ΣFy=0
N=Wcosα-Psinα -----(1)
ΣFx=0
-Pcosα-f-Wsinα=0 -----(2)
(1)代入(2)
-Pcosα+μ(Wcosα-Psinα)-Wsinα=0
μPsinα+Pcosα=-Wsinα+Wμcosα
P(μsinα+cosα)=W(-sinα+μcosα)
同除cosα
P(μtanα+1)=W(-tanα+μ)
P=W (-tanα+μ) / (μtanα+1)
μ=tanΦ(摩擦角的正切值=摩擦係數)代入
P=W (-tanα+tanΦ) / (tanΦtanα+1)
=W (tanΦ-tanα) / (1+tanΦtanα)
=W tan(Φ-α)