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Coulomb Friction

F_\max = \mu_s N,\quad F_k = \mu_k N

Impending slip uses the static coefficient μ_s. Once sliding, kinetic friction μ_k N opposes velocity. The friction force can be less than μN if the body is not at impending motion. For a block on a slope, impending slide occurs at α = arctan μ_s.

μ_{s}

Static friction coefficient

μ_{k}

Kinetic friction coefficient

N

(N)

Normal force

Step-by-step solved example

A 200 kg crate rests on a horizontal floor, μ_s = 0.35. What horizontal force starts motion? g = 9.81 m/s².

Block on a rough plane. Impending slip when F = μN and α = arctan μs.

1. Normal force
N = mg = 200×9.81 = 1962 N.
2. Impending friction
F = μ_s N = 0.35×1962 = 687 N.
$F = 687 N$

Answer: 687 N

10 practice questions

0/10 correct

1.If μ_s = 0.4 and N = 500 N, max static friction is

2.A block on a rough horizontal surface with no applied load has friction

3.Angle of repose is

4.Typically μ_k compared with μ_s is

5.Wedge of angle θ, μ = 0, self-locking never occurs because

6.A 50 lb block, μ_s = 0.25, just moves under P. P is

7.On a 20° slope, μ_s = 0.5, a block

8.Belt friction (no slip impending) uses

9.Normal force on a horizontal floor under a 10 kN crate is

10.If applied force is 30 N and μ_s N = 50 N, friction is