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I. INTRODUCTION One of the most interesting demonstrations for an introductory mechanics course is the Falling Chimney-Free Fall Paradox, as it was named by Sutton in his classical book Demonstration Experiments in Physics. In the original version of this demonstration a ball is placed at one end of a uniform stick, which is pivoted at the other end and makes initially an angle of about 30 with the horizontal. The elevated end of the stick is suddenly dropped together with the ball, thus showing a very counter-intuitive behavior. The falling end of the stick accelerates at a greater rate than the free-falling ball, proving that its acceleration is greater than g, the acceleration of gravity A simplified version of the experiment can be performed just with a meter stick and a coin. The stick is supported in the horizontal position by two fingers, placed near the two ends. a coin is set on the stick near one end, which is suddenly released. The effect is similar to the previous demonstration: the falling end of the rotating stick eventually acquires ar acceleration greater than that of the freely falling coin, which loses contact with the stick surface and lags behind the falling stick a description of the first version of the experiment can be found in almost every book of physics demonstrations, ,3,4 sometimes with different names("Falling Stick","Hinged Stick can be found on-line in several web-pages (see our web-page cn and Falling Ball", and others). Photographic descriptions or even video-clips of this demo or a collection of related links In addition, countless papers exist in the literature; we have traced several of these, from the 1930's to the present. Some of the earliest discussions can be found in Constantinides and Ludeke(as well in the book by Sutton), followed by many others. 8. 9, 10, 11,2These concentrate mostly on the simple explanation of the effect, which relies on the concept of "center of percussion"of the rotating stick(a simple introduction to this concept can be found in Bloomfield). This particular point of the stick (located at a distance from the hinged end equal to two thirds of the length, for a uniform stick) is moving with the same acceleration as a particle under gravity, constrained to move along the same circular path. Points on the stick beyond the center of percussion descend with accelerations greater than that of particles freely moving under gravity, on their respective circular paths. As a consequence of this, if the initial angle formed by the stick with the horizontal is less than about 35, the end point will possess at all times a vertical component of the acceleration greater than g, producing the effect described above Several variations of the basic demonstration also exist, 14, 15, 16, 17, 18, 19 the majority of which suggest attaching an additional mass to the rotating stick at different positions. The effect for the student or the viewer is even less intuitive than the original version: an additional mass placed near the end of the stick actually reduces the acceleration of the end point affecting substantially the outcome of the experiment. In general the addition of a mass at any point on the stick will increase both the total torque on the system(thus increasing th rotational acceleration) and the moment of inertia of the system around the axis of rotation (resulting in a decreased rotational acceleration). The center of percussion of the stick still plays a key role: if the additional mass is placed beyond it, the effect of the increased Momen of inertia dominates and the acceleration of the rotational motion will be reduced. If the placed before the center of percussion, the increase in the torque will dominate and the rotational motion will be enhanced. The effect is null if the mass is placed exactly at the center of percussion(a complete discussion of this effect can be found in BartlettandI. INTRODUCTION One of the most interesting demonstrations for an introductory mechanics course is the “Falling Chimney - Free Fall Paradox,” as it was named by Sutton in his classical book Demonstration Experiments in Physics.1 In the original version of this demonstration a ball is placed at one end of a uniform stick, which is pivoted at the other end and makes initially an angle of about 30◦ with the horizontal. The elevated end of the stick is suddenly dropped, together with the ball, thus showing a very counter-intuitive behavior. The falling end of the stick accelerates at a greater rate than the free-falling ball, proving that its acceleration is greater than g, the acceleration of gravity. A simplified version of the experiment can be performed just with a meter stick and a coin. The stick is supported in the horizontal position by two fingers, placed near the two ends. A coin is set on the stick near one end, which is suddenly released. The effect is similar to the previous demonstration: the falling end of the rotating stick eventually acquires an acceleration greater than that of the freely falling coin, which loses contact with the stick surface and lags behind the falling stick. A description of the first version of the experiment can be found in almost every book of physics demonstrations,2,3,4 sometimes with different names (“Falling Stick”, “Hinged Stick and Falling Ball”, and others). Photographic descriptions or even video-clips of this demo can be found on-line in several web-pages (see our web-page,5 for a collection of related links). In addition, countless papers exist in the literature; we have traced several of these, from the 1930’s to the present. Some of the earliest discussions can be found in Constantinides6 and Ludeke7 (as well in the book by Sutton1 ), followed by many others.8,9,10,11,12 These concentrate mostly on the simple explanation of the effect, which relies on the concept of “center of percussion” of the rotating stick (a simple introduction to this concept can be found in Bloomfield13). This particular point of the stick (located at a distance from the hinged end equal to two thirds of the length, for a uniform stick) is moving with the same acceleration as a particle under gravity, constrained to move along the same circular path. Points on the stick beyond the center of percussion descend with accelerations greater than that of particles freely moving under gravity, on their respective circular paths. As a consequence of this, if the initial angle formed by the stick with the horizontal is less than about 35◦ , the end point will possess at all times a vertical component of the acceleration greater than g, producing the effect described above. Several variations of the basic demonstration also exist,14,15,16,17,18,19 the majority of which suggest attaching an additional mass to the rotating stick at different positions. The effect for the student or the viewer is even less intuitive than the original version: an additional mass placed near the end of the stick actually reduces the acceleration of the end point, affecting substantially the outcome of the experiment. In general the addition of a mass at any point on the stick will increase both the total torque on the system (thus increasing the rotational acceleration) and the moment of inertia of the system around the axis of rotation (resulting in a decreased rotational acceleration). The center of percussion of the stick still plays a key role: if the additional mass is placed beyond it, the effect of the increased moment of inertia dominates and the acceleration of the rotational motion will be reduced. If the mass is placed before the center of percussion, the increase in the torque will dominate and the rotational motion will be enhanced. The effect is null if the mass is placed exactly at the center of percussion (a complete discussion of this effect can be found in Bartlett17 and 2
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