Answer:
a) F = 43 N
b) F = 17 N
Explanation:
Sum forces to zero (no acceleration in F = ma) acting parallel to the slope
Let's assume up slope is the positive direction
a) up the incline means that friction acts down slope
Fcosθ - mgsinθ - μN = 0
Fcosθ - mgsinθ - μ(mgcosθ + Fsinθ) = 0
Fcosθ - μFsinθ = mgsinθ + μmgcosθ
F(cosθ - μsinθ) = mg(sinθ + μcosθ)
F = mg(sinθ + μcosθ) / (cosθ - μsinθ)
F = 5(9.8)(sin30 + 0.20cos30) / (cos30 - 0.20sin30)
F = 43.062... ≈ 43 N
b) down the incline means that friction acts up slope
Fcosθ - mgsinθ + μN = 0
Fcosθ - mgsinθ + μ(mgcosθ + Fsinθ) = 0
Fcosθ + μFsinθ = mgsinθ - μmgcosθ
F(cosθ + μsinθ) = mg(sinθ - μcosθ)
F = mg(sinθ - μcosθ) / (cosθ + μsinθ)
F = 5(9.8)(sin30 - 0.20cos30) / (cos30 + 0.20sin30)
F = 16.576...≈ 17 N
