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Chapter IV Work and Energy A. Work Done by a Constant Force B. The Work-Energy Theorem C. Work Done by a Varying Force or on Curved Path D. Power E. Gravitational Potential Energy and Elastic Potential Energy F. When Total Mechanical Energy is Conserved

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A. Work Done by a Constant Force F W = F X W = F Cos X F x = F cos x F x W The work W done on an object by an agent exerting a constant force on the object is the product of the component of the force in the direction of the displacement and the magnitude of the displacement :

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B. The Work-Energy Theorem W = F x = m a x v 2 = v o a x Kinetic energy K = ½ m v 2 W = K – K o W t = K work-kinetic energy theorem The net work done on a particle by a constant net force F acting on it equals the change in kinetic energy of the particle

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C. Work Done by a Varying Force or on Curved Path F x W W W = F x W = W = Limit F x x 0 W = F dx = m a dx a = dv/dt = (dv/dx)(dx/dt) = (dv/dx) v W = m a dx = m (dv/dx) v dx W = m dv v W = ½ m v 2 - ½ m v o 2 = K – K o W t = K x By spring F = - k x By hand F = k x W = F dx = k x dx = ½ k x 2 Elastic Potential Energy The net work done on a particle by the net force acting on it is equal to the change in the kinetic energy of the particle.

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D. Power P = Power (watt W) W = work (joule J) t = time (second s) x = displacement (meter m) v = velocity (m/s) The time rate of doing work is called power.

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E. Gravitational Potential Energy and Elastic Potential Energy h1h1 W K = work done by concervative force (J) g = acceleration of gravity (m/s 2 ) m = mass(kg) V = Potential energy (J) h2h2 v W = F y = mg (h 2 – h 1 ) = m g h 2 - m g h 1 Gravitational potential energy = V = mgh W = V 2 – V 1 W = V work done by palm force W = - V work done by gravitation force W K = - V W K = - ( ½ k x ½ k x 1 2 ) work done by spring force k = force constant of the spring(J/m 2 N/m )

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Conservative Force Conservative forces have two important properties: 1. A force is conservative if the work it does on a particle moving between any two points is independent of the path taken by the particle. 2. The work done by a conservative force on a particle moving through any closed path is zero. (A closed path is one in which the beginning and end points are identical.)

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E. When Total Mechanical Energy is Conserved W t = W NK + W K W NK = W t – W K W NK = K – (- V) W NK = (K 2 – K 1 ) + ( V 2 – V 1 ) W NK = work done by nonconcervative force (J) If W NK = 0, than K 1 + V 1 = K 2 + V 2 Mechanical energy M = K + V M 1 = M 2 M = constant ½ m v 2 + mgh = constant Conservation of Mechanical Energy

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Increase (or decrease) in potential energy is accompanied by an equal decrease (or increase) in kinetic energy. The total mechanical energy of a system remains constant in any isolated system of objects that interact only through conservative forces.

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