Mechanical Advantage Calculations
Mechanical Advantage
The ratio of output force to input force in a mechanical system.
Key formula:
$$\text{Mechanical Advantage (MA)} = \frac{\text{Load}}{\text{Effort}}$$
Mechanical advantage is a unitless value, as it represents a ratio of forces.
Types of Mechanical Systems
- Gears
- Pulleys
- Belts
- Levers
Gears
$$\text{MA} = \frac{\text{Number of teeth on driven gear}}{\text{Number of teeth on driving gear}}$$
Used to increase torque or speed (e.g. bicycle gears, drill motors).
A gear with 40 teeth driving a gear with 20 teeth → MA = 0.5 (speed increases, torque decreases).
Pulleys
- MA = Number of rope segments supporting the load.
- More pulleys = less effort required, but more rope length pulled.
- Types of Pulley Systems:
- Fixed Pulley: MA = 1 (changes direction of force).
- Movable Pulley: MA = 2 (reduces force by half).
- Compound Pulley: MA = Number of supporting ropes.
A 3-pulley block and tackle system has an MA of 3.
Factors affecting pulley MA
- Number of Ropes: Directly proportional to mechanical advantage.
- Friction: Can reduce the effective MA in real-world applications.
- Its a misconception that adding more pulleys always increases efficiency.
- While it increases mechanical advantage, it also introduces more friction.
Belts
- Similar to gears, $$\text{MA} = \frac{\text{Radius of driven pulley}}{\text{Radius of driving pulley}}$$
- Can be used for quiet, smooth transmission in fans or machines.
A belt from a 10 cm driving pulley to a 20 cm driven pulley → MA = 2
When designing belt systems, ensure proper tension to minimize slippage and maintain efficiency.
Levers
$$\text{MA} = \frac{\text{Distance from fulcrum to effort}}{\text{Distance from fulcrum to load}}$$
Types of levers (Class 1, 2, 3) affect efficiency and direction of force.
A seesaw with effort 2 m from the fulcrum and load 1 m away → MA = 2
- MA > 1: Machine multiplies force.
- MA < 1: Machine increases speed or distance, but reduces force.
