Answer:
A) F = 8.57N
B) F = 38.64N
Explanation:
A) The formula for least magnitude of force F, parallel to the plane, that will prevent the sled from slipping down the plane is given as;
F = mgsinθ - μ_s•mgcosθ
Where;
mg is weight of Penguin = 80N
θ is angle of the inclined plane = 20°
μ_s is coefficient of static friction = 0.25
Thus,F = mg(sinθ - μ_s•cosθ) = 80(sin20 - 0.25cos20)
F = 80(0.342 - 0.2349)
F = 8.57N
B) The formula to calculate the value of F required to move the sled up the plane at a constant velocity is given as;
F = mgsinθ + μ_k•mgcosθ
F = mg(sinθ + μ_k•cosθ)
Where;
mg is weight of Penguin = 80N
θ is angle of the inclined plane = 20°
μ_k is coefficient of kinetic friction = 0.15
Thus,
F = mg(sinθ + μ_k•cosθ) = 80(sin20 - 0.15cos20)
F = 80(0.342 + 0.141) = 38.64
