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hw6solution

hw6solution - CHANG 1(a Work done by a constant force on...

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Homework 6 Solution CHANG 1 (a) Work done by a constant force on the body is W F F cos s where is the angle between the force and the displacement. Here the applied force F 50 N makes an angle 30 with the upward displacement s 1 .5m .Sowehave W F F cos s 50 cos30 1.5 65.0 J Since the vertical component of F is upward, in the same direction of the displacement, the work is indeed positive. (b) The weight of the collar is w mg pointing downward, and the displacement is upward, so using the definition of work we have W g mgs . We can also directly use the formula and get the same result: Take the starting point A as the reference with y upward to measure the vertical positions, and we have: W g mg y A y B mg 0 s mgs 2 9.8 1.5 29.4 J Note that gravity does negative work here because the weight (downward) is in the opposite direction of the displacement (upward). (c) The work done by the spring is W s 1/2 k x A 2 x B 2 . From geometry, the deformations in the spring x A and x B at the initial and final points A and B can be found to be x A l A l 0 2 1.6 0.4 m x B l B l 0 2 2 1.5 2 1.6 0.9 m Hence the work by the spring is: W s 1 2 k x A 2 x B 2 1 2 24 0.4 2 0.9 2 7.8 J CHANG 2 (a) The applied pushing force F

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hw6solution - CHANG 1(a Work done by a constant force on...

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