More On Mechanical Advantage
A block and tackle, is characterized by the use of a single continuous rope to transmit a tension force around one or more pulleys to lift or move a load---the rope may be a light line or a strong cable. If the rope and pulley system does not dissipate or store energy, then its mechanical advantage is the number of parts of the rope that act on the load. This can be shown as follows.
Consider the set of pulleys that form the moving block and the parts of the rope that support this block. If there are p of these parts of the rope supporting the load W, then a force balance on the moving block shows that the tension in each of the parts of the rope must be W/p. This means the input force on the rope is T=W/p. Thus, the block and tackle reduces the input force by the factor p.
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A gun tackle has a single pulley in both the fixed and moving blocks with two rope parts supporting the load W.
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Separation of the pulleys in the gun tackle show the force balance that results in a rope tension of W/2.
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A double tackle has two pulleys in both the fixed and moving blocks with four rope parts supporting the load W.
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Separation of the pulleys in the double tackle show the force balance that results in a rope tension of W/4.
The mechanical advantage of the gun tackle can be increased by interchanging the fixed and moving blocks so the rope is attached to the moving block and the rope is pulled in the direction of the lifted load. In this case the block and tackle is said to be "rove to advantage." Diagram 3 shows that now three rope parts support the load W which means the tension in the rope is W/3. Thus, the mechanical advantage is three.
By adding a pulley to the fixed block of a gun tackle the direction of the pulling force is reversed though the mechanical advantage remains the same, Diagram 3a. This is an example of the Luff tackle.
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Diagram 3: The gun tackle "rove to advantage" has the rope attached to the moving pulley. The tension in the rope is W/3 yielding an advantage of three.
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Diagram 3a: The Luff tackle adds a fixed pulley "rove to disadvantage." The tension in the rope remains W/3 yielding an advantage of three.
Read more about this topic: Block And Tackle
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