Figure 13.9 shows Weston’s differential pulley block arrangement consisting of two blocks A and B. Upper block A is provided with two pulleys 1 and 2, having differential diameters. Both pulleys behave as one pulley. Lower block B carries a movable to which load W is attached. One string passes over all the pulleys. The effort is applied to the string passing over the bigger pulley of block A, which causes unwinding of rope from pulley 1 and winding on the pulley 2. The string on the effort side lengthens while the string on load side shortens, thereby raising the load.
Figure 13.9 Weston’s Differential Pulley Block
Let W = load lifted by lower block B
P = Effort applied to upper block A
D = Diameter of pulley 1
d = Diameter of pulley 2
When upper pulley rotates one by revolution, the effort will move by π D. Length of string will be reduced by the smaller pulley by π d. Net shortening of the string length = π (D – d).
Shortening of string is divided equally between the two portions of the string. Distance moved by the load 
Example 13.9: A differential pulley block consists of a lower block and an upper block. The upper block has two grooves one of which has a radius of 200 mm and the other a radius of 120 mm. If the efficiency of the machine is 45%, calculate the effort required to raise a load of 1,200 N.
Solution:
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