A Simple Classroom Demo for helping students understand the affect of air resistance on a falling object Andrew Sannes Department of Physics State University of New York College at Buffalo 1300 Elmwood Avenue Buffalo NY 14222 amsannes yahoo com Keywords book drop freefall air resistance gravity Logger Pro PACS codes 01 50 ht 01 50 My 01 55 b 01 65 g 45 20 da 45 40 Aa Abstract In introductory mechanics problems involving falling objects we usually neglect air resistance though many instructors and students are unable to decide when and why this is a legitimate approximation These book and paper drop demonstrations help students analyze the forces acting on a falling object in a concrete situation Four discrete demos and teacher discourse strategies are described with web accessible video freely available for download The videos can be subjected to video analysis to allow the teacher and students to determine g Acknowledgements The manuscript attached was completed to fulfill requirements for Physics 690 at SUNY Buffalo State College and was partially supported by NSF DUE 0302097 supervised by Dan MacIsaac The video was filmed and edited by Patrick A Trinkley Paul J Smith and Kenneth C Giangreco of the Instructional Resources Department at SUNY College at Buffalo Errors and omissions are the responsibility of the author The Wu Li Master does not speak of gravity until the student stands in wonder at the flower petal falling to the ground He does not speak of laws until the student on his own says How strange I drop two stones simultaneously one heavy and one light and both of them reach the earth at the same moment He does not speak of mathematics until the student says There must be a way to express this more simply 1 According to Gunstone and White2 of 131 university students who predicted that an iron sphere and a plastic sphere of the same diameter would take an equal amount of time to travel the same freefall distance only 7 referred to personal experience as the basis of their knowledge 21 invoked Galileo as an authority Most of the 131 simply asserted that all things fall at the same rate For students to extend their conceptual understanding of freely falling objects beyond a reliance on authority they must carefully analyze the various forces acting on the objects to gain a better understanding of how air resistance impacts falling objects Air resistance is neglected in introductory kinematics problems to help simplify models of motion and allow students to see the underlying mechanics of motion specifically for freely falling objects Traditionally a guinea and feather tube is used for this demonstration Alternatively the following series of simple demonstrations involving a piece of paper and a textbook can be performed by students and teachers in the classroom are more accessible to students and can open up a discussion about freefall that can enrich the depth of student understanding beyond simply statements like all objects fall at the same rate in a vacuum I have created a video of four demonstrations that can be used as a catalyst for the discussion of forces freefall and air resistance or as a model for teachers to guide their own live demonstration After analysis of these four situations instead of simply reciting that all objects fall at the same rate students should understand that the rate at which an object falls depends on the sum of all the forces acting on the object namely the drag force and the force of gravity and that in some cases air drag becomes trivial Videos of these demonstrations are freely available online at http PhysicsEd BuffaloState edu pubs PHY690 Sannes2004AirRes Videos 8Mar05 The only materials required for these demonstrations are a table or chair to stand on a book and several pieces of paper The video is an elaboration of a demonstration noted by Ed and Rosea van den Berg3 The demonstrations consist of a series of four drops in which a physics textbook chosen to be approximately 1000 pages and of roughly 8 5 x 11 dimensions is dropped at the same time as a sheet of paper with similar surface area The textbook can therefore be claimed to be rudely 103 times more massive than the piece of paper while air resistance can be claimed to be similar for both objects Student attention has to be explicitly drawn to these ideas of similar air resistance but radically differing masses for both objects The demonstration drops are carried out in a fashion similar to Sokoloff and Thornton s Interactive Lecture Demonstrations or ILDs 4 The first drop demonstrates the importance of surface area Holding up the flat unfolded piece of paper and the physics textbook tell your students that both objects will be dropped from the same height at the same time and ask them Which object will reach the ground first and why After students have made individual and small group predictions and some have shared with the whole class the instructor should crumple the paper into a ball and drop both objects After both objects fall to the ground at the same rate your students can begin a discussion of what occurred and why and how merely changing the surface area of the paper had such an effect on the outcome of the drop After the surface area issue has been raised drop both the paper and book but do not crumple up the paper The paper will waft gently to the floor following a chaotic zigzag motion while the book will plummet straight to the ground At this time it would be appropriate to have the class create free body diagrams of the forces acting upon both objects and in both situations See Figure 1 and 2 by themselves To help guide the discussion ask questions such as why did the book fall faster than the flat piece of paper After students have created their own diagrams the students should break up into groups and whiteboard a free body diagram of both objects just after the moment of release for both situations This should help them to see that the magnitude of the drag force is similar for both objects but that the force of the earth on the book colloquially the weight of the book is 1000 times greater than the force of the earth on the paper This point may cause trouble for some students because they may reason that if the force acting on one object is 1000 times greater than the force acting on another object how could they fall at the same rate Students often miss the idea that a textbook that is 1000X more massive than a sheet of paper requires 1000X as much net
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