"LEARNING CYCLE – NEWTONS THIRD LAW"
LEARNING CYCLE – NEWTON’S THIRD LAW Learning Cycle Teacher Notes GETTING STARTED Overview After completing this learning cycle, students should be able to correctly apply Newton's Third Law to common experiences. The activity, Can You Budge Me, allows students the opportunity to explore action-reaction forces. In Probing The Third Law uses force probes and The Scale Wars utilizes spring scales to reinforce Newton's Third Law. The cycle concludes with Balloon Rockets. Students should be able to explain that forces always act in pairs, which are called action-reaction pairs. They should be able to determine when a force is acting on an object, which force causes the object to acceleration as opposed to the reaction force that the object exerts on something else. National Science Education Standard(s) Being Addressed Content Standard 5-8 Physical Science B Motions and Forces Not listed. Content Standard 9-12 Physical Science B Motions and Forces Objects change their motion only when a net force is applied. Laws of motion are used to calculate precisely the effects of forces on the motion of objects. The magnitude of the change in motion can be calculated using the relationship F = ma, which is independent of the nature of the force. Whenever one object exerts force on another, a force equal in magnitude and opposite in direction is exerted on the first object. Benchmark(s) for Science Literacy Being Addressed Benchmark 6-8 The Physical Setting 4F Motion Not listed. Benchmark 9-12 The Physical Setting 4F Motion Whenever one thing exerts a force on another, an equal amount of force is exerted back on it. Prerequisite Knowledge and Skills Force is a vector quantity Setting the Stage for Student Learning Students will assume that Newton's Third Law is the easiest of all the motion laws to understand. Yet, it is this law that causes more misconceptions than the first two. This law comes to play whenever two objects interact. It is impossible to touch without being touched in return. To introduce this learning cycle, the following questions can be discussed: a) If a cart pulls back on a horse with the same force that the horse exerts on the cart, how can the cart ever move? b) How do rocket ships work? Can they work in outer space where there is no atmosphere? c) A bug crashes into the windshield of a car. Which object experiences the greater force, the bug or the windshield? UI:TG-Newton’s 3rd Law 1 Most students will have a hard time answering these questions. Most will recognize that, of course the cart can move, but they will not be able to explain why. They will also respond that rocket ships work because the air pushes them forward. When it is pointed out that rockets do work in outer space, they will not be able to explain why. Students will also respond that the bug experiences the bigger force because they know that the bug gets smashed but nothing much seems to happen to the windshield. It is the objective of this learning cycle to clear up these common misconceptions, to give students direct evidence that, when they push on an object, the same force pushes back, and to have students correctly explain how objects can move, even when they are themselves pushing on something else. Taking Account of Student Ideas A common student misconception is that whenever two objects exert forces on each other the object with the larger mass will exert a larger force. Students also have problems understanding that the forces being considered in the 3rd law are not acting on the same object. It might be of value to emphasize that Newton's 3rd Law applies only to two forces acting on two different objects. Activity Teacher Notes EXPLORATION: CAN YOU BUDGE ME? Lab setup easy moderate difficult Calculations easy moderate difficult Reliability excellent good fair Interest excellent good fair Lab time -1 class 1 class +1 class Process Skill A B C D E F Reasoning 1 2 3 4 5 Engaging the Students with Phenomena Materials Spring scales, rope, 2 skateboards (or pairs of roller blades) Teaching Strategies 1. You may ask a student to stand in front of the class and then give him/her a mild push. Ask the question, “How does the force that you feel compare to the force that I feel?” You don’t need to arrive at any conclusion, but point out that in this learning cycle this question will be investigated. 2. This activity is divided into two parts. Assign three students in a laboratory group. In the first part, students use spring scales to explore action-reaction forces using connected spring scales. No matter what the students do, the readings on the connected scales are always the same. In the second part, two students on skateboards are engaged in a tug of war. Results will vary with the choice of students and the quality of the skateboards. You will want to think about your groups. Students of approximately equal masses will find it impossible for one student to UI:TG-Newton’s 3rd Law 2 move without the other moving. Students of very different masses may find that only one student moves, especially if a skateboard is not of high quality. Students should answer the questions to the first part and you should