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Work, Energy and Power
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Work Work is done when a force moves a body Work = force X distance Unit : The Joule Example : How much work is it to lift a 20 kg mass vertically 6.5m? Force = Weight = 20 X 9.8 = 196 N Work = Force X Distance = 196 X 6.5 = 1274 J
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Calculate the work done climbing the ladder.
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Example Find the work done bringing a 3000Kg car from 30m/s to rest in 10s. Work = force X distance Force = decelerating force = ma Need to find acceleration and distance v2 = u2 + 2as 02 = (3)(s) 6S = 900 S = 150m Work = F X S = 9000 X 150 Work= J u=30 t = 10 v = 0 v=u+at 0=30 +(a)(10) 10a = -30 a=3m/s2 F = 3000 X 3 F = 9000N
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Energy Energy is the ability to do work. Unit : Joule Kinetic energy is energy due to movement. Kinetic Energy = ½ mass x (speed)2 = ½ mv2
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Potential energy is energy due to
position or condition Potential Energy = mass X g X height
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The Principle of conservation of energy.
Energy cannot be created or destroyed but is converted form one form to another. Example: The highest point reached by a child on a swing is 1.5m. Calculate their maximum speed.
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Power Power is the rate at which work is done Power = Unit : Watt Example A weight lifter can lift 30Kg through a height of 60cm. He does this 100 times a minute. Find his average power. Work = Force X Distance = Weight X distance (30)(9.8) X 0.6 = J for one lift 17640 J for 100 lifts Power = = W 60
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Efficiency Percentage Efficiency = Power Output X 100 Power Input
Example An engine has an input power of 4500W and the useful power is 3000W. Calculate it percentage efficiency. Percentage Efficiency = 3000 X 100 = 66.67% 4500
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Example A crane with a 60kW motor lifts a mass of 4000kg a height of 10m in 20s. Calculate the percentage efficiency of the crane. Power output = work = force x distance Time Time = 4000x9.8x10 = W 20 % Efficiency = x 100 = 32.67% 60000
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