Friction revisited: rough surfaces, μ and the angle of friction
Answers are for parents and teachers.
1
A 12 kg suitcase (weight 120 N) on a rough floor is just about to slide under a horizontal pull of 36 N. Find N, μ, R′ and λ.
N = 120 N; μ = 36/120 = 0.3; R′ = √(120² + 36²) = √15696 ≈ 125.28 N; λ = tan⁻¹ 0.3 ≈ 16.7°.
2
A 400 N load stands on a surface with μ = 0.6, and the same load sliding has μk = 0.45. Find the limiting friction, the kinetic friction, and the two angles λ.
Fs = 0.6 × 400 = 240 N and Fk = 0.45 × 400 = 180 N. λs = tan⁻¹ 0.6 ≈ 31.0° and λk = tan⁻¹ 0.45 ≈ 24.2°.
3
A 150 N trunk on a floor with μ = 0.5 is dragged by a rope at 20° above the horizontal. Find the pull P that just starts it moving.
P = 0.5 × 150 / (cos 20° + 0.5 sin 20°) = 75 / 1.1107 ≈ 67.52 N.
4
A 40 N book starts to slide when a board is tilted to 24°. Find μ. Then find the friction on the book when the board is tilted only 15°.
μ = tan 24° ≈ 0.445. At 15° the book is at rest, so F = 40 sin 15° ≈ 10.35 N (not μN).