plan on discussing their results with the class before moving on to the second part. 3. There is a great opportunity for you to informally extend the activity and increase student understanding. Repeat the activity using connected spring scales instead of the rope for the students to pull on. No matter what the masses of the students, the spring scales will show the same force. Part A Sample Observations/Calculations In Part A, students will find the spring scales always have the same reading. Even when a third scale is used, they read the same. Developing and Using Scientific Ideas 1. How would you describe the relationship between the readings on the scales? First do it in the form of a sentence and then also with the notation described in the introductory paragraph. Ans. The readings on the scales are always equal. FA on B = -FB on A 2. Do the readings depend on who is pulling? Explain. Ans. No, the readings are always the same. The force is equal in both directions. 3. Can the two rubber bands be used to compare forces between two objects? Explain. Ans. Yes, the two rubber bands could be used because the force is proportional to the stretch of a rubber band. If two forces on two identical rubber bands are equal, then the extension of the two rubber bands will be the same. Part B Sample Observations/Calculations In Part B, (if the students are of similar mass) they will move toward each other. If the students are of very different mass, only one may move. If the surface is hard and the skateboards are of low friction, then the distances moved will be inversely proportional to the masses on the skateboards. Developing and Using Scientific Ideas 1. Which student moved in each case? Explain your observations. Ans. Each student should have moved. If one student was significantly more massive than the other, the more massive student should have moved less. Sometimes the larger person increases friction on the wheels and hardly moves. 2 Was it possible for a student to remain at rest during the tug-of -war? Explain. Ans. This would be possible only if there was considerable friction between some students and the ground or floor, otherwise both students would move. UI:TG-Newton’s 3rd Law 3 3. If the force you exerted on your partner and the force your partner exerted on you were equal and opposite in direction, explain why you were able to move each other. Ans. To determine whether a student moves one looks at all the forces on one person. The forces on one student will be one of the pair of action-reaction forces and friction on the cart. If the force is greater than friction, then the cart will move. 4. What will happen if two students with very different masses compete in a tug-of-war on skateboards? Use Newton's 2nd and 3rd Laws in your explanation. Ans. The forces on each student will be the same as per Newton’s 3rd Law. The net force on each student will also depend on the friction on each cart. The acceleration will be inversely proportional to the mass of the student and cart. Extending the Activity 1. Organize a tug of war on a floor or outside as directed by your teacher. Explain the results using Newton’s 2nd and 3rd Laws. Show all the forces involved in the people- rope-earth system. Ans. The pairs of action-reaction forces should include: Students on rope and rope on students; students pushing down on surface and surface pushing up on students; gravitational attraction of the earth for students and gravitational attraction of students for the earth. For a side to win, their opponents must have a net force on them toward the winning team. Therefore, friction plays a very important part in this activity. If your frictional force on your team is less than the pulling force in the action-reaction pair of forces, you lose. 2. Why is a tug-of-war on wheels different from a tug-of-war on the ground? Ans. The tug-of-war on wheels minimizes the frictional force on the students and therefore, the motion is primarily an influence of the inverse mass effect. CONCEPT DEVELOPMENT: PROBING THE THIRD LAW Lab setup easy moderate difficult Calculations easy moderate difficult Reliability excellent good fair Interest excellent good fair Lab time -1 class 1 class +1 class Process Skill A B C D E F Reasoning 1 2 3 4 5 Engaging the Students with Phenomena Materials Computer, computer interface, 2 force sensors, graphing and analysis software to display two force graphs simultaneously, 500 g mass, string, rubber band, 2 dynamics carts per station UI:TG-Newton’s 3rd Law 4 Part A Teaching Strategies 1. If you have sufficient computers and sensors divide your class into laboratory groups of four students. You will need analysis software that allows the plotting of two force sensor readings simultaneously, such as Vernier Logger Pro. You should consult your software and force sensor instructions to calibrate both force sensors accurately and to assign one of them a negative value for pulling and the other one positive for pulling. With some force sensors, it may not be necessary to calibrate them. In addition, the analysis software may prevent you from using data rates within a range of 250 points/second to 1000 points/second. If this is the case, you could reduce the experiment length (e.g., 0.2 seconds), set the sample speed at 1000 samples/second, and enable the triggering. Or you could reduce the sample speed to about 20 samples/second, increase the experiment length to 10 seconds, and disable the triggering. Consult your software and sensor instructions for details. 