Two different objects perhaps its not surprising that

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two different objects . Perhaps it’s not surprising that students find it so hard to identify action/reaction pairs! The major research paper on interacting systems is McDermott et al. (1994). As a first test, shown in the figure below, they asked students in the calculus- based course at the University of Washington to compare the tension at the point at which the string in (a) is attached to the wall to the tension in the middle of the string in (b). After students had finished studying Newton’s laws, only 50% answered correctly that the tensions are equal. Most students expected the tension in string (b) to be twice as large. 5 kg 5 kg 5 kg (a) (b) Two other questions involving tension are of interest. In the first, shown below, a person pulling on a string accelerates blocks A and B, connected by massless strings, across a frictionless surface. After noting that m B > m A , students were asked to compare the force exerted by string 1 on block A with the force exerted by string 2 on block B. Only 40% answered correctly that F 1 on A > F 2 on B . The other answers were divided between F 1 on A = F 2 on B because the tension in string 1 is somehow “transmitted” through block A to string 2. F 2 on B > F 1 on A because m B > m A , so it takes a larger force to accelerate block B. A B #2 #1 m B m A Pull Frictionless surface How does the force string 1 exerts on A compare to the force string 2 exerts on B? Neither response shows awareness that the tension in string 2 exerts a “backward” force on block A. Indeed, students giving these responses failed to show a force F 2 on A when asked to draw free- body diagrams. It’s also of interest to note that 15% of students, in a preliminary question, failed to recognize that blocks A and B must have the same acceleration. In the other tension question, shown here, block A can slide across a frictionless table when pulled by falling block B and a massless string. Initially, block A was held in place by someone’s hand. Students were asked how, or if, the tension in the string would change if the hand were removed. Only 25% of students, after studying Newton’s laws, answered correctly that the tension would decrease. Nearly all predicted no change. In a related question, 55% of students predicted that block B would fall with an acceleration of 9.8 m/s 2 . Interacting-system problems are difficult and frustrating for students. There are no magic formulas to search for, so students must correctly apply Newton’s second law to each object. But n r n r w r A B
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Chapter 8: Newton’s Third Law 8-3 even if they realize this to be the proper approach, they cannot succeed without first identifying all the interaction forces and then making proper use of the third law. Student Learning Objectives To learn how two systems interact.
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