Static Friction Adjusts Up to μs N; Kinetic Friction Is a Fixed μk N
Friction questions turn on two distinctions: whether the object is at rest (friction adjusts, up to a limit) or sliding (friction takes a fixed value), and what the normal force really is, which is not always mg.
Motion and force questions become simpler when direction, starting condition, time and the acting forces are marked first.
Static versus kinetic friction
Static friction adjusts to whatever balances the applied force, up to the limit fₛ ≤ μs N; sliding friction is fₖ = μk N with μk smaller than μs.
once moving, friction drops to 0.2 x 200 = 40 N, so with the same 120 N the net force is 80 N and a = 4 m/s². The coefficient of friction is a pure ratio of two forces, so it has no dimensions, and rolling friction is smaller than sliding friction.
Normal force changes the limit
Because 6.4 N exceeds 6 N, the block stays at rest and friction equals the applied force, 6 N, not 6.4.
Inclines
A block at rest on an incline has friction f = m g sinθ, not μ m g cosθ: a 10 N frictional force on a 30° incline means 5m = 10 and m = 2 kg, regardless of μ.
If a block takes n times as long to slide down a rough 45° incline as down a smooth one, a_smooth = g sinθ and a_rough = g (sinθ - μ cosθ), and since t is proportional to 1/sqrt(a), n² = 1/(1 - μ), so μ = 1 - 1/n².
Hanging masses and stacked loads
A block on a table pulled by a hanging mass starts to slide when the pull equals μs M g. If a 6 kg mass hangs from a cord pulling a 4 kg block with μ = 0.4, an extra mass m on the block stops the acceleration when 0.4 (4 + m) g = 6 g, so m = 11 kg. A load placed on a 10 kg block that is pressed on a rough surface prevents slipping when the friction μ (10 + m) g equals 10 g, giving m = 10 kg for μ = 0.5. In movable-pulley set-ups, the hanging weight is shared by two string segments, so the tension on the block is half the hanging weight.
OlympIQ exam lens
- ✓Static friction is f ≤ μs N and adjusts to the applied force; kinetic friction is μk N
- ✓Check whether the applied force exceeds μs N before deciding the block moves
- ✓Normal force N is not always mg: include vertical pushes, pulls and accelerations
- ✓At rest on an incline: friction = m g sinθ; sliding starts at tanθ = μs
- ✓Sliding-time ratio on a rough and a smooth 45° incline: μ = 1 - 1/n²
Do not use μ N as the friction on a block that is not sliding. Friction on a stationary block equals the force it opposes, which is less than μ N unless the block is about to slip.
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