Probing students critical thinking processes by presenting ill-defined physics problems

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3 PROBING STUDENTS CRITICAL THINKING PROCESSES BY PRESENTING ILL-DEFINED PHYSICS PROBLEMS 67 FIGURE 2. The tennis player. FIGURE 1. The girl with a balloon stands on the scale. 2. Problems The respondents were presented following problems 1 and 2 i : 1. Wishing to measure body mass, the girl stands on the scale and reads the value of 30 kg. If she takes a kids helium balloon in hand (Fig. 1), the scale shows the lower value. 1.1) What is the mass of the girl with a balloon that reads on the scale if buoyancy of the balloon is 100 N? (g 10 m/s 2 ) 1.2) Are the data in the problem realistic? Why? 2. The physics teacher gave his students the following problem: The tennis player serves a ball (Fig. 2) with the speed 36 m/s. A third of a second later, a poorly served ball stops suddenly at the net 12 m away. What is the stopping acceleration of the ball? (Air resistance is negligible.) What would you answer to him? To obtain the correct answer to question 1.1 the correct application of physics concepts and the following solving procedure is needed. The girl on a scale in Fig. 3 is in equilibrium because the two main forces acting on her in opposite directions with equal magnitudes, cancel out. The gravitational force F g is acting downwards, and the the reaction (normal) force F N upwards. Buoyancy force on the girl associated with the air pressure gradient is negligible, so the force F g is balanced by a force F N, i.e. F N = F g. The scale shows the mass of m = 30 kg due to the force that the girl is acting on the scale with the magnitude equal to the magnitude of the normal force: F N = F g = mg = 300 N. The forces acting on the girl after she took the balloon are shown in Fig. 4. The mass of the balloon is negigible, so that the gravitational force did not change. Now, the two forces are acting upwards. These are the buoyancy force on the balloon F B exerted by the air and the normal force F N which magnitude is now reduced. To calculate the modified mass m, that now reads on the scale, we find the net force

4 68 N. ERCEG, I. AVIANI, AND V. MEŠIĆ FIGURE 3. Sketch and a free-body diagram of a girl standing on a scale. acting on the scale when the girl holds a balloon. This force is equal to the difference between the gravitational force and the buoyancy (see Fig. 4) and is balanced by a normal force F N = F g F B = 200 N, so that the scale reads the modified, mass m = F N/g = 20 kg. To answer correctly to question 1.2, students should note that the result, although obtained using the correct physics, is unrealistic. It is not possible that after the girl took a balloon the scale shows the value that is as much as 10 kg less then before. Consequently, one should find out that the problem is not correctly set because the given value of 100 N for the buoyancy force of the kids hellium baloon is not realistic. The balloon volume should be V = F B /(ρ air g) 10 m 3, (1) which is obviously too much for a kids balloon. Since physical reasoning is based on a judgment of the significance of particular interactions, it is important to discuss why in the first case we neglect the buoyancy force and FIGURE 4. Sketch and a free-body diagram of a girl standing on a scale and holding a hellium balloon. in the second case not. While solving the problem situation, one should keep in mind the buoyancy force is exerting not only on the balloon, but also on the girl giving an additional contribution to the upward force ρ air g V girl = ρ air g (m/ρ girl ) = F g (ρ air /ρ girl ). Since the air density is about one thousand times less than the density of a human body, from the above expression it turns out that the buoyancy force is only about one thousandth that of the gravitational force and thus can be neglected. Here, it is worth noting the importance of neglecting the irrelevant contribution in physics. We are seeking for the explanation of the main effect, the one responsible for the observed phenomenon. Other effects should be neglected and included in consideration only if we study the effects they produce. In our case, the equilibrium of the scale is explained by considering the forces acting on the girl before and after she took the balloon. At first we neglect the air buoyancy on the human body, not measurable on a body scale. Even if we would have a highly accurate body scale, e.g. with 10 g res-

5 PROBING STUDENTS CRITICAL THINKING PROCESSES BY PRESENTING ILL-DEFINED PHYSICS PROBLEMS 69 FIGURE 5. Scans of selected student solutions: (a) for question 1.1 (b) for question 1.2 and (c) for question 2. olution, we would not be able to measure buoyancy because this would require removal of the air and use of the special space suit. Now, a question arises why in the second part of the task we consider the effect of the buoyancy force on the balloon that is equally small or even smaller than the buoyancy force on the girl which we have neglected. The explanation is as follows. We first consider the main forces acting on the girl in equilibrium. After she takes a balloon, a new, changed equilibrium is set up. This change is what we are interested in the second part of the task. As the change is due to the appearance of the buoyancy force of the balloon it can be explained only if we take this force into account, although in reality being very small. So, initially we should neglect buoyancy,

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