First System of Pulleys:

Figure illustrates the arrangement of pulleys in the first system of pulleys. In this system one pulley remains in the similar position with the help of fixed block, while other pulleys move with their blocks. One end of the string or rope is tied to the fixed support and the other end is fastened to the block of the next higher pulley after it passes round the periphery of bottom pulley. The load is linked to the lower most pulleys. The number of pulleys that are utilized depends on the velocity ratio required.

Let y be the distance covered by effort. This length of the string has been contributed by the string around pulley 3. For movement of the string through a distance y, pulley centre moves by y/2 . The upward movement of the pulley 3 is y/2. The upward movement of the centre of pulley 2 shall be(1/2)(y/2) by virtue the same type of argument. Applying the same reasoning, the centre of pulley 1 shall move by

(½) (y /(2)²  =  y/ 2³

Since weight is associated to the block of pulley 1, thus, movement of the load =   y /2³

Thus, velocity ratio (V. R.) =   y/  (y /2³) = 23  = 8

If there are 'n' moving pulleys V. R. = 2ⁿ

Mechanical advantage (M. A.) = W/ P