Question

A cord is used to lower vertically a block of mass M by a distance d with constant downward accelaration g/4 . Work done by the cord on the block is

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{If}\mathrm{we}\mathrm{sum}\mathrm{the}\mathrm{forces}\mathrm{acting}\mathrm{on}\mathrm{our}\mathrm{block},\mathrm{we}\mathrm{find}, \\ \mathrm{T}-\mathrm{Mg}=\mathrm{M}\left(\frac{-\mathrm{g}}{4}\right) \\ \mathrm{So}\mathrm{the}\mathrm{tension}\mathrm{is}\mathrm{given}\mathrm{by}, \\ \mathrm{T}=\frac{3\mathrm{Mg}}{4} \\ \mathrm{The}\mathrm{work}\mathrm{done}\mathrm{by}\mathrm{the}\mathrm{tension}\mathrm{is}\mathrm{the}\mathrm{force}\mathrm{times}\mathrm{the}\mathrm{distance}, \\ \mathrm{W}=\mathrm{T}\left(-\mathrm{d}\right) \\ \mathrm{W}=\frac{3\mathrm{Mg}}{4}\times \left(-\mathrm{d}\right) \\ \mathrm{W}=-\frac{3\mathrm{Mgd}}{4} \end{gathered}$$