Mechanical Advantage of Simple Machines: Levers and Pulleys

Simple Machines: Levers and Pulleys

The Principle of the Lever

A machine is a set of simple devices that perform work. The lever is a fundamental simple machine. It is classified as a machine because it can multiply force (strength), and it is simple because it consists of very few elements: a rigid bar and a fulcrum (pivot point). Using a lever, one can lift a heavy weight by applying relatively little force.

When a lever is in equilibrium, the principle of moments dictates that the moment of the applied force equals the moment of the resistance force.

Calculating Lever Equilibrium

The condition for equilibrium is expressed by the formula:

F · B_f = R · B_r

Where:

• F (Force): The effort applied.
• R (Resistance): The load or force to be overcome.
• B_f (Force Arm): The distance from the point where the force (F) is applied to the fulcrum.
• B_r (Resistance Arm): The distance from the point where the resistance (R) acts to the fulcrum.

Both force and resistance are measured in Newtons (N).

Classification of Levers

Levers are classified into three types based on the relative positions of the Fulcrum (F), the Effort (E), and the Resistance (R):

1. First-Class Lever

   The Fulcrum is located between the Effort and the Resistance (E-F-R). Depending on the relative lengths of the arms, the applied force can be higher, lower, or equal to the resistance.

2. Second-Class Lever

   The Resistance is located between the Fulcrum and the Effort (F-R-E). These levers always provide a mechanical advantage, meaning that applying a small effort can overcome a strong resistance.

3. Third-Class Lever

   The Effort is located between the Fulcrum and the Resistance (F-E-R). These levers result in a mechanical disadvantage, meaning it is necessary to apply a great force to overcome a small resistance. They are often used to increase speed or distance of movement.

Compound Lever Systems

By joining several levers together using mobile connections, complex mechanisms—known as compound levers or articulated levers—can be constructed to perform more complicated functions, such as the mechanism found in a car lift or elevator.

The human body itself is an intricate set of coupled levers, where the bones act as the rigid bars, the muscles exert the force (effort), and the joints serve as the mobile fulcrums.

Pulleys and Hoists

Lifting a load by simply pulling it upwards is often uncomfortable and limits the height of elevation.

The Pulley

A pulley is a wheel with a groove (slot) in the rim designed to hold a rope or belt. Pulleys are used to lift loads more easily, primarily by changing the direction of the applied force.

The Hoist (Block and Tackle)

The most significant advantage of pulleys is realized when they are combined to form a hoist (or block and tackle). A hoist is a combined set of pulleys that allows one to raise a great weight by applying very little force.

A simple hoist is typically composed of:

• Fixed Pulley: This pulley only rotates when the rope is pulled. It changes the direction of the force but does not multiply it.
• Movable Pulley: This pulley rotates and moves upward along with the load. It helps divide the required force, providing mechanical advantage.

In illustrations, we can understand how it is possible to decrease the force applied using fixed and moving pulleys.