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Ladder Friction
adjust θ · change μ · watch it slip
Equilibrium ✓
θ =
60
°
N₁
N₂
f₁
f₂
W
Angle θ with floor
θ
60°
Floor friction μ₁
μ₁
0.35
Wall friction μ₂
μ₂
0.20
Mode
Both rough (μ₁, μ₂)
Wall smooth (μ₂=0)
Same friction (μ₁=μ₂)
Floor smooth (μ₁=0)
Critical θ
Forces (W=1)
N₁
—
N₂
—
f₁
—
↺ Reset Ladder
Formulas
Both Rough
tan(θ) =
(1−μ₁μ₂)/(μ₁+μ₂)
cot(θ) =
(μ₁+μ₂)/(1−μ₁μ₂)
Wall Smooth (μ₂=0)
μ₁ =
(1/2)·cot(θ)
Same Friction (μ₁=μ₂=μ)
μ =
(1−sin θ)/cos θ
μ =
sec θ − tan θ
Floor Smooth (μ₁=0)
No equilibrium possible
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