The big idea: Try to shove a heavy sofa. At first it won't budge — then suddenly it gives and slides more easily.
That's friction: the force between two touching surfaces that opposes sliding. It comes in two kinds — static (holding a still object in place) and dynamic (once it's sliding).
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Static friction (not moving)
- Acts while the object is still stuck
- Grows to match whatever pushes it
- Has a limit — push past it and the object slips
Dynamic friction (sliding)
- Acts while the object is sliding
- Stays a fixed size, however hard you push
- Usually smaller than the biggest static friction
Spot the difference: Static = stuck. Friction is whatever it needs to be to hold the object still — up to a limit.
Dynamic = sliding. Once it is moving, friction settles to a steady, usually smaller value.
Either way it points against the way you are trying to slide the object.
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Before any formula, it helps to know what actually changes the size of friction. Only two things do.
1 · How hard the surfaces are pressed together: Pile books on a box and it gets much harder to shove — the two surfaces are squeezed together more tightly, so they grip more.
The surface pushes back on the object at a right angle to it. That push is called the normal force, R. On flat ground it simply balances the object's weight.
Your push (right) and friction (left) act along the surface — friction always opposes the push. Weight (down) and the normal force R (up) act at right angles to the surface.
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2 · How rough the two surfaces are: The same box slides easily on ice and barely at all on carpet — same object, same weight, completely different grip.
Physics packs that roughness into a single number: the coefficient of friction, μ. Rougher pair → bigger μ → more friction.
So friction's size comes from how hard they press (R) and how rough they are (μ) — which is exactly what the formula in the next section puts together.
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Both friction rules are given in the data booklet. The normal force R is how hard the surface pushes back; on flat ground R is just the object's weight, R = mg.
- friction force, parallel to the surface (N)
- coefficient of STATIC friction (no unit — just a number)
- normal force — the support push, perpendicular to the surface (N). Also written F_N.
- friction force while sliding, parallel to the surface (N)
- coefficient of DYNAMIC (kinetic) friction (no unit — just a number)
- normal force — the support push, perpendicular to the surface (N). Also written F_N.
The same push, step by step — and where the 8 N ceiling comes from.
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Why is μ just a number?: Rearrange Ff = μR to μ = Ff ÷ R — that's a force ÷ a force. The newtons on top and bottom cancel, so μ has no unit: it is dimensionless (a pure number, usually between 0 and 1).
Friction triangle: Ff = friction, μ = coefficient, R = normal force. Cover the one you want — two side by side → multiply (Ff = μR); one above the other → divide (μ = Ff ÷ R).
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A crate of mass 20 kg is dragged across a flat floor at steady speed. The coefficient of dynamic friction is μd = 0.30. (Take g = 9.8 m s⁻².) Find the friction force. (On flat ground R = mg.)
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How this is tested — friction shows up in force and motion questions. It comes up two ways:
Paper 1A
- Quick concept — why μ is dimensionless.
- Static vs dynamic friction.
Paper 1B / Paper 2
- The classic 'show that' calculation.
- The minimum force to start an object moving.
The classic trap: To start motion you must beat the largest static friction (μs R), not the smaller sliding friction. Use μs, not μd.
Minimum force to start moving: An object stays still until your push beats the biggest static friction it can muster. So the minimum force to start it sliding equals μs R — the maximum value of Ff ≤ μs R.
A box of mass 1.2 kg sits on a flat bench. The coefficient of static friction is μs = 0.35. (Take g = 9.8 m s⁻².) Show that the minimum horizontal force to start it moving is about 4 N.
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