04-Energy

04-Energy - Work& Kinetic Energy F = m a F v i m F v f m...

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Unformatted text preview: Work & Kinetic Energy F = m a F v i m F v f m v f 2 = v i 2 + 2ad F = m (v f 2- v i 2 )/ 2d W o rk F i n a l K i n e t i c E n e r g y In itia l K in e tic E n e rg y d a = (v f 2- v i 2 )/ 2d F d = ½ m (v f 2- v i 2 ) F d = ½ m v f 2- ½ m v i 2 W = (KE) f- (KE) i Work F m ∆x F m ∆x θ Fcosθ W = F ∆x W = (Fcosθ) ∆x W = F . ∆x W = Dot product of F times ∆x Only the component of F parallel to ∆x does work. Fcosθ does do work. Fsinθ does not do work. The component of F perpendicular to ∆x does no work. Work with a Variable Force F x Work = ∫ Fdx ∫ Fdx = Area under the graph of Force vs distance x F F = kx W = ∫ (-kx)dx W = -½ kx 2 This work is stored as potential energy. The potential energy can then be released as kinetic energy. Work = F∆x This is true if F is constant. If F is not constant. F s F s = -kx F S x Conservation of Energy Types of Energy KE = K = ½ mv 2 PE = U U g = mgh U S = - ½ kx 2 TE = Thermal Energy E = K + U + TE E’ = K’ + U’ + TE’ E’ = E K’ + U’ + TE’ = K + U + TE The unit of Work and Energy is the Joule (J). 1J = 1Nm Energy is defined as the ability to do work. Energy is a scalar. Work & Gravitational Potential Energy F h W = F d W = mgh PE = mgh (PE) i = 0 (PE) f = mgh (PE) B = 0 (PE) A = mgh h A v B (KE) A = 0 (KE) B = ½ mv 2 (PE) A + (KE) A = (PE) B + (KE) B (PE) A = (KE) B Conservative Gravitational Field...
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04-Energy - Work& Kinetic Energy F = m a F v i m F v f m...

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