Friction: Static, Kinetic, and the Angle of Repose

Free notes · JEE Main Physics

Formulas

f_s \le \mu_s N, \qquad f_k = \mu_k N, \qquad \tan\theta_0 = \mu_s

The three friction laws: static limit, kinetic value, angle of repose

a = g\,(\sin\theta - \mu_k \cos\theta)

Acceleration of a block sliding down an incline

Key points

Static friction is NOT always μ_s N. It is whatever it needs to be, up to that ceiling. Writing f_s = μ_s N for a block that is not about to slip is the #1 friction error in JEE papers.

Worked example

A 5 kg block rests on an incline at 30° with μ_s = 0.6, μ_k = 0.4 (g = 10 m/s²). (a) Does it slide? (b) If the incline is raised to 40°, find its acceleration.

(a) tan 30° ≈ 0.577 < μ_s = 0.6 → static friction can hold it: it does NOT slide; f_s = mg sin 30° = 25 N
(b) tan 40° ≈ 0.839 > 0.6 → it slides: a = g(sin 40° − μ_k cos 40°) = 10(0.643 − 0.4 × 0.766) ≈ 3.37 m/s²

Answer: (a) no, f_s = 25 N; (b) a ≈ 3.37 m/s²