Static Equilibrium and Elasticity PHYS116 A03 31312 Lecture

Static Equilibrium and Elasticity PHYS-116 A-03, 3/13/12, Lecture 15 Momchil Velkovsky

Conditions for equilibrium • The sum of all forces present in the x, y, and z directions are each distinctly equal to zero. • The sum of all torques for any given point are equal to zero.

Which of the following situations satisfy both the first condition for equilibrium (net force = 0) and the secondition for equilibrium (net torque = 0)? 1. an automobile crankshaft turning at an increasing angular speed in the engine of a parked car 2. a seagull gliding at a constant angle below the horizontal and at a constant speed 3. a thrown baseball that does not rotate as it sails through the air 4. more than one of the above 5. none of the above

A rock is attached to the left end of a uniform meter stick that has the same mass as the rock. How far from the left end of the stick should the triangular object be placed so that the combination of meter stick and rock is in balance? 1. 2. 3. 4. 5. less than 0. 25 m between 0. 25 m and 0. 50 m more than 0. 50 m

A metal advertising sign (weight w) is suspended from the end of a massless rod of length L. The rod is supported at one end by a hinge at point P and at the other end by a cable at an angle q from the horizontal. Which of these forces is least? • • A. the weight of the sign B. the tension in the cable C. the vertical force component exerted on the rod by hinge P D. two or more of these are tied for greatest

Solving rigid-body equilibrium problems

Stable and unstable equilibrium

The ladder against a wall

Daily Physics Joke An interesting example how words can be used for quantitative measurements was presented by a Chicago University professor. His students didn’t know if the voltage of the power supply they were going to use was 110 V or 220 V. They didn’t have a voltmeter handy, so the professor told them just to touch the leads. “But I’ll just get a shock and that’s it, ” protested the student. “Yes, but if it is 110 V, you’ll just say ”Oh, damn!” and if it was 220 V, you will use a stronger expression!” The next day a student told his colleagues “This morning I met a fellow on the street, who apparently had been connected to 440 V!”

Elastic moduli (stretching in one, two, and three dimensions)

F Two rods are made of the same kind of steel and have the same diameter. F length L F length 2 L A force of magnitude F is applied to the end of each rod. Compared to the rod of length L, the rod of length 2 L has • • • A. more stress and more strain. B. the same stress and more strain. C. the same stress and less strain. D. less stress and less strain. E. the same stress and the same strain. F

F Two rods are made of the same kind of steel. The longer rod has a greater diameter. F length L F length 2 L A force of magnitude F is applied to the end of each rod. Compared to the rod of length L, the rod of length 2 L has • • • A. more stress and more strain. B. the same stress and more strain. C. the same stress and less strain. D. less stress and less strain. E. the same stress and the same strain. F