Simple Machines

You need to lift a 200 kg crate onto a 1.5 m high truck bed. You could deadlift it straight up — a couple thousand newtons of force, briefly. Or you could roll it up a 6 m ramp, using only one-quarter the force, but pushing it four times as far.

You do the same total work either way (about 3000 J in both cases). What changes is how that work is split between force and distance. The ramp lets a single human do what would otherwise require a forklift. That trade — give up distance to save force — is the magic of every simple machine, from the inclined plane the Egyptians used to build pyramids to the gear ratios in a modern bicycle.

The Core Principle: Energy Conservation

Every simple machine obeys the same rule: $W_{in} = W_{out}$ (in an ideal, frictionless machine). Since $W = Fd$:

$F_{in} \times d_{in} = F_{out} \times d_{out}$

If the machine reduces the force you need ($F_{in} < F_{out}$), it must increase the distance you move ($d_{in} > d_{out}$). The ratio is fixed by conservation of energy. There’s no free lunch.

Ideal Mechanical Advantage (IMA)

Levers

A lever is a rigid bar that pivots around a fixed point called the fulcrum. There are three classes, distinguished by which of three things — fulcrum, load, effort — sits in the middle.

For levers, $IMA = (\text{distance from effort to fulcrum}) / (\text{distance from load to fulcrum})$. A longer effort arm means greater mechanical advantage. (Why third-class levers always have IMA < 1: the effort sits closer to the fulcrum than the load, so the load arm is longer than the effort arm.)

Pulleys

Pulleys redirect force, and (when combined cleverly) multiply it. The key MCAT shortcut:

Inclined Plane (Ramp)

The ramp is the most intuitive simple machine — you’ve used one every time you’ve walked up a hill instead of a vertical cliff. A gentle slope (long ramp, small rise) takes little force over a long distance. A steep slope (short ramp, big rise) takes more force over a shorter distance.

In the frictionless ideal case, the force needed to push an object up a ramp at constant speed is $F = mg\sin\theta$, where $\theta$ is the ramp angle. (This is the down-slope component of gravity from §1.11.)

Wheel and Axle

A wheel and axle is essentially a rotating lever. The IMA equals the ratio of the wheel radius to the axle radius:

$IMA = \dfrac{R_{wheel}}{R_{axle}}$

A large steering wheel makes it easy to turn a small steering shaft. A doorknob (big radius) makes it easy to turn a small latch mechanism. A screwdriver handle (wide grip) gives big mechanical advantage to the narrow shaft turning the screw.