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# Lect_14 - ACT Zero net work The system of pulleys shown...

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Lecture 14 Work: Varying forces and curved trajectories Power ACT: Zero net work ACT: Zero net work The system of pulleys shown below is used to lift a bag of mass M at constant speed a distance h from the floor. What is the work done by the person? M h A. Mgh B. ½ Mgh C. 2 Mgh The force by the person is Mg /2 (see lecture 10), but he needs to pull on a length of rope of 2 h. net 0 (constant speed) W KE = ∆ = ( ) g T W W Mgh = − = − − The story so far: net W K = ∆ Kinetic energy 2 1 2 K mv = r F r F r F W = = = cos // θ G G Work by a constant force, along a straight path: Work/Kinetic energy theorem The journey is divided up into a series of segments over which the force is constant. Work by non-constant force, with straight line trajectory An object moves along the x-axis from point x 1 to x 2 . A non-constant force is applied on the object. What is the work done by this force? x 1 F A x A F B x B F C x C F D x D F E x E E Ex D Dx C Cx B Bx A Ax x F x F x F x F x F W + + + + = The total work is the sum of the works for each of the intervals: x 2

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F x x x A x B x C x D x E Work=area F A x F B x F C x F D x F E x E Ex D Dx C Cx B Bx A Ax x F x F x F x F x F W + + + + =
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