2. Students may feel the observations seem trivial, but the consistent application of Newton’s 3rd Law is one that presents considerable difficulty for students. Make sure that students have a good intuitive feel for the action-reaction pair of forces in addition to observing the evidence on the graphs. 3. This activity is divided into two parts. In the first part, students explore action- reaction forces using two force sensors that are connected together directly and via a string and rubber band. No matter what the students do, the force sensor readings will be equal in magnitude and opposite in direction. In the second part, students explore action-reaction forces with the force sensors attached to two colliding dynamics carts. No matter what the students do, the force sensor readings will be equal in magnitude and opposite in direction. Students should answer the questions to the first part and you should plan on discussing their results with the class before moving on to the second part. Sample Observations/Calculations Figure TG 1.11.1 UI:TG-Newton’s 3rd Law 5 Figure TG 11.1 is a graph that represents the pair of interaction forces when students pull on each other via the string and force sensors. Developing and Using Scientific Ideas 1. Examine the two data runs. What can you conclude about the two forces (your pull on your partner and your partner's pull on you)? How are the magnitudes related? How are the signs related? Ans. My pull is equal to my partners pull. They are equal in magnitude but the signs (directions) are opposite to one another. 2. Does the rubber band change the results? Ans. The rubber band does not change the results at all. 3. In the last activity you had a force sensor on the left, a rubber band and a force sensor on the right. List all of the pairs of action-reaction forces in the system. Which ones are equal? Ans. Fleft on rb & Frb on left, and Frb on right & Fright on rb. The pairs of forces are equal and opposite in direction. 4. Is there any way to pull on your partner's force sensor without your partner's force sensor pulling back with the same force? Describe such conditions. Try it. Ans. No 5. A bug crashes into the windshield of a car. Which object (the bug or the windshield) experiences the greater force? Explain your reasoning. Ans. They each experience equal action-reaction forces. However, since the mass of the bug is so much smaller than the truck, its acceleration will be extremely large compare to the truck. Since the molecules that make up the bug experience such huge acceleration, the forces between molecules will be very large compared to their intermolecular binding forces and hence will get smashed. Part B Teaching Strategies 1. The concept of interactive forces becomes more difficult for students when the forces involve collisions. The intuition that the mass of the colliding objects has an effect on the force delivered is a very strong one. It is supported by the observations that when a small car collides with a large truck, the person in the small car is more likely to sustain serious injury compared to the truck driver. 2. During the course of this investigation when students are having difficulty with internalizing that the force of a large object on a small object is equal and opposite in direction to the force of a small object on a large object it may be a good idea to address the issue of physical harm to passengers in a small car compared to a large truck. It needs to be recognized that in collisions, the primary forces are contact forces of molecules near the colliding surfaces. Forces that cause injury to passengers UI:TG-Newton’s 3rd Law 6 are not the contact forces between vehicles. The forces that cause injury to passengers are forces on the passengers, not the forces between vehicles. 3. The harm to a passenger comes from the collision he/she has with the steering column, dashboard, air bag, seat belt or whatever makes contact with the passenger to create an acceleration (positive or negative) on the passenger. Since the passenger in the small car experiences such a large acceleration, the force on the passenger will be enormous. The 3rd Law applies to the force of passenger on steering column and steering column on passenger. Applying the 2nd Law to the passenger, the force can be calculated by finding the product of the mass of the passenger and the acceleration of the passenger. This will equal the net force on the passenger. 4. You can take the collision down one more step and look at the force on the brain, or some other organ in the body, of a person in a crash. The head may stop suddenly, but the inertia of the brain will carry it into the cranium. The force on the brain is equal to the product of the mass of the brain and the acceleration of the brain. This is why some people say that it is the second collisions that kills. 