The physics of blocks and pulleys

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  • The main sail pulls a 10 tonne boat at 6 knots. So where do you find the force to trim the main sail?

    This is usually done using a system of blocks. A block is a mounting for one or more pulley. One block is mounted on the boom and one on a traveller or rail near the cockpit. A rope connects them. Using the blocks, a modest force can be used to move the boom and sail. Systems of blocks are used for several things on sailing boats, and elsewhere. Here we look at how they work.

Diagram (i) shows a pulley being used just to change the direction of a force. You can pull on the end of rope marked a with force F and the end b moves an equal distance with load force L (neglecting friction).

(ii) shows an arrangement that doubles the force. You pull with force F on the section a. Again neglecting friction, the sections of the same rope marked b and c are also under tension F, so the second block is pulled up by 2F, so the load lifted L = 2F. This extra force does not come 'free', however. When you pull a distance x on a, x is the total amount of shortening in both b and c, so each of b and c is shortened by x/2, which is how much the load L rises. The work you do is Fx, the work done on the load is L.x/2 = Fx.

In (iii), pulling on a causes four sections of the rope to shorten and to share the load. So these blocks multiply the force by four times, but you have to pull 4 times as far.

diagram of blocks

In iv, there are six sections of rope. So these blocks multiply the force by six times, but you have to pull 6 times as far. The diagrams show the blocks in arrangements suitable for lifting. For the main sheet on a boat (the rope that controls the mainsail), systems like (iii) and (iv) are used, but they are mounted the other way up, so that the end upon which you pull is at the traveller on deck. Usually there is a cleat: a system for holding the main sheet in fixed position once the sail is set.

diagram of blocks

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