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MECHANICAL ADVANTAGE With a single fixed sheave, the force of your down pull on the fall must be equal to the weight of the object hoist. You cant use this rig to lift a heavy load or resistance with a small effort-you can change only the direction of your pull. A single fixed block is a first-class lever with equal arms. The arms (EF and FR) in figure 2-3 are equal; hence, the mechanical advantage is 1. When you pull down at A with a force of 1 pound, you raise a load of 1 pound at B. A single fixed block does not magnify force nor speed. You can, however, use a single block and fall to magnify the force you exert. Notice in figure 2-4 that the block is not fixed. The fall is doubled as it supports the 200-pound cask. When rigged this way, you call the single block and fall a runner. Each half of the fall carries one-half of the total bad, or 100 pounds. Thus, with the runner, the sailor is lifting a 200-pound cask with a 100-pound pull. The mechanical advantage is 2. Check this by the formula:
Figure 2-4.-A runner.
Figure 2-5.-Its 2 to 1.
Figure 2-6.-A gun tackle. The single movable block in this setup is a second-class lever. See figure 2-5. Your effort (E) acts upward upon the arm (EF), which is the diameter of the sheave. The resistance (R) acts downward on the arm (FR), which is the radius of the sheave. Since the diameter is twice the radius, the mechanical advantage is 2. When the effort at E moves up 2 feet, the load at R is raised only 1 foot. Thats something to remember about blocks and fallsif you are actually getting a mechanical advantage from the system. The length of rope that passes through your hands is greater than the distance that the load is raised. However, if you can lift a big load with a small effort, you dont care how much rope you have to pull. The sailor in figure 2-4 is in an awkward position to pull. If he had another single block handy, he could use it to change the direction of the pull, as in figure 2-6. This second arrangement is known as a gun tackle. Because the second block is fixed, it merely changes the direction of pulland the mechanical advantage of the whole system remains 2. You can arrange blocks in several ways, depending on the job to be done and the mechanical advantage you
Figure 2-7.-A luff tackle. want to get. For example, a luff tack consists of a double block and a single block, rigged as in figure 2-7. Notice that the weight is suspended by the three parts of rope that extend from the movable single block. Each part of the rope carries its share of the load. If the crate weighs 600 pounds, then each of the three parts of the rope supports its share200 pounds. If theres a pull of 200 pounds downward on rope B, you will have to pull downward with a force of 200 pounds on A to counterbalance the pull on B. Neglecting the friction in the block, a pull of 200 pounds is all that is necessary to raise the crate. The mechanical advantage is:
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