Levers, pulleys, and simple machines
Six classic simple machines, the lever, pulley, wheel and axle, inclined plane, wedge, and screw, underlie almost every mechanical device. Each trades distance for force.
The lever
A lever is a rigid bar turning about a fulcrum. Its mechanical advantage is the effort arm divided by the load arm. Archimedes, who stated the law of the lever, is said to have boasted that with a long enough lever and a place to stand, he could move the Earth.
Three classes of lever
In a first-class lever, the fulcrum is between effort and load, as in a seesaw or crowbar. In a second-class lever, the load is between fulcrum and effort, as in a wheelbarrow or nutcracker, always giving MA above 1. In a third-class lever, the effort is between fulcrum and load, as in tweezers or a fishing rod, giving MA below 1 but greater speed and range of motion.
The human forearm
The forearm is a third-class lever. The biceps attaches about 4 cm from the elbow, while a hand holding a 50 N weight is about 35 cm away. Moments about the elbow require a biceps force of 50 x 35 / 4, about 438 N, nearly nine times the load. Muscles trade force for speed.
Wheel and axle
A wheel fixed to an axle multiplies force by the ratio of their radii. A screwdriver handle 15 mm in radius turning a 3 mm screw tip gives an ideal MA of 5. Steering wheels, doorknobs, and winches use the same principle.
Inclined planes and wedges
An inclined plane reduces the force needed to raise a load, with ideal MA equal to slope length divided by height: pushing a cart up a 6 m ramp to a 1 m high platform needs ideally one sixth of its weight. A wedge is a moving inclined plane, used in axes, chisels, and doorstops, where friction plays a big role.
Screws
A screw is an inclined plane wrapped around a cylinder. Turning a handle of radius R once advances the screw by its pitch p, so the ideal MA is 2 pi R / p. A car jack with a 0.25 m handle and a 2 mm pitch has an ideal MA of about 785, though friction reduces the actual value greatly.
Pulleys revisited
Pulleys redirect tension and, in a block and tackle, provide an MA equal to the number of rope segments supporting the moving block. Cranes combine pulleys, winches, and levers to lift loads of many tonnes.
Worked example
A builder uses a 2 m crowbar to lift a 1,500 N slab, placing the fulcrum 0.25 m from the slab end. The effort arm is 1.75 m, so the ideal MA is 1.75 / 0.25 = 7, and the builder needs about 1,500 / 7, roughly 214 N, a bit over 20 kg of push. Moving the fulcrum closer to the slab would reduce the effort further.
Key takeaways
Simple machines trade distance for force. A lever's MA is effort arm over load arm; first-class levers have the fulcrum in the middle, second-class the load in the middle (MA above 1), and third-class the effort in the middle (MA below 1, more speed), like the human forearm. Wheel and axle MA is the ratio of radii; an inclined plane's is length over height; a screw's is 2 pi R over the pitch. Friction always lowers actual MA below the ideal.
Flashcard
Rigid bar turning about a fulcrum
Check your understanding
Which is a third-class lever?