Instructors_Guide_Ch08

# The truck and the box have separate propulsion forces

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the truck and the box have separate propulsion forces, but both are static friction acting in the forward direction. These exercises show that the members of an action/reaction pair act in opposite directions. But what about the magnitudes of these forces? Unfortunately, it isn’t easy to provide a demonstration of the equal magnitudes. By far the most convincing demonstration I know of is the colliding-force- probe experiment from Thornton, Sokoloff, and Law’s RealTime Physics . Two low-friction carts of very different masses are pushed toward each other such that the collision occurs between the tips of their respective force probes. This gives instant and dramatic confirmation that the forces between two colliding carts are always equal in magnitude, regardless of the masses or the initial velocities of the carts. A simpler demonstration is to have two students of different size push against each other with bathroom scales, each calling out the reading on “their” scale as they move forward or backward. Lacking these, you’re forced to assert the third law as a hypothesis that will be tested on the basis of its predictions about the motions of interacting systems. DAY 2: The idea of tension as “pulling in both directions” is easier if the first day has called attention to the “backward” reaction force when one object pushes a second. Start by asking students to compare the tension in two ropes: one is tied to the wall and pulled by a student with a 100 N force, the other is pulled by two students in a tug-of-war as each pulls with a 100 N force. Research has shown that most students expect the tension in the tug-of-war rope to be twice as large because “it’s Spring scale 5 kg 5 kg 5 kg

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Chapter 8: Newton’s Third Law 8-7 being pulled twice as hard.” It’s good to demonstrate the equal tensions by using spring scales in a set-up such as that shown in the figure. Then have students go through the force analysis, making an imaginary division of the rope into two halves so that they can see the tension force as “holding the rope together.” You can present examples in which students are asked to compare or to rank the sizes of various forces. The McDermott et al. questions discussed in the Pedagogical Approaches section are all worth pursuing. There are similar exercises in the Student Workbook , some of which could be done in class. To the extent possible, demonstrate these question with real blocks and strings, using spring scales to ascertain the size of the forces. There’s nothing like reality to help convince students that two forces are, or are not, equal! You can end the second day with a discussion of the massless string approximation. Arons (1990) suggests a good example in which an initial mathematical analysis using the third law helps to reveal the role of the string’s mass. As shown below, a string of mass m S is used to accelerate a block of mass m B across a frictionless surface. It is straightforward to show that T 1 T 2 = 1 + m S m B , although students would never think of casting the result in this form. Now it’s easy to see what happens as m S 0. This can lead into a discussion of how two objects interacting through a
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