Mechanical Advantage
High-Yield Summary
- Mechanical advantage (MA = Fout/Fin) is the factor by which a machine multiplies applied force.
- The six simple machines — lever, pulley, wedge, screw, wheel and axle, inclined plane — each change the magnitude or direction of an applied force.
- Reducing the force needed always increases the distance the force is applied over — work stays constant (force-distance trade-off).
- Single pulley systems (MA = 1) only redirect force; multiple pulley systems (block and tackle) reduce effort by distributing load across rope segments.
- Efficiency (work output / work input) is always less than 100% in real machines due to friction and other energy losses.
Mechanical Advantage
MA = Fout / Fin
- Fout = Output force exerted on the load
- Fin = Input force applied to the machine
The Six Simple Machines
- Lever
- A rigid bar rotating around a fulcrum; smaller input force lifts a heavier load over a longer distance.
- Pulley
- A wheel that redirects force applied to a rope/cable; systems of pulleys reduce input force needed.
- Wedge
- Thick-to-thin taper for splitting/cutting; MA = ratio of slope length to width.
- Screw
- An inclined plane wrapped around a cylinder; closer threads give greater MA but need more turns.
- Wheel and Axle
- A wheel attached to a smaller axle; a larger wheel reduces the input force needed to turn the axle.
- Inclined Plane
- A tilted flat surface; MA = ratio of incline length to height lifted.
Pulley Systems and Mechanical Advantage
| System | Effort for a 100 N Load |
|---|---|
| Single pulley (MA = 1) | 100 N, rope pulled 1 m |
| Two-pulley system (MA = 2) | 50 N, rope pulled 2 m |
| Four-pulley system (MA = 4) | 25 N, rope pulled 4 m |
Common MCAT Trap
- A machine never gets you more work for free — reducing input force by a mechanical advantage of n always means pulling/moving n times the distance. Don't treat mechanical advantage as "free" energy savings.
- Real machines are never 100% efficient — friction and other non-conservative forces always dissipate some energy, even in a well-designed system.
Quick Recall
If a pulley system has a mechanical advantage of 4, how much effort is needed to lift a 100 N load, and how far must the rope be pulled to lift it 1 m?
Why is real-world machine efficiency always below 100%?