Forces and Interactions
Defining Your System
Action and Reaction on Different Masses
Summary of Newton
Vectors
Force Vectors
Velocity Vectors
Components of Vectors
Up to here a force is seen as a push or a pull. Newton
In discussing action and reaction emphasize the word “between.” The forces between the Earth and Moon, for example.
This is the shorter of the three chapters on Newton
The student supplement Problem Solving in Conceptual Physics has a section on trigonometry, followed by problems that make use of lightweight trigonometry.
There are 3 OHTs for this chapter: Figures 5.7, 5.22, and 5.27-5.29.
In the Practicing Physics book:
• Action and Reaction Pairs • Force and Velocity Vectors
• Interactions • Force Vectors and the Parallelogram Rule
• Vectors and the Parallelogram Rule • Force-Vector Diagrams
• Velocity Vectors and Components • More on Vectors
In the Next-Time Questions book:
• Reaction Forces • Leaning Tower of Pisa
• Apple on a Table • Apple on Table
• Scale Reading
• Tug of War • Airplane in the Wind
• Tug of War 2 • No-Recoil Cannon
SUGGESTED LECTURE PRESENTATION
Forces and Interactions
Hold a piece of tissue paper at arms length and ask if the heavyweight champion of the world could hit the paper with 50 pounds of force. Ask your class to check their answer with their neighbors. Then don’t give your answer. Instead, continue with your lecture. Reach out to your class and state, “I can’t touch you, without you touching me in return—I can’t nudge this chair without the chair in turn nudging me—I can’t exert a force on a body without that body in turn exerting a force on me.” In all these cases of contact there is a single interaction between two things—contact requires a pair of forces, whether they be slight nudges or great impacts, between two things. This is Newton
Extend your arm horizontally and show the class that you can bend your fingers upward only very little. Show that if you push with your other hand, and thereby apply a force to them, or have a student do the same, they will bend appreciably more. Then walk over to the wall and show that the inanimate wall does the same (as you push against the wall). State that everybody will acknowledge that you are pushing on the wall, but only a few realize the fundamental fact that the wall is simultaneously pushing on you also—as evidenced by your bent fingers.
Do as Linda E. Roach does and place a sheet of paper between the wall and your hand. When you push on the paper, it doesn’t accelerate—evidence of a zero net force on the paper. You can explain that in addition to your push, the wall must be pushing just as hard in the opposite direction on the paper to produce the zero net force. Linda recommends doing the same with an inflated balloon, whereupon your class can easily see that both sides of the balloon are squashed.
CHECK QUESTION: Identify the action and reaction forces for the case of a bat striking the ball.
Action and Reaction on Different Masses
Discuss walking on the floor in terms of the single interaction between you and the floor, and the pair of action and reaction forces that comprise this interaction. Contrast this to walking on frictionless ice, where no interaction occurs. Ask how one could get off a pond of frictionless ice. Make the answer easy by saying one has a massive brick in hand. By throwing the brick there is an interaction between the thrower and the brick. The reaction to the force on the brick, the recoiling force, sends one to shore. Or without such a convenient brick, one has clothing. Or if on clothing, one has air in the lungs. One could blow air in jet fashion. Exhale with the mouth facing away from shore, but be sure to inhale with the mouth facing toward shore.
CHECK QUESTION: Identify the force that pushes a car along the road. [Interestingly enough, the force that pushes cars is provided by the road. Why? The tires push on the road, action and the road pushes on the tires, reaction. So roads push cars along. A somewhat different viewpoint!]
Most people say that the Moon is attracted to the Earth by gravity. Ask most people if the Earth is also attracted to the Moon, and if so, which pulls harder, the Earth or the Moon? You’ll get mixed answers. Physicists think differently than most people on this topic: Rather than saying the Moon is attracted to the Earth by gravity, a physicist would say there is an attractive force between the Earth and the Moon. There is an important difference here.
Asking if the Moon pulls as hard on the Earth as the Earth pulls on the Moon is similar to asking if the distance between New York and Los Angeles is the same as the distance between Los Angeles and New York New York and Los Angeles
Support this point by showing your outstretched hand where you have a stretched rubber band between your thumb and forefinger. Ask which is pulling with the greater force, the thumb or the finger. Or, as you increase the stretch, which is being pulled with more force toward the other—the thumb toward the finger or the finger toward the thumb. After neighbor discussion, stress the single interaction between things that pull on each other. The Earth and the Moon are pulling on each other. Their pulls on each other comprise a single interaction. This point of view makes a moot point of deciding which exerts the greater force, the Moon on the Earth or the Earth on the Moon, or the ball on the bat or the bat on the ball, et cetera. Pass a box of rubber bands to your class and have them do it.
