Pulleys

i. Single fixed pulley

This is a type of pulley that is attached to a fixed point, such as a ceiling or frame. The wheel does not move, only rotates. When effort is applied at one end of the rope, it raises the load at the other end.

Purpose: Changes the direction of force — you can pull downward to lift a load upward.

Example: Flagpoles, well water bucket systems, window blinds.

ii. Single movable pulley

In this pulley system, the pulley itself moves along with the load. One end of the rope is fixed, and effort is applied to the free end.

Purpose: Reduces the effort needed to lift the load.

Example: Construction cranes, some gym machines.

iii. Block and tackle system

This is a combination of fixed and movable pulleys arranged to form a system. It is used to multiply mechanical advantage and greatly reduce the amount of effort required to lift a load.

Purpose: Used for lifting very heavy loads with less effort.

Example: Used in shipyards, garages, and lifting heavy cargo.

The Mechanical Advantage (M.A) and Velocity Ratio (V.R) of a single fixed pulley and single movable pulley are as follows:

Single fixed pulley

Effort (E) = Tension (T) = Load (L)

Mechanical Advantage (M.A):

$\text{M.A} = \dfrac{Load}{Effort}$

So, $\text{M.A} = \dfrac{L}{E}$

Velocity Ratio (V.R):

$\text{V.R} = \dfrac{Distance\ moved\ by\ effort}{Distance\ moved\ by\ load}$

$\text{V.R} = \dfrac{X}{Y}$

Single movable pulley

A single movable pulley is the one where the load is multiple of the effort.

Load = 2 × Effort

Mechanical Advantage (M.A):

$\text{M.A} = \dfrac{Load}{Effort}$

So, $\text{M.A} = \dfrac{2E}{E}$

$\text{M.A} = 2$

Velocity Ratio (V.R):

$\text{V.R} = \dfrac{Distance\ moved\ by\ effort}{Distance\ moved\ by\ load}$

$\text{V.R} = 2$

The Mechanical Advantage (M.A) and Velocity Ratio (V.R) of a single movable pulley are as follows:

Mechanical Advantage (M.A):

$\text{M.A} = \dfrac{\text{Load}}{\text{Effort}}$

But, Load = $2 \times \text{Effort}$

$\text{M.A} = \dfrac{2 \times \text{Effort}}{\text{Effort}}$

$\text{M.A} = 2$

Velocity Ratio (V.R):

$\text{V.R} = \dfrac{\text{Distance moved by effort}}{\text{Distance moved by load}}$

When effort moves a distance = $x$

When load moves a distance = $\dfrac{1}{2}x$

$\text{V.R} = \dfrac{x}{\dfrac{1}{2}x}$

$\text{V.R} = \dfrac{2x}{x}$

$\text{V.R} = 2$

The block and tackle system of pulley when two or more pulleys are fixed in a frame, a block is formed. The pulleys in each block are fixed independently on separate axles. Consider the diagram below:-

Example 5: A block and tackle pulley system has a velocity ratio of 4. If a load of 200N is raised by using a force of 75N, calculate the mechanical advantage and efficiency of the system.

Solution:

Data given:

Velocity Ratio (V.R) = 4

Load = 200N

Effort = 75N

Mechanical Advantage (M.A):

$\text{M.A} = \dfrac{\text{Load}}{\text{Effort}}$

$\text{M.A} = \dfrac{200\,N}{75\,N}$

$\text{M.A} = 2.67$

Efficiency (e):

$\text{Efficiency} = \dfrac{\text{M.A}}{\text{V.R}} \times 100\%$

$e = \dfrac{2.67}{4} \times 100\%$

$e = 66.75\%$

Velocity Ratio (V.R) of block and tackle:

When the lower two pulleys move up a vertical distance $y$, corresponding to movement $y$ of the load $L$, each pulley releases a length $y$ of the rope on each side giving a total length $2y$.

With all this movement of pulleys, the effort $E$ is moved down a distance of $2 \times 2y = 4y$.

$\text{V.R} = \dfrac{\text{Distance moved by effort}}{\text{Distance moved by load}} = \dfrac{4y}{y} = 4$

$\text{V.R} = \text{Number of pulleys of the system}$

Efficiency of block and tackle:

$\epsilon = \dfrac{\text{M.A}}{\text{V.R}} \times 100\%$

$\epsilon = \dfrac{\text{Number of pulleys}}{\text{Number of pulleys}} \times 100\% = 100\%$

For a perfect block and tackle pulley system,

$\epsilon = 100\%$

But in a practical case, the M.A is less than the number of pulleys, hence the efficiency is less than 100% due to friction losses.

Mechanical Advantage (M.A) of block and tackle:

$\text{M.A} = \dfrac{\text{Load}}{\text{Effort}}$

Also,

$\text{M.A} = \dfrac{\text{Effort} \times \text{Number of pulleys}}{\text{Effort}} = \text{Number of pulleys of the system}$

1. Lifting and Moving Heavy Objects: Pulleys are commonly used in various lifting devices like cranes, elevators, and hoists to move heavy objects with less effort. The system allows for the mechanical advantage to lift large loads easily.
2. Ship Sails and Cargo Handling: Historically, pulleys have been essential for raising and adjusting sails on ships and boats. They are also used in the loading and unloading of cargo, making it easier to lift heavy loads on board and off ships.
3. Cranes: Pulleys are integral to cranes, which are used in construction and other heavy-lifting industries. They are part of the block and tackle systems that increase the lifting capacity of cranes.
4. Aircraft Rudder Control: Pulleys are crucial in aircraft systems, especially for controlling the rudders. The pulley systems help adjust the aircraft's direction by controlling the rudder, making it an essential part of the flight control systems.
5. Exercise Machines: Pulleys are often used in gym equipment like weight machines. They help adjust the resistance and provide mechanical advantage for lifting weights or performing various exercises.
6. Theater Curtains and Stage Mechanisms: In the entertainment industry, pulleys are used to operate stage curtains, backdrops, and other elements in a theater. They allow quick and easy changes in scenery and can lift and lower curtains smoothly.
7. Garage Doors and Window Blinds: Pulleys are used in the operation of garage doors and window blinds. For garage doors, a pulley system helps in lifting the heavy door with minimal effort, while pulleys in window blinds make it easy to raise or lower the blinds.