5. The obviously important concept is to recognize that under all conditions, given two interacting objects, the forces between objects always come in equal pairs and are opposite in direction. This applies to colliding cars, charges in an electric field, an airplane in flight and the earth, a student and the earth, the sun and earth, etc. Sample Observations/Calculations Force Vs. Time – Head on Force Vs. Time – Small Cart into Large Cart The first graph (Figure TG 11.2) represents a stationary cart being hit by a cart with half the mass. Th Dev Figure TG 1.11.2 Figure TG 1.11.3 e loping and Using Scientific Ideas 1. Summarize the general relationship of the FA on B and FB on A. Ans. FA on B = - FB on A. 2. How does the FA on B and FB on A compare when car A was pushing and accelerating car B? Ans. FA on B = -FB on A. UI:TG-Newton’s 3rd Law 7 3. Under what conditions is FA on B and FB on A not equal and opposite in direction? Ans. There are no such conditions. Extending the Activity Fasten one Force Sensor to your lab bench and repeat the experiments. Does the bench pull back as you pull on it? Does it matter that a person does not hold the second force sensor? Ans. The demonstration shows that the interaction pair does not depend on animate or inanimate objects for the force pairs to be equal. CONCEPT DEVELOPMENT: THE SCALE WARS Lab setup easy moderate difficult Calculations easy moderate difficult Reliability excellent good fair Interest excellent good fair Lab time -1 class 1 class +1 class Process Skill A B C D E F Reasoning 1 2 3 4 5 Engaging the Students with Phenomena Materials Rubber band, 2-500 gram masses, string, 2 spring scales, 2 pulleys, support apparatus as needed Teaching Strategies If you have no force sensors or software to be able to analyze two simultaneous forces, then this is an alternative to be used to give students an intuitive understanding of Newton’s 3rd Law. Organize your class into laboratory groups of three students. 1. These activities are again designed to have the students be able to identify the interacting force pairs. In a collection of three objects interacting with one another, it should be recognized that there are two combinations of pairs of forces and students should always be able to recognize them. The concept of tension on a string arises in situations as illustrated in this activity. Tension should be seen as forces acting in opposite directions within the same object imposed by two opposite forces on this object. Since tensions within the object are equal, then the two opposite forces on the object are also equal, but strictly speaking they are not the action-reaction pair of forces. 2. A pulley can be used to alter the direction of the applied force on a hanging mass. The upward tension needs to remain the same and the pulley only changes the direction of the force. Students should find that the direction of the applied force by the hand on the scale is always transmitted to an upward force by the string on the mass as a result of the pulley and hence, the angle the scale and connecting string makes with the UI:TG-Newton’s 3rd Law 8 hanging mass has no effect on the tension of the string. The scale should be oriented so that all forces are in the same plane. Sample Observations/Calculations The tension in the string should everywhere be equal to the weight of the mass suspended from the string. Developing and Using Scientific Ideas 1. What is true about the tension in the string when the mass is suspended from the string alone or placed over a pulley? Ans. The tension is the same, regardless of the direction the force is applied by the scale. The resulting tension on the mass remains upward by the same amount. 2. What happens to the reading on the scale when a rubber band is placed into the system? Ans. It remains the same. 3. How does the force that the earth exerts on your body compare to the force that your body exerts on the earth? Ans. They are equal and opposite in direction. 4. When a small car crosses the median of a highway and hits a semi-trailer truck head on, why is the driver of the car likely to be more severely injured compared to the driver of the semi truck? Ans. Only the forces on him/her, not by forces between the vehicles, determine the injury of the driver of the car. Damaging forces can be calculated by taking the product of the mass of the object being accelerated and the acceleration of the object. Extending the Activity 1. What affect does the length of the string have on the scale reading? Design and carry out an experiment to answer? Ans. The length of the string should have little or no effect if common string is used. The scale reading should be the same as before. If heavy cord (relatively large mass/unit length) is used, the scale reading will increase with length since the tension read by the scale would equal the sum of the weight of the mass and weight the string. 