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Center of Gravity The point at which the sum of the weights of all particles that compose the matter may be concentrated. How to Determine the Center of Gravity 1. Uniform objects – geometric center 2. Non uniform objects – by hanging or plumb-line method 3. CG outside the body – the weight of the object can still be considered to act at this point even if it is not on the body of the object. Example, hanger, ring, doughnut Equilibrium An object is said to be in equilibrium if it is in a state of balance States of equilibrium 1. Stable – the object cannot be easily toppled down 2. Unstable – the object can be easily toppled down 3. Neutral – the object can roll from one side to the other Factors that Affect Equilibrium Conditions Position of center of gravity – the lower the center of gravity, the more stable 2. Area of the base – the wider the base, the more stable 3. Mass of the object – the higher the mass, the more stable 1. Conditions of Equilibrium 1st Condition – the sum of all forces = 0 2nd condition – the sum of the torques = 0 Torque (τ) = product of the force and lever arm τ = Fxl Sample Problems A car weighing 2000N on a bridge is 6.0m from one end of the bridge piers and 4.0 m from the other. How much force does each pier of the bridge exert to support the car? 2. A 75 kg adult sits at one end of a 9.0 m long board. His 25-kg child sits on the other end. a. Where should the pivot be placed so that the board is balanced (neglecting the board’s mass) b. Find the pivot point if the boarddis uniform and has a mass of 15.0 kg. 1. Sample Problems 3. A girl weighing 450N sits on one end of a seesaw that is 3.0m long and is pivoted 1.3m from the girl. If the seesaw is just balanced when a boy sits at the opposite end, what is his weight in N? (Neglect the weight of the seesaw) Assignment 1. A farmer sells sweet potatoes in the market. He and his son place sweet potatoes in a sack and carry it on a uniform piece of bamboo, 3.0 m long. The bamboo weighs 19.6N and the sack with potatoes weighs 490N. The farmer carries a load of 294N. (The bamboo is carried at the ends by the farmer and the son) Determine: a. the load carried by the son b. how far from the farmer’s end should be load be placed? Assignment 2. Three children are trying to balance a seesaw which consists of a fulcrum rock, acting as a pivot at the center and a very light board 3.6 m long. Two playmates are already on either end. Boy A has a mass of 50 kg and girl B has a mass of 35 kg. Where should girl C, whose mass is 25 kg. place herself so as to balance the seesaw.