Simple Machines and Mechanical Advantage

Simple machines are fundamental to the OAR Mechanical Comprehension Test. You need to understand how each machine works, calculate mechanical advantage, and recognize when one machine is more efficient than another.

Mechanical Advantage

Mechanical Advantage (MA) = Output Force / Input Force

Alternatively: MA = Input Distance / Output Distance

A machine with MA > 1 multiplies force (but you must move the input a greater distance). A machine with MA = 1 changes direction of force but does not multiply it. A machine with MA < 1 multiplies speed/distance at the cost of greater input force.

The Trade-Off

Work In = Work Out (in an ideal machine)

Since Work = Force × Distance:

• If the machine multiplies force by 3, you must push 3 times the distance
• You never get "free" work — you always trade force for distance or vice versa

The Six Simple Machines

1. Levers

A lever is a rigid bar that pivots around a fixed point called the fulcrum.

Three Classes of Levers

Lever Formula

MA = Distance from fulcrum to effort / Distance from fulcrum to load

Or for balance: F₁ × d₁ = F₂ × d₂ (moments must balance)

Example: A lever has the fulcrum 2 meters from the load and 6 meters from the effort. What is the MA?

MA = 6/2 = 3 (you can lift 3 times the force you apply)

Example: A 180-pound person sits 3 feet from the fulcrum on a seesaw. Where must a 120-pound person sit to balance?

180 × 3 = 120 × d → d = 540/120 = 4.5 feet

2. Wheel and Axle

A large wheel attached to a smaller axle. When you apply force to the wheel, the axle turns with greater force but less distance.

MA = Radius of wheel / Radius of axle

Example: A steering wheel has a radius of 15 cm and the steering column (axle) has a radius of 3 cm. MA = 15/3 = 5

Common examples: doorknobs, screwdrivers, wrenches, winches, bicycle gears.

3. Pulleys

Single Fixed Pulley

• Changes the direction of force (pull down to lift up)
• MA = 1 — no force multiplication
• Advantage: easier to pull down than lift up

Single Movable Pulley

• Moves with the load
• MA = 2 — force is halved
• Disadvantage: must pull rope twice the distance

Compound Pulley Systems (Block and Tackle)

MA = Number of rope segments supporting the load

Key rule: Count the rope segments attached to or running through the movable pulley block.

Example: A block and tackle has 4 rope segments supporting the load. How much force is needed to lift a 200 lb crate?

Force = 200/4 = 50 lb

But you must pull 4 feet of rope for every 1 foot the crate rises.

4. Inclined Plane (Ramp)

A flat surface set at an angle to the horizontal. It reduces the force needed to raise an object by spreading the lifting over a longer distance.

MA = Length of ramp / Height of ramp

Force along ramp = Weight × (Height / Length) or equivalently F = W × sin(θ)

Example: A ramp is 10 meters long and 2 meters high. What force is needed to push a 500 N crate up the ramp (ignoring friction)?

MA = 10/2 = 5 Force = 500/5 = 100 N

Without the ramp, you would need to apply 500 N straight up. The ramp reduces the force by a factor of 5, but you must push over 5 times the vertical distance.

5. Wedge

A wedge is essentially two inclined planes placed back-to-back. It converts a force applied to its blunt end into forces perpendicular to its sloped surfaces.

MA = Length of wedge / Width (thickness) of wedge

Examples: Axe, knife, chisel, doorstop, nail, ship's bow

Example: A wedge is 12 cm long and 3 cm thick at the blunt end. MA = 12/3 = 4

6. Screw

A screw is an inclined plane wrapped around a cylinder. Each rotation advances the screw by one pitch (the distance between threads).

MA = 2πr / pitch

Where:

• r = radius of the screwdriver or handle
• pitch = distance between threads (or distance advanced per turn)

Example: A screw has a pitch of 2 mm and is turned with a screwdriver handle of radius 10 mm. MA = 2π(10)/2 = 62.8/2 ≈ 31.4

This extremely high MA explains why screws hold so well — a small turning force creates enormous clamping force.

Compound Machines

Most real-world machines are compound machines — combinations of simple machines.

The total MA of a compound machine is the product of the individual MAs:

MA_total = MA₁ × MA₂ × MA₃ × ...