picture of motion (the points are drawn at equal 1 second time intervals) Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram: Verbal description of motion: A TIME for Physics First Unit 4 –Newton’s Laws Page 53 B. Picture of motion (the points are drawn at equal 1 second time intervals) Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram: Verbal description of motion: C. Picture of motion (the points are drawn at equal 1 second time intervals) Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram: Verbal description of motion: A TIME for Physics First Unit 4 –Newton’s Laws Page 54 D. Picture of motion (the points are drawn at equal 1 second time intervals) Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram Verbal description of motion E. Picture of motion Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram: Verbal description of motion A TIME for Physics First Unit 4 –Newton’s Laws Page 55 F. Picture of motion Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram Verbal description of motion G. Picture of motion Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram: Verbal description of motion and force diagram A TIME for Physics First Unit 4 –Newton’s Laws Page 56 H. Picture of motion Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram Verbal description of motion I. Picture of motion Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram Verbal description of motion A TIME for Physics First Unit 4 –Newton’s Laws Page 57 3. In the following table you are given either the motion diagram, force diagram, verbal description, or a graph. Fill in the rest of the table. A. Motion Diagram Force Diagram (you must label all forces) Verbal Description Position, velocity and acceleration vs time graphs B. Motion Diagram Force Diagram (you must label all forces) Verbal Description: You throw a ball up into the air. Describe what happens from the instant it leaves your hand up until it reaches its highest point. Position, velocity and acceleration vs time graphs A TIME for Physics First Unit 4 –Newton’s Laws Page 58 C. Motion Diagram of an airplane on a runway Force Diagram (you must label all forces) Verbal Description Position, velocity and acceleration vs time graphs D. Motion Diagram Force Diagram (you must label and draw all forces) Verbal Description: A ball is pulled up a ramp that has no friction. Continue the description of its motion: Position, velocity and acceleration vs time graphs A TIME for Physics First Unit 4 –Newton’s Laws Page 59 E. Motion Diagram Force Diagram (you must label and draw all forces) Verbal Description: Position, velocity and acceleration vs time graphs 4. The motion of a cart in three different situations is described below. Match the diagram to the motion described and explain your reasoning. A. A cart is released from the top of a frictionless ramp. Which of the following best describes the situation after the cart was released? Explain your reasoning. B. After the cart reaches the bottom of the ramp, a boy gives it a shove and sends it moving up the ramp. Which of the following best describes the situation just after the cart was shoved? C. After it was shoved upward in the previous problem, the cart reaches the highest point it can reach on the ramp. Which of the following best describes the situation at the instant when the cart is at its highest point? A TIME for Physics First Unit 4 –Newton’s Laws Page 60 Upward and Downward Ride Lab Purpose: What kinds (types) of forces are felt while riding an elevator? 5E: Elaborate Concepts addressed: - experience and analyze forces felt in an elevator. - recognize that acceleration influences the actual forces felt by an object Materials: An elevator A bathroom scale or A spring scale (preferably 0-10 or 0-20 N) and an object of weight 5-8 N Pre-lab discussion: Students, in groups of two or three ride in an elevator. One of them stands on the bathroom scale (or holds a spring scale with object hanging on it) and the others record observations. Have students make their predictions before they get on the elevator. Test your elevator ahead of time: some elevators will show a larger effect traveling upward, others while traveling downward. Directions: Downward: Beginning -- starting from rest Prediction (circle one): Data (circle one): I think the scale will read The scale reads MORE MORE LESS SAME as the elevator just starts moving LESS Force diagram Beginning: SAME as the elevator just starts moving Explain: Fnet = a= Downward: Middle -- steady Prediction (circle one): Data (circle one): I think the scale will read The scale reads MORE MORE LESS SAME in the middle of the ride LESS Force diagram Middle: SAME in the middle of the ride Explain: A TIME for Physics First Fnet = a= Unit 4 –Newton’s Laws Page 61 Downward: End -- coming to a stop Prediction (circle one): Data (circle one): I think the scale will read The scale reads MORE MORE LESS SAME as the elevator comes to a stop LESS Force diagram End: SAME as the elevator comes to a stop Explain: Fnet = a= Now you will repeat this activity when the elevator is going upward Upward: Beginning -- starting from rest Prediction (circle one): Data (circle one): I think the scale will read The scale reads MORE MORE LESS SAME as the elevator just starts moving LESS Force diagram Beginning: SAME as the elevator just starts moving Explain: Fnet = a= Upward: Middle -- steady Prediction (circle one): Data (circle one): I think the scale will read The scale reads MORE MORE LESS SAME in the middle of the ride LESS Force diagram Middle: SAME in the middle of the ride Explain: A TIME for Physics First Fnet = a= Unit 4 –Newton’s Laws Page 62 Upward: End -- coming to a stop Prediction (circle one): Data (circle one): I think the scale will read The scale reads MORE MORE LESS SAME as the elevator comes to a stop LESS Force diagram End: SAME as the elevator comes to a stop Explain: Fnet = a= White boarding and discussion is recommended at this point. Post-Lab discussion: Remember that your "true weight" is equal to the force of gravity acting on you. What does the reading on the scale tell you? Did the true weight ever change? What was changing and why? What would happen if the elevator went faster during the “middle” phase of its motion? What would happen if the elevator accelerated faster when it was starting on its way down? On its way up? Is there any way by which you could get a zero net force acting on an object in an elevator? A TIME for Physics First Unit 4 –Newton’s Laws Page 63 4.7. Practice: Elevator Problems Recommended: = class, whiteboard; = homework; = challenge problems 1. An elevator is moving up at a constant velocity of 2.5 m/s, as illustrated in the diagram below: the man has a mass of 85 kg. o Construct a force diagram for the man. o How much force does the floor exert on the man? 2. The elevator now accelerates upward at 2.0 m/s2. o Construct a force diagram for the man. o What force does the floor now exert on the man? 3. Upon reaching the top of the building, the elevator accelerates downward at 3.0 m/s2. o Construct a force diagram for the man. o What force does the floor now exert on the man? 4. While descending in the elevator, the cable suddenly breaks. What is the force of the floor on the man? 5. Consider the situation where a person that has a mass of 68 kg is descending in an elevator at a constant velocity of 4.0 m/s. At some time "t", the elevator starts to slow to a stop at the rate of 2.0 m/s2. o Construct a qualitative motion diagram indicating the positions, velocities and accelerations of the elevator as it descends. o Construct quantitative force diagrams (include magnitudes) for the person in the elevator as it descends at (i) constant speed and (ii) during its period of acceleration. o If the person in the elevator were standing on a bathroom scale calibrated in newtons, what would the scale read while the elevator was (i) descending at constant speed and (ii) while slowing to a stop? Explain your answers. A TIME for Physics First Unit 4 –Newton’s Laws Page 64 4.8. Practice: Newton’s Second Law and Motion Recommended: = class, whiteboard; = homework; = challenge problems For each of the problems below, you must begin your solution with a force diagram. Some require more than one diagram. 1. The maximum force that a grocery bag can withstand without ripping is 250 N. Suppose that the bag is filled with 20.0 kg of groceries and lifted with an acceleration of 5.0 m/s2. Do the groceries stay in the bag? Explain your reasoning. 