Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_4

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The designer of a ski resort wishes to have a portion of a beginner’s slope on which the skier’s speed will remain fairly constant. Tests indicate the average coefficients of friction between skis and snow to be and . What should be the slope angle of the constant-speed section? Problem 6/4 (a) Determination of the slope angle for constant speed 1. Formula: For the skier's speed to remain constant, the net force acting along the slope must be zero (acceleration ). Summing the forces parallel and perpendicular to the slope: Since the skier is in motion, we use the kinetic friction force . Substituting the expression for : 2. Substitution: Substitute the given value for the coefficient of kinetic friction, : 3. Calculation: Solve for the angle using the arctangent function: 4. Result: ● Final Conclusion: To maintain a constant speed, the slope angle must be such that the component of weight down the slope exactly balances the kinetic friction force. This occurs μ = s 0.10μ = k 0.08θ θ a=0 F = ∑ y 0⟹N−Wcosθ=0⟹N=Wcosθ F = ∑ x 0⟹Wsinθ−F = k 0⟹Wsinθ=F k F = k μ N k N Wsinθ=μ Wcosθ k tanθ=μ k μ = k 0.08 tanθ=0.08 θ θ=tan(0.08) −1 θ≈4.5739 ∘ θ≈4.57 ∘ θ when , resulting in an angle of . ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 6/4 tanθ=μ k θ=4.57 ∘ θ=4.57 ∘