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 200 kgf. If the effort end moves a distance 60 cm, what distance does the load move?

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Solution

Part 1: Velocity ratio of a block and tackle system:
In a system of n pulleys, the velocity ratio is
$V . R . = \frac{d_{E}}{d_{L}} = \frac{n d}{d} = n$
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.
Given:
Velocity ratio of block and tackle system is
$V . R . = 3$
Distance moved by the effort end $d_{E} = 60 c m$
$V . R . = \frac{d_{E}}{d_{L}} = 3$
So distance moved by the load
$\Rightarrow d_{L} = \frac{d_{E}}{V . R .} = \frac{60 c m}{3}$
$= 20 c m$

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