1.

A chain of length L and mass per unit length rho is piled on a horizontal surface. One end of the chain is lifted vertically with constant velocity by a force P.

Answer»

P as function of height X of the end above the surface will be `rho(gx+v^(2))`
no energy will loss in this process.
work DONE by force will be `1/2rhogL^(2)+rhov^(2)L`
loss in energy `1/2rhogLv^(2)`

Solution :`F_(ext)=V_(rel)(DM)/(dt)+m(dv)/(dt)`
`(dv)/(dt)=0`(v is contant)
`P=rhoxg+rhov^(2)`
`w_(P)+w_(G)=DeltaKE`
`w_(P)=+underset0oversetLint rhoxgdx+underset0oversetLint(rhodx)v^(2)`
`w_(P)=(rhoL^(2)g)/2+rhoLv^(2)`


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