On this picture mg denotes the gravity force, Ffric=μN - static frictional force and N - normal force. According to the problem, mg=500N, μ=0.3 and θ=30°.
According to the Newton's second law, the projections on the y axis will be:
N−mgcosθ−Psinθ=0N=mgcosθ+Psinθ
The projections on the x axis will be:
Ffric+mgsinθ−Pcosθ=0μN+mgsinθ−Pcosθ=0 Substituting N from the first expression, get:
μ(mgcosθ+Psinθ)+mgsinθ−Pcosθ=0 Expressing P, obtain:
P=mg1+μtanθμ+tanθ P=500⋅1+0.3⋅tan30°0.3+tan30°≈373.9N Answer. 373.9 N.
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