2. What affect does the mass of the string have on the scale reading? Design and carry out an experiment to answer? Ans. If common string is used, it should have little or no effect. The scale reading should be the same as before. If heavy cord (relatively large mass/unit length) is used and the length is the same as the original string, the scale reading will increase since the tension measured by the scale would equal the sum of the weight of the mass and the weight of the string. CONCEPTUAL PRACTICE UI:TG-Newton’s 3rd Law 9 Answer Key 1. A horse, on Earth’s surface, is hitched to a wagon and is starting to pull on the wagon. As the horse is pulling, the force of the horse on the wagon (Fh on w) is equal to the force of the wagon on the horse (Fw on h). Identify as many action/reaction forces as you can. Then explain whether it is possible for the horse to move the wagon and if so, how does that work. Ans. In addition to the force of the horse on the wagon (Fh on w) and wagon on the horse (Fw on h), there is the force of friction of the Earth’s surface on the wagon wheels and the horse’s feet and the force of friction of the wagon wheels and the horse’s feet on the Earth’s surface. There is the contact force (normal force) of the wagon wheels and horse down on the Earth’s surface and the normal force of the Earth’s surface pushing up on the wagon wheels and the horse. The Earth exerts a gravitational pull on the horse and wagon and the horse and wagon exert an equal and opposite gravitational force on the Earth. 2. You are observing a softball game at your school. The pitcher winds up and pitches a fastball and the batter takes a big swing and hits a tower fly ball high in the air that just clears the fence for a home run. Describe this event applying Newton’s laws to the motion of the softball described above. Focus on all the interactions of the softball with the named and implied objects in this event. Ans. When the pitcher throws the ball, her hand exerts a force on the ball and thus the ball exerts an equal but opposite force on her hand. The force on the ball causes it to accelerate while in contact with her hand. The force of the bat on the ball is equal but opposite to the force the ball exerts on the bat. The net force on the ball causes it to accelerate in the opposite direction over the wall. If the ball strikes an object over the fence, then that object exerts an equal and opposite force on the ball. During the entire event the Earth is pulling on the ball with a gravitational force and ball is pulling on the Earth with a force equal but opposite to this gravitational force. While the ball is in flight it collides with air molecules causing the ball to apply a force on the air molecules and the air molecules exert an equal but opposite force on the ball. 3. A student sits on a skateboard on a smooth level surface with a bowling ball in his hand. The mass of the bowling ball is 7.0 kg. His mass plus the mass of the skateboard is 120 kg. He applies a force of 150 N to the bowling ball throwing it in a direction parallel to the wheels. There is a frictional force between the skateboard and the walkway surface of 50 N. On a diagram show all the action/reaction forces. What acceleration will the student experience as a result of throwing the bowling ball? Ans. Fhand on ball Fball on hand Ff Earth on cart Ff cart on Earth Fwheels on surface Fgrav Earth on boy cart UI:TG-Newton’s 3rd Law 10 The student is part of the student-skateboard-wheels system. To determine what happens to the motion of this system, you look at all the forces acting on this system. Figure TG 11.5 illustrate all the action forces acting on the system and their reaction forces acting on other objects. The vertical forces on this system are the force of Earth’s gravity on the system and the force of the surface of the roadway on the student-skateboard-wheels system. These forces add to zero and hence, there is no vertical motion of the system. The horizontal forces on the system are force of the ball on the hand and the force of friction on the cart. The sum of these forces is the net force that causes the system to accelerate. astudent = (Fnet on student)/(mstudent) Fnet = Fapplied + Ffriction Fnet = 150 N + (-50 N) = 100 N a = (100 N)/(120 kg) = 0.83 m/s2 APPLICATION: BALLOON ROCKETS Lab setup easy moderate difficult Calculations easy moderate difficult Reliability excellent good fair Interest excellent good fair Lab time -1 class 1 class +1 class Process Skill A B C D E F Reasoning 1 2 3 4 5 Engaging the Students with Phenomena Materials Cylindrical balloons, tape, straws, paper clips, scissors, line(s) extending across the classroom to serve as a guide wire for launching the balloon rockets. Teaching Strategies 1. This activity needs little introduction when presented as a challenge. Allow the students to be creative in their rocket designs. Assign your class into laboratory groups of three students. Monofilament fishing line works well as a guide wire. The most efficient designs usually attach the balloon to a straw and slip the guide wire through the straw. Feel free to use additional materials as desired. It is fun to put out some of the most outrageous items for the students to ponder over. Paper cups, sheets of paper, aluminum foil, packing material, lightweight cardboard, etc are fun additions. Some teachers restrict each group to using the same materials and others do