Everything you are allowed to ignore.

A crate on a rope is a mess of corners, sag, friction and air. Mechanics begins by deciding what to throw away — and almost every word in this chapter is the name of something thrown away.

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A 20 kg crate, 1.2 m wide, dragged across a floor. It has corners, so it could tip. The rope has weight, so it sags. The floor grips and the air pushes back.

Nothing here can be solved as it stands.

Put all 20 kg at a single point. Size, shape and the chance of tipping go with it — and so, usually, does air resistance.

The real gain is that every force now acts at the same place, which is what lets you add them.

Light means the rope has no weight of its own: no sag, and the same tension at every point along it.

Inextensible means it cannot stretch, so the crate moves exactly as the end of the rope does.

Four arrows, all at one point. The weight is a force, so it is measured in newtons:

The rope is horizontal, so the floor pushes back just as hard: $R = 196\text{ N}$. Call the floor smooth and $F$ disappears — three arrows left.

"Smooth" is almost always the least realistic thing you have said. A real floor grips, so the real crate accelerates less than the model predicts.

That is the last step of the modelling cycle: compare, then refine. Call the floor rough and give $F$ back.

An assumption is not a fact.

The modelling cycle, the full vocabulary of assumptions, SI units and conversions, scalars against vectors, $\mathbf{i}$–$\mathbf{j}$ velocities and bearings, and twelve graded exam questions with full worked solutions are waiting.

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