how velocity is related to the no. of pulleys in a block and tackle system?
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Block and tackle

A block and tackle[1][2] is a system of two or more pulleys with a rope or cablethreaded between them, usually used to lift heavy loads.
The pulleys are assembled together to form blocks and then blocks are paired so that one is fixed and one moves with the load. The rope is threaded through the pulleys to provide mechanical advantage that amplifies the force applied to the rope.[3]
Hero of Alexandria described cranes formed from assemblies of pulleys in the first century. Illustrated versions of Hero's "book on raising heavy weights" show early block and tackle systems.[4]
OverviewEdit

Various ways of rigging a tackle. All these are "rove to disadvantage"[5] (see below).
A block is a set of pulleys or sheaves mounted on a single frame. An assembly of blocks with a rope threaded through the pulleys is called tackle. A block and tackle system amplifies the tension force in the rope to lift heavy loads. They are common on boats and sailing ships, where tasks are often performed manually.
In the diagram shown here, the number of rope sections of the tackles shown is as follows:
Gun tackle: 2
Luff tackle: 3
Double tackle: 4
Gyn tackle: 5
Threefold purchase: 6
Note that the gun tackle, double tackle and threefold purchase all have the same number of pulleys in both blocks (one, two and three, respectively) whereas the Luff tackle and Gyn tackle have mis-matched blocks with differing numbers of pulleys.
Mechanical advantageEdit
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. Its mechanical advantage is the number of parts of the rope that act on the load. The mechanical advantage of a tackle dictates how much easier it is to haul or lift the load.
If frictional losses are neglected, the mechanical advantage of a block and tackle is equal to the number of parts in the line that either attach to or run through the moving blocks—in other words, the number of supporting rope sections.

A gun tackle has a single pulley in both the fixed and moving blocks with 2 rope parts (n) supporting the load (FB) of 100N. The mechanical advantage is 2, requiring a force of only 50N to lift the load.
An ideal block and tackle with a moving block supported by n rope sections has the mechanical advantage (MA),
{\displaystyle MA={\frac {F_{B}}{F_{A}}}=n,\!}
where FA is the hauling (or input) force and FB is the load.
Consider the set of pulleys that form the moving block and the parts of the rope that support this block. If there are n of these parts of the rope supporting the load FB, then a force balance on the moving block shows that the tension in each of the parts of the rope must be FB/n. This means the input force on the rope is FA=FB/n. Thus, the block and tackle reduces the input force by the factor n.

A double tackle has two pulleys in both the fixed and moving blocks with four rope parts (n) supporting the load (FB) of 100N. The mechanical advantage is 4, requiring a force of only 25N to lift the load.

A block and tackle[1][2] is a system of two or more pulleys with a rope or cablethreaded between them, usually used to lift heavy loads.
The pulleys are assembled together to form blocks and then blocks are paired so that one is fixed and one moves with the load. The rope is threaded through the pulleys to provide mechanical advantage that amplifies the force applied to the rope.[3]
Hero of Alexandria described cranes formed from assemblies of pulleys in the first century. Illustrated versions of Hero's "book on raising heavy weights" show early block and tackle systems.[4]
OverviewEdit

Various ways of rigging a tackle. All these are "rove to disadvantage"[5] (see below).
A block is a set of pulleys or sheaves mounted on a single frame. An assembly of blocks with a rope threaded through the pulleys is called tackle. A block and tackle system amplifies the tension force in the rope to lift heavy loads. They are common on boats and sailing ships, where tasks are often performed manually.
In the diagram shown here, the number of rope sections of the tackles shown is as follows:
Gun tackle: 2
Luff tackle: 3
Double tackle: 4
Gyn tackle: 5
Threefold purchase: 6
Note that the gun tackle, double tackle and threefold purchase all have the same number of pulleys in both blocks (one, two and three, respectively) whereas the Luff tackle and Gyn tackle have mis-matched blocks with differing numbers of pulleys.
Mechanical advantageEdit
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. Its mechanical advantage is the number of parts of the rope that act on the load. The mechanical advantage of a tackle dictates how much easier it is to haul or lift the load.
If frictional losses are neglected, the mechanical advantage of a block and tackle is equal to the number of parts in the line that either attach to or run through the moving blocks—in other words, the number of supporting rope sections.

A gun tackle has a single pulley in both the fixed and moving blocks with 2 rope parts (n) supporting the load (FB) of 100N. The mechanical advantage is 2, requiring a force of only 50N to lift the load.
An ideal block and tackle with a moving block supported by n rope sections has the mechanical advantage (MA),
{\displaystyle MA={\frac {F_{B}}{F_{A}}}=n,\!}
where FA is the hauling (or input) force and FB is the load.
Consider the set of pulleys that form the moving block and the parts of the rope that support this block. If there are n of these parts of the rope supporting the load FB, then a force balance on the moving block shows that the tension in each of the parts of the rope must be FB/n. This means the input force on the rope is FA=FB/n. Thus, the block and tackle reduces the input force by the factor n.

A double tackle has two pulleys in both the fixed and moving blocks with four rope parts (n) supporting the load (FB) of 100N. The mechanical advantage is 4, requiring a force of only 25N to lift the load.
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