The Physics
Opus in profectus

Simple Machines

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In the most general sense, a machine is any device that can be used to perform a task. In the mechanical sense, a machine is a device for transmitting work from one location to another.

Work is defined as the product of force and displacement…

W = Fs

Machines are devices by means of which a primary force (called the effort) exerted over some displacement at one location gives rise to a secondary force (called the load) and displacement at a different location. The work done on the machine at the effort end is called the work in and the work done by the machine at the load end is called the work out.

work done on the machine
Win = Feffortseffort
work done by the machine
Wout = Floadsload

The load and effort usually differ in magnitude and direction as well as location. In the ideal world, mechanical energy is never lost to other forms and work in equals work out. (Oh happy day!) In the real world, however, mechanical energy is always lost, so work in is strictly greater than work out. (Curses, foiled again!)

ideal machine
Win = Wout
Feffortseffort = Floadsload
real machine
Win > Wout
Feffortseffort > Floadsload

Efficiency, Well, I like this part.

η = Wout

Except for the Greek eta (η) symbol. It looks too much like the Latin letter n.

mechanical advantage, ho hum

MA =  Feffort

velocity ratio, hum ho.

VR =  vload

classical machines, simple machines. Is this topic even worth teaching anymore?

The classical list counts 6 devices, but 3 of them are variations of the same thing.

1st use in english 1545, for a different purpose

1545 in J. Schäfer Early Mod. Eng. Lexicogr. (1989) II. (at cited word), The hole machyne of this world is divided in .2. parte. That is to saye, in the celestiall and into the elementall regions.

More OED

1704 J. Harris Lexicon Technicum Machine, or Engine, in Mechanicks, is whatsoever hath Force sufficient either to raise or stop the Motion of a Body... Simple Machines are commonly reckoned to be Six in Number, viz. the Ballance, Leaver, Pulley, Wheel, Wedge, and Screw... Compound Machines, or Engines, are innumerable.

simple machine n. one in which there is no combination of parts, e.g. a lever, or any other of the so-called mechanical powers.

Why is the inclined plane on this list? In my opinion, it doesn't belong here because we shouldn't be using the word "machine". On an inclined plane, there is no distinction between load and effort locations, unless a machine is…

Effort is the unaltered force. Load is the altered force.