StaticsStatic EquilibriumStatic ForcesOffset ForcesStatic TorquesPivot PointThe LeverHuman LeverStabilityStaticsStaticsStatic EquilibriumStatic EquilibriumThere are three conditions There are three conditions for static equilibrium.for static equilibrium.1.1.The object is at restThe object is at rest2.2.There is no net forceThere is no net force3.3.There is no net torqueThere is no net torque0v0F0FrStatic ForcesStatic ForcesWith no motion, forces must With no motion, forces must sum to zero.sum to zero.•Each component is treated Each component is treated separatelyseparatelyFind the tension in the ropes.Find the tension in the ropes.•TT is the tension to the left is the tension to the left•SS is the tension to the right is the tension to the right•WW is the weight downward is the weight downwardVertical equalityVertical equality•TT sin sin = = WW = = mgmg•T = mg / T = mg / sinsin= 3.9 x 10= 3.9 x 1033 N NHorizontal equalityHorizontal equality•S = TS = T cos cos = 3.4 x 10 = 3.4 x 1033 N Nm = 200 kg = 30ºOffset ForcesOffset ForcesBalanced forces do not insure static equilibrium.Balanced forces do not insure static equilibrium.The center of mass is stationary, but the object The center of mass is stationary, but the object rotates.rotates.F-FStatic TorquesStatic TorquesWith no rotation, torques With no rotation, torques must sum to zero.must sum to zero.A ladder leans against a wall A ladder leans against a wall with friction against the floor.with friction against the floor.•Length Length ll•Angle Angle •Coefficient of static friction Coefficient of static friction The sum of torques givesThe sum of torques gives-mgFNWFNF = mgFfr mg21tantan2/0sincos)2/(mgFFmglFlmgNWfrNWPivot PointPivot PointThe calculation of torques is The calculation of torques is independent of the pivot point.independent of the pivot point.Select the wall for the pivot.Select the wall for the pivot.-mgFNWFNF = mgFfr mg21tan2/tan0sincos)2/(cosmgmgmgllmgmglThe LeverThe LeverThe lever is a simple The lever is a simple machine that increases machine that increases force.force.The downward force is The downward force is multiplied by the lever arm of multiplied by the lever arm of the stick to become a torque.the stick to become a torque.The torque on the rock The torque on the rock matches the torque from the matches the torque from the person.person.Human LeverHuman LeverThe elbow joint is a pivot point for a The elbow joint is a pivot point for a lever.lever.•Assume all forces are vertical.Assume all forces are vertical.•Levers may not reduce force.Levers may not reduce force.N 330N 400/)(00BAMJMBBAAMBBAAMMBAJMFFFFxFxFxFFxFxFxFFFFStabilityStabilityWhen is an object in static equilibrium?When is an object in static equilibrium?•Check the forces and torquesCheck the forces and torques•If the torques are from gravity, find the center of massIf the torques are from gravity, find the center of
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