Question

A flexible chain of length l and mass m is slowly pulled at constant speed up over the edge of a table by a force F parallel to the surface of the table. Assuming that there is no friction between the table and chain, calculate the work done by force F till the chain reaches to the horizontal surface of the table.

Answer 1

Its total weight is M and total length is L

Let the x length of a chain is not lying on the table its weight is

$mg=\frac{Mgx}{L}$

work done required to move a dx part of a chain to upward is=

$dW=Fdx$

$F=mg=\frac{Mgx}{L}$

${\int }_0^{W}dW={\int }_l^0\frac{Mgx}{L}dx$

$W={\left(\frac{Mg{x}^2}{2L}\right)}_l^0$

$W=-\frac{MgL}{2}$N/m