Question

A block and tackle system has the velocity ratio 3. Draw a labelled diagram of the system indicating the points of application and the directions of load L and effort E. A man can exert a pull of $200kgf$. What is the maximum load he can raise with this pulley system if its efficiency is 60%?

Answer 1

Part 1: Velocity ratio of a block and tackle system:
In a system of n pulleys, 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.
Part 2 : 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 lower block, so as to apply the
effort in the downward direction.
​​​​​​Part 3: Calculate the maximum load
Given:
Velocity ratio $V.R.=n=3$
Efficiency $\eta =60\%=0.6$
So the mechanical advantage
$M.A.=\eta \times V.R.$
$=0.6\times 3$
$=1.8$
Given:
Man can exert a pull of $200kgf$
So 𝐸𝑓𝑓𝑜𝑟𝑡 $E=200kgf=2000N$
$M.A.=1.8$
$M.A.=\frac{loadL}{effortE}$
$\Rightarrow LoadL=E\times M.A.=2000\times 1.8$
$=3600N=3600kgf$