Lecture24-2A

Lecture24-2A - Chapter 14 Chapter 14 Static Equilibrium II Static Equilibrium II Chapter 15 Chapter 15 Oscillatory Motion Oscillatory Motion

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Unformatted text preview: Chapter 14 Chapter 14 Static Equilibrium II Static Equilibrium II Chapter 15 Chapter 15 Oscillatory Motion Oscillatory Motion onditions for Equilibrium onditions for Equilibrium A body is in static equilibrium when it is stationary and when both the net external force and the net external torque are zero! i F i and i i If the tension in the support cable does not act at the center of gravity for the beam and the worker then the beam will rotate! Not good! For static equilibrium we also have i p i net R cm M g xample: Teeter xample: Teeter-- Totter Totter Consider a teeter-totter as shown in the figure. If a child of mass m is a distance x from the fulcrum and the weight of mass M is a distance y , what is the ratio of x / y for the teeter-totter to be in equilibrium? As usual we must first choose an origin from which to find the torques. First we consider the fulcrum as the origin: The larger the mass M , the further the child must sit from the fulcrum. Now choose the location of the weight as the origin. The normal force at the fulcrum must equal the weight of the child and the mass M . Hence: mgx Mgy x / y M / m g x y M m gy mx My This leads to the same result. What if the board is at an angle q wrt the horizontal? Example: Crane Equilibrium xample: Crane Equilibrium Consider the crane as shown in the figure. The boom is supported by a cable attached to its center point. Find the tension in the cable when angle of the boom is 50 o above the horizontal and the mass of the boom is 1700kg. The hanging mass is 2200kg . Summing torques about the pivot point P : T 9sin50 1700 g 9cos50 2200 g 18cos50 Solving for T : T 4400 1700 sin50 9.8cos50 50 kN Again the normal forces at the pivot balance all of the forces. xample: Tip or Slide, that is the Question. xample: Tip or Slide, that is the Question. A rectangular block, twice as high as it is wide, is resting on an incline with an angle q and a coefficient of static friction m . What condition on m will cause the block to slide before it tips? The maximum torque resulting from the normal force occurs when the normal force acts at the lowest edge of the block. If the torque from the gravitational force is greater than this restoring torque, the block will tip!...
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This note was uploaded on 04/16/2008 for the course PHYS PHYS2A taught by Professor Hicks during the Spring '08 term at UCSD.

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Lecture24-2A - Chapter 14 Chapter 14 Static Equilibrium II Static Equilibrium II Chapter 15 Chapter 15 Oscillatory Motion Oscillatory Motion

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