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Tough mechanics question. See details.?-Physics Questions
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Tough mechanics question. See details.?

Answers:1   |   LastAnswerAt:2010.10  


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Philippmikio 
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Asked at 2010.10.19 20:05:23
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A heavy-duty waterproof cloth, 4.0 m long and with a weight of 10.0 Kg, hangs with half of its length from a table. When applying a horizontal force to pull the cloth onto the table, what is the work needed? Frictional coefficient: 0.7.
Find an expression for dW=F dx and use calculus
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answer Ivan A 
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Answered at 2010.10.19 20:05:23
The total work needed is the work against friction plus the change in potential energy of the part of the cloth that is hanging. The change in the potential energy of the part that is hanging is just

Change PE = (m/2)(L /4) g (10/2)(9.8)(1) = 49 J

where I used the center of gravity of the hanging part of the cloth to calculate the change in potential energy. The frictional force is calculated by assuming that the normal force will increase as

N = (5 + 10/2 x) 9.8

thus

Friction = uk N = 0.7 *9.8*(5 + 10/2 x)

Integrating from 0 to 2 to obtain the work we get

Work Friction = 0.7*9.8*(5*2+10/4*2^2) = 102.9 J

Total Work = 102.9 + 49 = 151 J
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