Question

A pulley system has a velocity ratio 3 and an efficiency of 80%. Draw a labelled diagram of this pulley system. Calculate the mechanical advantage of the system

Answer 1

Velocity ratio of a block and tackle system:
The velocity ratio is
$V.R.=\frac{d_E}{d_L}=\frac{nd}{d}=n$
Thus to get a block and tackle system of
$V.R.=3$, we will need 3 pulleys.
Diagram

The number of pulleys in the movable lower block (=1) will be one less than the number of pulleys in the fixed upper block (=2). One end of the string is attached to the hook of the ower block, so as to apply the effort in the downward direction.
Given:
Efficiency $\eta =80\%=0.8$
Velocity ratio $V.R.=3$
We know
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 $\eta =\frac{M.A.}{V.R.}$
So mechanical advantage of the system:
$\Rightarrow M.A.=V.R.\times \eta$
$=3\times 0.8$
$=2.4$