2. A student, standing on a scale in an elevator at rest, sees that his weight is 840 N. As the elevator rises, his weight increases to 1050 N, then returns to normal. When the elevator slows to a stop at the 10th floor, the reading on the scale drops to 588 N, then returns to normal. Draw a motion diagram for the student during his elevator ride. Determine the acceleration at the beginning and end of the trip. 3. A sign in an elevator states that the maximum occupancy is 20 persons. Suppose that the safety engineers assume the mass of the average rider is 75 kg. The elevator itself has a mass of 500 kg. The cable supporting the elevator can tolerate a maximum force of 30,000 N. What is the greatest acceleration that the elevator’s motor can produce without snapping the cable? What is the direction of this acceleration? 4. A race car has a mass of 710 kg. It starts from rest and travels 40.0 m in 3.0 s. The car is uniformly accelerated during the entire time. What net force is acting on the car? 5. Suppose that a 1000 kg car is traveling at 25 m/s (~55 mph). Its brakes can apply a force of 5000 N. What is the minimum distance required for the car to stop? 6. During a head-on collision, a passenger in the front seat of a car accelerates from 13.3 m/s (~ 30 miles/hour) to rest in 0.10 s. o What is the acceleration of the passenger? o The driver of the car holds out his arm to keep his 25 kg child (who is not wearing a seat belt) from smashing into the dashboard. What force must he exert on the child? o What is the weight of the child? o Convert these forces from N to pounds (1 lb = 4.45 N ). What are the chances the driver will be able to stop the child? A TIME for Physics First Unit 4 –Newton’s Laws Page 65 APPENDIX A TIME for Physics First Unit 4 –Newton’s Laws Page 66 Materials List for Unit 4 Labs General Supplies Materials for Labs a pair of spring scales (Newtons); platform or two bathroom scales Two Force plates String Two force probes Two rubber stoppers to attach to end of force probe A rubber band A small and a large wood block, with Velcro to attach force probe to block (Optional) Two carts with repelling magnetic bumpers Track for carts above Cart and spring scale on low-friction surface Or large spring scale and a skateboard Or car, spring scale and track Car(t) and track Mass hanger and masses Pulley Motion detector or smart pulley and picket fence to measure acceleration An elevator A bathroom scale or An object of weight 5-8 N A TIME for Physics First Unit 4 –Newton’s Laws Page 67 Sample Data for Unit 4 Labs NEWTON’S THIRD LAW WITH FORCE PROBES LAB Students are expected to get graphs that look like the ones below: Station 1 (1,2) Station 1 (3) Station 2 (1) Station 2 (2) Station 2 (3) Station 2 (2) A TIME for Physics First Unit 4 –Newton’s Laws Page 68 Station 3 (1) Station 3 (2) Station 3 (3) Station 3 (4) Station 3 (5) Station 3 (6) Station 4 (3) Not all possibilities are shown here. A TIME for Physics First Unit 4 –Newton’s Laws Page 69 Sample Worksheet for What Does It Take to Move? – Lab Purpose: What is the connection between force and motion–related factors such as time, displacement, velocity and acceleration? Materials: A cart A spring scale on low-friction floor Or, a large spring scale and a skateboard Or, a spring scale and track Directions: 1. Identify all the forces acting on the cart when it is sitting motionless on the frictionless surface. Using appropriate names, list them below. 2. Draw a force diagram for the motionless cart. Draw the corresponding motion diagram next to it. What conclusion can you draw about the connection between the net force exerted on the moving cart and its velocity? 3. Describe in words what you need to do to make the cart move? 4. Suppose you were to attach a spring scale to the motionless cart and pull on it to make it move. What do you think the spring scale will read during the time the cart is being pulled but has not moved yet? Write down your predictions below and try it. A TIME for Physics First Unit 4 –Newton’s Laws Page 70 5. As the cart just begins to move, carefully watch what the spring scale read and write down the details below. Draw a force diagram and a motion diagram. 