Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_3

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The force is applied to the 50-kg block when it is at rest. Determine the magnitude and direction of the friction force exerted by the surface on the block if (a) , (b) , and (c) . (d) What value of is required to initiate motion up the incline? The coefficients of static and kinetic friction between the block and the incline are and , respectively. Problem 6/3 (a) Friction force for 1. Formula: First, calculate the weight and its components. Let the -axis be parallel to the incline (positive upwards) and the -axis be perpendicular to the incline (positive outwards). Determine the normal force and max static friction : 2. Substitution: 3. Calculation: Force tending to cause motion down the incline: . Check for equilibrium: Since , the block slips down the incline. Friction is kinetic: . P FP=0P= 200 NP=250 NP μ = s 0.25μ= k 0.20 P=0 W=mgx y W=mg,W = x −Wsin(15),W = ∘ y −Wcos(15) ∘ NF max F = ∑ y 0⇒N=Wcos(15) ∘ F = max μ N s W=50×9.81=490.5 N N=490.5cos(15)= ∘ 473.79 N F = max 0.25×473.79=118.45 N ∣W ∣= x 490.5sin(15)= ∘ 126.95 N 126.95 N>F = max 118.45 N F=μ N= k 0.20×473.79=94.76 N Direction: Since the block moves down, friction acts up the incline. 4. Result: up the incline ● Final Conclusion: The friction force is acting up the incline. (b) Friction force for 1. Formula: Re-calculate normal force and with the applied force : Net force along the incline excluding friction: 2. Substitution: 3. Calculation: Check for equilibrium: