7.5 Simple Machines & Mechanical Advantage

Work and What Machines Actually Do

In physics, work is done when a force moves an object in the direction of the force: W = F × d, measured in joules (J). A simple machine is a device with few or no moving parts that makes work easier by changing the size or direction of the force needed to complete a task.

The most tested idea about machines on the Praxis 5005 is what machines do not do: no machine reduces the total amount of work. Ignoring friction, work in equals work out:

Input Force × Input Distance = Output Force × Output Distance

A machine lets you apply a smaller force over a longer distance (or a greater force over a shorter distance, or a force in a more convenient direction). Pushing a heavy box up a long, gentle ramp feels easier than lifting it straight up—but you push over a longer distance, so the total work is the same.

Mechanical Advantage

Mechanical advantage (MA) is the number of times a machine multiplies your effort force:

MA = Output Force ÷ Input Force

• A machine with MA = 1 changes only the direction of the force (a single fixed pulley).
• A machine with MA greater than 1 multiplies force (a movable pulley, a ramp, a second-class lever).
• A machine with MA less than 1 sacrifices force to gain speed or range of motion (a third-class lever such as a fishing rod).

The Six Simple Machines

The Three Classes of Levers

Levers are classified by the positions of the fulcrum (F), effort (E), and load (L):

1. First-class lever — fulcrum in the middle (F between E and L): seesaw, crowbar prying a nail, scissors. Can multiply force or change direction depending on the arm lengths. MA = effort arm length ÷ load arm length.
2. Second-class lever — load in the middle (L between F and E): wheelbarrow, nutcracker, bottle opener. Always multiplies force (MA > 1).
3. Third-class lever — effort in the middle (E between F and L): tweezers, baseball bat, fishing rod, and the human forearm (the biceps pulls between the elbow fulcrum and the load in the hand). Always trades force for speed and range of motion (MA < 1).

Calculating Mechanical Advantage and Efficiency

Ramp (Inclined Plane) Calculation

For an inclined plane, the ideal mechanical advantage equals the ramp's length divided by its height:

MA = Ramp Length ÷ Ramp Height

Example: A student pushes a 600 N box up a 4 m ramp onto a platform 1 m high. MA = 4 ÷ 1 = 4, so the required effort force is 600 N ÷ 4 = 150 N (ignoring friction). Check the work: 150 N × 4 m = 600 J of input work equals 600 N × 1 m = 600 J of output work—the machine traded distance for force, and total work stayed the same.

Pulley Systems

• A fixed pulley (attached to a beam) changes only the direction of the force: MA = 1. You pull down on the rope to lift the flag up.
• A movable pulley (attached to the load) splits the load between two rope segments: MA = 2, halving the effort force while doubling the length of rope you must pull.
• A block and tackle combines fixed and movable pulleys for even greater advantage; cranes use them to lift steel beams.

Compound Machines

Compound machines combine two or more simple machines: a bicycle links levers (pedals and brakes), wheel-and-axle systems (wheels and gears), and a pulley-like chain drive; scissors pair two first-class levers with two wedges (the blades); a can opener combines a wheel and axle, a lever, and a wedge.

Efficiency and Friction

In real machines, some input work is always converted to waste heat by friction, so the actual mechanical advantage is less than the ideal, and efficiency is always below 100%:

Efficiency = (Work Output ÷ Work Input) × 100%

Lubricants such as oil and grease reduce friction and raise efficiency—which is why a squeaky bicycle chain gets oiled.

Classroom Application & Common Misconceptions

• Ruler levers: Students balance a ruler on a pencil fulcrum and move the fulcrum to different positions, discovering how arm lengths change the effort needed to lift an eraser load.
• Spring-scale ramp lab: Students pull a toy car up ramps of different steepness using a spring scale, recording how a longer, gentler ramp lowers the required force while increasing the pulling distance—direct evidence for the force-distance trade-off.
• Playground machine hunt: Students sketch or photograph simple machines on the playground (seesaw = lever, slide = inclined plane, flagpole = pulley) and classify each one.

Misconceptions to Correct

1. Misconception: 'Machines create energy or reduce the total work.' Correction: By the Law of Conservation of Energy, machines can only redirect a force or trade force for distance—total work stays the same (or effectively increases because of friction).
2. Misconception: 'A longer ramp means less work.' Correction: A longer ramp means less force; the total work (force × distance) is unchanged.
3. Misconception: 'Friction is always helpful.' Correction: Friction provides needed grip for walking and braking, but inside machines it wastes input work as heat, lowering efficiency.