6. Suppose you wish to pull the cart and keep it moving with zero net force. Predict whether this is possible or not. Explain your reasoning. Now try it. Describe in detail what happens. 7. Draw a force diagram and a motion diagram for the above situation. What conclusion can you draw about the connection between the net force exerted on the moving cart and its velocity? 8. In this step, pull and keep the cart moving while maintaining a constant force of 2 N. First make a prediction: What do you think the motion will look like? Explain your reasoning. Draw a force diagram and a motion diagram. 9. Now try it. Describe what happens. Draw a force diagram, and a motion diagram. What conclusion can you draw between the net force exerted on the moving cart and its acceleration? 10.Based on your experimental evidence, answer the question: “What does it take to move?” Write down four things you learned about the qualitative connection between force and motion-related factors such as time, displacement, velocity, and acceleration. A TIME for Physics First Unit 4 –Newton’s Laws Page 71 Unit 4 - Newton’s Laws: GLE and Process Standards by Activity Activity Newton’s Third Law Lab Newton’s Third Law with Force Probes Lab Reading Page—Newton’s Third Law 4.1. Practice: Identifying Pairs of Forces I 4.2. Practice: Identifying Pairs of Forces II 4.3. Practice: Forces, Acceleration and Collisions 4.4. Practice: Newton’s Third Law with Blocks 4.5. Practice: Newton’s Third Law Problems What Does It Take To Move?—Lab Acceleration, Mass and Force: Pre-Lab Exercise Acceleration, Mass and Force Lab A TIME for Physics First GLEs 2.2.A.a; 2.2.D.e; 2.2.D.f; 2.2.D.g; 2.2.D.h; 7.1.A.a; 7.1.A.c; 7.1.B.a; 7.1.B.b; 7.1.B.c; 7.1.C.a; 7.1.C.b; 7.1.E.a 2.2.A.a; 2.2.D.e; 2.2.D.f; 2.2.D.g; 2.2.D.h; 7.1.A.a; 7.1.A.c; 7.1.B.a; 7.1.B.b; 7.1.B.c; 7.1.C.a; 7.1.C.b; 7.1.E.a 2.2.A.a; 2.2.B.a; 2.2.B.c; 2.2.D.g; 2.2.D.h 2.2.A.a; 2.2.D.g; 7.1.C.a; 7.1.E.a 2.2.A.a; 2.2.D.d; 2.2.D.e; 2.2.D.g; 2.2.E.b; 7.1.C.a; 7.1.E.a 2.2.A.a; 2.2.D.e; 2.2.D.g; 2.2.D.h; 7.1.C.a; 7.1.D.a; 7.1.D.b; 7.1.E.a; 7.1.E.b 2.2.A.a; 2.2.D.c; 2.2.D.e; 2.2.D.f; 2.2.D.g; 7.1.C.a; 7.1.E.a 2.2.A.a; 2.2.D.f; 2.2.D.g; 2.2.D.h; 7.1.C.a; 7.1.E.a 2.1.A.a; 2.2.A.a; 2.2.D.e; 2.2.D.f; 2.2.D.g; 2.2.D.h; 7.1.B.a; 7.1.B.b; 7.1.B.c; 7.1.C.a; 7.1.C.b; 7.1.D.a; 7.1.E.a; 7.1.E.b 2.2.A.a; 2.2.D.c; 2.2.D.d; 2.2.D.e; 2.2.D.f; 2.2.D.g; 2.2.D.h; 7.1.A.a; 7.1.A.b; 7.1.A.c; 7.1.E.a 2.2.D.c; 2.2.D.d; 2.2.D.e; 2.2.D.f; 2.2.D.g; 2.2.D.h; 7.1.A.c; 7.1.B.a; 7.1.B.b; 7.1.B.c; 7.1.C.a; 7.1.C.b; 7.1.D.a; 7.1.E.a Unit 4 –Newton’s Laws DESE Show Me Standards Knowledge Goals Goals 1.3; 1.6; 1.8; 2.3; 2.4; 3.5; 4.1; 4.6 1.3; 1.6; 1.8; 2.3; 2.4; 3.5; 4.1; 4.6 N/A 1.6; 1.8; 2.4; 3.2 1.6; 1.8; 2.4; 3.3 1.6; 1.8; 2.4; 3.3; 4.1 1.6; 1.8; 3.3 1.6; 2.4; 3.3; 4.1 1.2; 1.3; 1.6; 2.3; 2.4; 3.5; 4.1; 4.6 1.1; 1.2; 1.3, 2.4 1.2; 1.3; 1.6; 1.8; 2.3; 2.4; 3.5; 4.1; 4.6 Page 72 Reading Page—Newton’s Second Law 4.6. Practice: Newton’s Second Law 4.7. Practice: Force Diagrams, Motion Diagrams and Newton’s Second Law Upward and Downward Ride Lab 4.8. Practice: Elevator Problems 4.9. Practice: Newton’s Second Law and Motion 2.2.D.a; 2.2.D.c; 2.2.D.f N/A 2.2.A.a; 2.2.B.d; 2.2.D.c; 2.2.D.d; 2.2.D.e; 2.2.D.f; 2.2.D.g; 2.2.D.h; 7.1.C.a; 7.1.D.a; 7.1.E.a; 7.1.E.b 2.1.A.a; 2.1.B.a; 2.2.A.a; 2.2.B.d; 2.2.D.c; 2.2.D.d; 2.2.D.e; 2.2.D.f; 2.2.D.g; 2.2.D.h; 7.1.C.a; 7.1.C.b; 7.1.D.a; 7.1.E.a; 7.1.E.b 2.2.A.a; 2.2.D.d; 2.2.D.e; 2.2.D.f; 2.2.D.g; 7.1.A.c; 7.1.B.a; 7.1.B.b; 7.1.B.c; 7.1.C.a; 7.1.C.b; 7.1.D.a; 7.1.E.a; 7.1.E.b 2.1.A.a; 2.1.B.a; 2.2.A.a; 2.2.B.c; 2.2.D.d; 2.2.D.e; 2.2.D.f; 2.2.D.g; 7.1.C.a; 7.1.D.a; 7.1.E.a; 2.1.A.a; 2.1.A.c; 2.1.B.a; 2.1. B.b; 2.2.A.a; 2.2.B.c; 2.2.D.c; 2.2.D.d; 2.2.D.e; 2.2.D.f; 2.2.D.g; 2.2.D.h; 7.1.C.a; 7.1.E.a 1.6; 2.4; 3.2; 4.1 1.6; 1.8; 2.4; 3.3; 4.1 1.3; 1.6; 1.8; 2.3; 2.4; 4.1; 4.6 1.6; 1.8; 2.4; 3.2; 4.1 1.6; 1.8; 2.4; 3.3; 4.1 Note: Many of the Mathematics Knowledge Standards may apply. Each teacher should check with the math department to determine which standards are appropriate. A TIME for Physics First Unit 4 –Newton’s Laws Page 73 Unit 4 Recommended Timeline This timeline is based on each “day” being approximately 50 minutes long. Day Classwork 1 Framing Questions. Prelab Newton’s 3rd Law Lab 2 Do N3 Lab 3 Whiteboard postlab of N3 Lab. Have each lab group take a station. 