Show that work input equals work output for a hydraulic system assuming no losses due to friction. Do this by showing that the distance the output force moves is reduced by the same factor that the output force is increased. Assume volume of the fluid is constant.

If $V=d_i{A}_i,$ what is $d_o?$ Let $d$ represent $d_i,$ a represent $A_i,$ and A represent $A_o,$

$d_o=$

Set up an equivalence statement using pressure to find $F_0.$ Let $F$ represent $F_i,$ a represent $A_i,$ and let A represent $A_o.$

$F_o=$

Using this information, find the output work done. Let $F$ represent $F_i,$A represent $A_o,$ let a represent $A_i,$ and d represent $d_i.$

$W=$