DEMONSTRATION: Tug of war in class. Have a team of women engage in a tug of war with a team of men. If you do this on a smooth floor, with men wearing socks and women wearing rubber-soled shoes, the women will win. This illustrates that the team who wins in this game is the team who pushes harder on the floor.
Discuss the firing of a bullet from a rifle, as treated in the chapter. Illustrate Newton’s 3rd law with a skit about a man who is given one last wish before being shot, who states that his crime demands more punishment than being struck by a tiny bullet, who wishes instead that the mass of the bullet match the magnitude of his crime (being rational in a rigid totalitarian society), that the mass of the bullet be much much more massive than the gun from which it is fired—and that his antagonist pull the trigger!
Return to your question about whether a heavyweight boxer could hit a piece of tissue paper with a force of 50 pounds or so. Now your class understands (hopefully) that the fist can’t produce any more force on the paper than the paper exerts on the fist. The paper doesn’t have enough mass to do this, so the answer is no. The fighter can’t hit the paper any harder than the paper can hit back. Consider solving Problem 1 in the end matter here.
Philosophically we know that if you try to do one thing, something else happens as a result. So we say you can never do only one thing. In this chapter we similarly see that you can never have only one force.
Defining Your System: Discuss the different systems of orange and apple as in Figures 5.8-5.11. This practice will be useful in analyzing momentum in the next chapter (a practice sheet on systems, oriented to momentum conservation, is in the Practice Book).
Vectors: State that if one were sitting next to a physicist on a long bus ride, and the physicist attempting to explain some physical idea on the back of an envelope, that the physicist would likely make extensive use of little arrows. These little arrows, that illustrate size and direction, are part of a physicist’s language. They are vectors. Then explain how vectors make the ground speed of an airplane flying in the wind easier to understand—flying with the wind, against the wind, and then cross wind. Avoid information overload by avoiding cases that aren’t parallel or at right angles to the wind.
Consider the Next-Time Question on the airplane flying in a cross wind. The resulting speed can only be found with vectors. The only vector tools the student needs is the parallelogram rule, and perhaps the Pythagorean Theorem. Avoid sines and cosines unless your students are studying to be scientists or engineers. Here we distinguish between physics and the tools of physics. Tools for pre-engineers and scientists only. Physics for everybody!
The parallelogram rule, as shown applied in Figure 5.26 (Nellie Newton), is instructive. Present variations of this figure and guide your class to solutions.
DEMONSTRATION: Have two students hold the ends of a heavy chain. Ask them to pull it horizontally to make it as straight as possible. Then ask what happens if a bird comes along and sits in the middle (as you place a 1-kg hook mass on the middle of the chain!). What happens if another bird comes to join the first (as you suspend another 1-kg mass)? Ask the students to keep the chain level. Now what happens if a flock of birds join the others (as you hang additional masses). This works well!
Explain the above via the parallelogram rule (as shown in the Practice Pages). The chain must be directed slightly upward to provide the needed vertical components to offset the weight.
Force and Velocity Vectors
Have your students have a go at the vector exercises in the Practicing Physics book. Take care to avoid force and velocity vectors on the same diagram. Having both on a vector diagram is an invitation to confusion—what you don’t need. On the Practicing Physics box in the chapter, Boat A takes the shortest path to the opposite shore, Boat B reaches the opposite shore first, and the faster ride is provided by Boat C. Vectors giving these answers are obtained with the parallelogram rule. Note this is duplicated on page 13 in the Practice Book.
Components of Vectors
For components of vectors, again, the Practicing Physics worksheet on page 27 is instructive. The notion of component vectors will be useful in following chapters, particularly Chapters 6 and 10.
Appendix D nicely extends vectors, and describes the interesting case of a sailboat sailing into the wind. This and the crossed Polaroids later in Chapter 29 are to my mind, the most intriguing illustrations of vectors and what they can do. An interesting demo is the model sailboat which you can easily build yourself with a small block of wood and a piece of aluminum. Cut slots in
the wood and mount it on a car (or ideally, on an air track). A square-foot sheet of aluminum serves as a sail, and wind from a hand-held fan is directed against the sail in various directions. Most impressive is holding the fan in front, but off to the side a bit, so that the cart will sail into the wind. This is indeed an excellent vehicle for teaching vectors and their components!
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