not use this restriction. Have fun! Students might design a two-stage rocket to make the return trip. It is acceptable to manually release the second balloon (manned space probe) to make a return trip possible. Or if you have some students ready for a change, this could simulate an unmanned effort. UI:TG-Newton’s 3rd Law 11 2. This is an excellent activity for which to design a competition. Teams of two or three students work well. You can set up a racing competition, or simply stage an event to reward the designs that travel the furthest. Certificates of accomplishment for the students will add to the fun. You can make the competition more of a challenge by making sure that the balloons have a smaller air capacity. Developing and Using Scientific Ideas 1. Why does your rocket move along the guide wire when the air escapes? Base your answer on your understanding of Newton's Second and Third Laws of Motion. Draw a diagram of your system. On your diagram, show a vector representing the force accelerating the rocket. What is the direction of this force? How do you know? Ans. In the balloon-air system, molecules are colliding with molecules and demonstrating action-interaction force pairs. Air molecules are also colliding with the rubber membrane of the balloon. The resulting forces acting on the balloon by the air molecules are illustrated in Figure TG 11.4. So there are also balloon-air action- reaction pairs of forces. When the end of the balloon is closed, the sum of all the forces on the balloon is zero. If this were not so, the balloon would accelerate. When the right end of the balloon is opened, then the balloon begins to accelerate to the left, indicating a net force is acting on the balloon to the left. Since some of the forces that were on the balloon at the right end now have no membrane to push against, their contribution Fnet to the total force on balloon is now zero, and Figure TG 1.11.4 hence there is a net force in the direction opposite to the open end of the balloon. 2. How do rockets work in outer space? Ans. The atmosphere is not pushing on the rocket to propel it. Surrounding air is not required for rocket motion. An actual rocket is expelling spent fuel. The rocket rushes backwards on the fuel; the fuel pushes forward on the rocket. If the rocket wishes to achieve a large acceleration, it will push out spent fuel as fast as possible. Extending the Activity 1. Which designs worked best? How would you modify your design if you had another chance to do this activity? Ans. Answers will vary, but see the Teaching Strategies section above for some ideas. Many students will talk about getting rid of the turning motion (and hopefully suggest ways to do so!) and their method of attaching the balloon to the straw. 2. Design and build a car powered by a balloon that will travel across the floor in your classroom. If you wanted the car to travel the greatest possible distance, what factors would be most important to consider? If instead, you wanted to build a car to achieve the greatest possible speed, how would your design be different? UI:TG-Newton’s 3rd Law 12 Ans. Answers will vary and will depend upon the amount of time devoted to the activity. Learning Cycle Teaching Notes WRAPPING IT UP Building a Case and Promoting Student Reflection This learning cycle is about Newton's Third Law of motion. As noted at the beginning, students have many misconceptions about this topic, especially when objects of different mass collide. Present the following list of activities and have the students identify the action-reaction pair of forces in each. Have the students do the exercise individually and then find another student and discuss their results. If any students cannot reach agreement, then be sure to help them understand the identification of the pair of forces. 1. A student standing on the floor Ans. The student pushes down on the floor and the floor pushes up on the student. Also the gravitational force of the earth on the student and the gravitational force of the student on the earth. 2. A bird flapping its wings Ans. The bird's wings push down on the air and the air pushes back up on the wings. 3. Raindrops hitting the roof Ans. The drops push down on the roof and the roof pushes back up on the drops. The earth pulls on the drop and the drop pulls on the earth. 4. The Earth and the moon Ans. The Earth pulls on the moon and the moon pulls on the Earth. Go back to the section called Setting The Stage for Student Learning and use the questions as a follow up discussion. Watch for any remaining evidence of misconceptions and correct them immediately. Extending Student Knowledge and Promoting Open Inquiry Evidence of Newton's Laws is seen in our everyday world with every motion taken. Coaches and participants make use of them all the time - often without realizing it. Have each student (or group) choose a sporting activity. Design a poster that shows how each of Newton's laws are illustrated by the sport. Display the posters for the class to see. Have students grade a poster from another group. This gives the students two chances to demonstrate their knowledge of all three of the Laws. UI:TG-Newton’s 3rd Law 13