4 Practice identifying N3 pairs. 5 6 4.1 Practice: ID Pairs of Forces II (first 3 pages) Whiteboarding of Practice as needed and In class demo: forces on carts. Two students on carts pull each other. Which moves farther? Why? This will bridge students into thinking about Newton’s 2nd law Prelab Acceleration, Mass and Force Lab Do Acceleration, Mass and Force Lab lab Continue to do N2 lab 7 8 9 10 11 12 13 14 15 16 17 18 19 Begin post lab of N2 lab Finish post lab of N2 lab. Depending on your students, you might want to break it into two independent labs—changing net force, and changing mass of the system. Post lab each part individually and even give some practice data to analyze. Show how to apply Newton’s 2nd law to situations involving unbalanced forces. 4.5 Practice: Force Diagrams, Motion Diagrams and N2. Regular kids can do 1-2 Honors can do 3-4 also Whiteboard homework Upward and Downward Ride Lab Postlab discussion. What is “weightlessness?” Do example elevator word problem Whiteboard Elevator Problems 4.6 Practice Whiteboard 4.7 Practice Review Test A TIME for Physics First Unit 4 –Newton’s Laws Homework Finish predictions for N3 Lab Start working on force diagrams for N3 lab Continue working on force diagrams for N3 lab. Only honors students should do 2D force diagrams Reading Page: N3 4.1 Practice: Pairs of Forces I Make graphs Continue making graphs Reading Page: Newton’s 2nd Law Finish 4.5 Practice 4.6 Practice 4.7 Practice Page 74 4.9. Practice: Vertical Acceleration (for honors students) For questions 1-5 consider the 50 kg woman shown at right. Sketch the force diagram, motion map, including acceleration, and a graph for the woman appropriate to each situation. Find the value of each force acting on the woman. This elevator moves only in the vertical dimension with the kinematic quantities indicated for each problem. Upward is positive. Assume the elevator remains at rest once it comes to a stop. The elevator moves with a constant velocity of +2 m/s. 1. The elevator moves with a constant velocity of -3 m/s. 2. The elevator moves downward with a velocity of -4 m/s and has acceleration of +1 m/s2. 3. The elevator moves upward with a velocity of +3 m/s and has an acceleration of +1 m/s2. 4. The elevator moves downward with a velocity of -4 m/s and has an acceleration of -2 m/s2. 5. A helicopter holding a 90. kg box suspended from a rope 5.0 m long accelerates upward at a rate of 2.1 m/s2. Air resistance is negligible. o Draw and label a force diagram for the box. o Determine the tension in the rope. o At the moment that the upward velocity of the helicopter is 12 m/s, the rope is cut. The helicopter from then on accelerates upward at 2.5 m/s2. Determine the distance between the helicopter and the package 3.0 seconds after the rope is cut. 6. Having fallen down a well, a boy finds himself with the water bucket tied to a rope which goes over a pulley at the top. Fortunately the other end of the rope has fallen down to the bottom of the well, too. So, he decides to get into the bucket and start pulling on the other end of the rope in order to get himself out. His mass is 32 kg and the bucket has a mass of 3.0 kg. How much force will the boy have to exert on the rope in order to pull himself up with a relatively constant velocity? A TIME for Physics First Unit 4 –Newton’s Laws Page 75 7. A crane is used to hoist a load of mass m1 = 500 kg. The load is suspended by a cable from a hook of mass m2 = 50 kg, as shown above. The load is lifted upward at a constant acceleration of 2 m/s2. o o Draw a force diagram for the hook, and label each force clearly, identifying the agent exerting it. Determine the tension T1 in the lower cable and the tension T2 in the upper cable. 8. An elevator is rising at a speed of 5.00 m/s. It comes to a halt in 4.0 s. The guide rails on the side of the elevator each exert a 110 N frictional force on the elevator. The pulley has negligible friction and mass for the purposes of this analysis. o Find the tension in the cable during the slowing of the elevator. o Find the mass M that the counterweight must have in order for the elevator to stop as stated above. A TIME for Physics First Unit 4 –Newton’s Laws Page 76