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# ch9 - Static Equilibrium Chapter Outline GENERAL PHYSICS...

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Unformatted text preview: Static Equilibrium Chapter Outline GENERAL PHYSICS PHY 302K Statics of Rigid Bodies The Conditions for Equilibrium Chapter 9: Static Equilibrium Examples of Static Equilibrium Maxim Tsoi Physics Department, The University of Texas at Austin http://www.ph.utexas.edu/~tsoi/302K.htm 302K: Ch.9 302K: Ch.9 The Conditions for Equilibrium The Conditions for Equilibrium Static equilibrium 1. Scalar equations of static equilibrium The resultant external force must equal zero: F 0 F 0 0 F If all forces lie in the xy plane Translational equilibrium 2. In general x 0 6 scalar equations F y 0 z 0 If an object is in translational equilibrium and the net torque is zero about one axis then the net torque must be zero about any other axis The resultant external torque about any axis must be zero: 0 O r1 F1 r2 F2 r3 F3 ... O ' r1 r ' F1 r2 r ' F2 r3 r ' F3 ... r1 F1 r2 F2 r3 F3 ... r ' F1 F2 F3 ... Rotational equilibrium 302K: Ch.9 302K: Ch.9 The Center of Mass The Center of Mass Special point How to determine the center of mass? • The center of mass of the system moves as if all the mass of the system were concentrated at that point • Coordinate of the center of mass: xCM m1 x1 m2 x2 m1 m 2 xCM mi xi i m i • An experimental technique for mi x i rCM i M mi ri i M i • Thinking of extended object as a system of a large m i 0 x m i i M wrench: The wrench is hung freely first from point A and then from point C. The intersection of the two lines number of particles: xCM lim determining the center of mass of a i rCM lim m i 0 r m i AB and CD locates the center of i mass i M • The center of mass of any symmetric object lies on an axis of symmetry and on any plane of symmetry 302K: Ch.9 302K: Ch.9 1 Center of Gravity Rigid Objects in Static Equilibrium Point of application of the gravitational force Examples • The center of gravity is located at the center of mass Balanced mechanical system as long as g is uniform over the entire object • Center of mass: xCM mx m1 x1 m2 x2 m3 x3 ... i i i m1 m2 m3 ... mi i • Center of gravity: m1 g1 m2 g2 m3 g3 ...xCG m1 g1 x1 m2 g2 x2 m3 g3 x3 ... for g=const xCG When working static equilibrium problems recognize all the external forces acting on the object! m1 x1 m2 x 2 m3 x 3 ... xCM m1 m2 m3 ... 302K: Ch.9 302K: Ch.9 Example 1-5 SUMMARY Static Equilibrium • A rigid object is in equilibrium only if the resultant external force acting on it is zero and the resultant external torque on it is zero about any axis: F 0 0 • The center of gravity is located at the center of mass as long as g is uniform over the entire object xCG m1 x1 m2 x 2 m3 x 3 ... xCM m1 m2 m3 ... 302K: Ch.9 2 ...
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