Atwood’s Machine without Hanging Masses

Atwood’s machine is presented in introductory physics courses as an exercise in the simultaneous solution of Newton’s second law for translational and rotational motions, assuming the pulley has nonnegligible mass. Occasionally it is also used as a lecture demonstration or for quantitative laboratory measurements of a system undergoing constant acceleration. As discussed in this paper, one can progressively simplify the apparatus while maintaining these pedagogical goals, to end up with an easy way to measure the value of the freefall acceleration, g, by counting to ten. Atwood’s machine consists of two hanging weights, of masses m1 and m2, at opposite ends of an ideal string (i.e., which is massless and does not stretch) passing around a pulley, as sketched in Fig. 1. Suppose that the pulley has moment of inertia I and radius r (at the location where the string passes around it), that the bearings of the pulley on its axle are frictionless, and that the string does not slip on the pulley. There are at least three pedagogical reasons that time is devoted in introductory physics classes to analyzing Atwood’s machine. First, as an example of constructing free-body diagrams and deducing the relevant equations from them, it is an instructive application of both the translational ( F = ma ) and rotational ( = I ) forms of Newton’s second law. Second, it furnishes mathematical practice in the simultaneous solution of linear equations, a skill that physics students will need repeatedly (e.g., when Kirchhoff’s rules of circuit analysis are encountered). Finally, Atwood’s machine (or some straightforward modification of it) is often used in the laboratory as an experimental Selected by the Chesapeake Section of the American Association of Physics Teachers as the best presentation by a 4-year college faculty member at the Fall 2005 meeting. Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 2006 2. REPORT TYPE 3. DATES COVERED 00-00-2006 to 00-00-2006 4. TITLE AND SUBTITLE Atwood’s Machine Without Hanging Masses 5a. CONTRACT NUMBER