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A chain of length L and mass density s lies straight on a frictionless horizontal surface. You grab one end and pull it back along itself, in a parallel manner (see Fig.). Assume that you pull it at...

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A chain of length L and mass density s lies straight on a frictionless horizontal surface. You grab one end and pull it back along itself, in a parallel manner (see Fig.). Assume that you pull it at constant speed v. What force must you apply? What is the total work that you do, by the time the chain is straightened out? How much energy is lost to heat, if any?

Answered Same Day Dec 24, 2021

Solution

David answered on Dec 24 2021
131 Votes
Work done by the force for the total distance d = 2L
So, Wf = F*2L = 2FL
Let the linear density of chain be = m/L
We observe from x=0 to x= L, the friction gradually increases
For 0friction = u* *x*g
So, work done by friction between x=0 to x=L,
W' = -u* *x*g*dx
So, W' = -u*...
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