(14) Work- Varying Forces, Curved Trajectories, and Power

# (14) Work- Varying Forces, Curved Trajectories, and Power -...

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Lecture 14 Work: Varying forces and curved trajectories Power

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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. ½Mgh C. 2Mgh The force by the person is Mg/2 (see lecture 10), but he needs to pull on a length of rope of 2h. net 0 (const ant speed) W KE = ∆ = ( 29 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 Work by a constant force, along a straight path: Work/Kinetic energy theorem

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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 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 + + + + = The total work is the sum of the works for each of the intervals: x 2
x x x x x x x Work=area F A x F Bx F Cx F Dx F Ex E Ex D Dx C Cx B Bx A Ax = This is still an approximation, because the force is not really constant in each interval…

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(14) Work- Varying Forces, Curved Trajectories, and Power -...

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