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Newton's Third Law and Free-Body Diagrams

Forces come in pairs — but the pair acts on different bodies. Meet the normal force and tension, then learn the one diagram that unlocks every dynamics problem.

Every force comes in a pair

Press your hand against a wall and you feel the wall press back. That is Newton's third law: whenever object A exerts a force on object B, object B exerts an equal and opposite force back on A. Forces never appear alone — they appear as interaction pairs.

\vec{F}_{A \to B} = -\,\vec{F}_{B \to A}

The force A exerts on B is equal in magnitude and opposite in direction to the force B exerts on A.

The forces you will meet again and again

Most first-year problems use a small cast of forces. Gravity (W = mg, always straight down) you already know. Two contact forces round out the toolkit. The normal force is the perpendicular push a surface gives to whatever rests on it; it adjusts itself to whatever value stops objects passing through each other.

The tension is the pull transmitted along a rope, string or cable. In the usual idealization of a massless, inextensible string running over a frictionless pulley, the tension is the same at every point — the string simply redirects the pull without changing its size.

The free-body diagram: your master tool

A free-body diagram (自由體圖) is a picture of one object, alone, with an arrow for every force acting on it — and nothing else. No scenery, no forces the object exerts on other things, no imaginary "force of motion." Drawing it well is the single most important habit in mechanics: get the diagram right and the equations almost write themselves.

Three worked free-body diagrams — a hanging mass, a block resting on a table, and a block being pushed — with every force on the object labelled.

Reading a diagram back into physics

Once drawn, the diagram tells you the motion. A lamp hanging still shows two arrows, tension up and weight down; since it is in equilibrium the first law demands they balance, so T = mg. A book resting on a table shows normal force up and weight down, again equal. The instant the arrows don't balance, the leftover is the net force and the second law gives the acceleration.

So far our surfaces have been frictionless idealizations. Real surfaces grip: they resist sliding with a force that can hold a book on a tilted desk or bring a car to a stop. That force — friction — is the missing piece, and it is where we turn next.