Pulleys and inclined planes

Simple machines make jobs easier by changing how big the force must be or which direction you push. They never reduce the total work. A machine doesn't save work; it changes the force.

Three words:

• Effort: the force you apply.
• Load: the force you have to overcome.
• Mechanical advantage (MA) = load ÷ effort. An MA of 2 means your effort is half the load.

The fixed pulley. It is a grooved wheel fixed in place, with a rope over it. It only changes the direction of your pull: you pull down to lift a load up, which is easier because you can use your body's weight. The effort is the same as the load, so MA = 1. Movable pulleys and pulley systems can have an MA greater than 1; lifts and cranes use them.

The inclined plane (ramp). Pull a cart up a plank: it takes less force than lifting it straight up. A gentler (longer) plank takes even less force, but you pull it over a longer distance.

Why it works. With no friction, the work along the ramp equals the work of lifting straight up: effort × length = load × height, or F′L = mgh. So MA = L/h: the length of the ramp ÷ its height. Since the ramp is longer than its height, the MA is more than 1.

A ramp for a step. A step 30 cm high, with the ramp starting 40 cm away. The ramp's length is √(30² + 40²) = 50 cm, so MA = 50 ÷ 30 ≈ 1.67.

Look around you: roads that wind round hills are long, gentle ramps, so vehicles can climb with less force. A sloping ladder is easier to climb than a straight-up one for the same reason.