Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_60

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The coefficient of static friction between the 100-lb body and the 15° wedge is 0.20. Determine the magnitude of the force required to begin raising the 100-lb body if (a) rollers of negligible friction are present under the wedge, as illustrated, and (b) the rollers are removed and the coefficient of static friction applies at this surface as well. Problem 6/60 (a) Rollers of negligible friction under the wedge 1. Formula: When a wedge is used to raise a load constrained by vertical guides, the required force (neglecting ground friction) is given by: where: is the weight of the load. is the wedge angle. is the angle of static friction between the body and the wedge. 2. Substitution: Substitute the given values , , and : 3. Calculation: First, calculate the friction angle: Calculate the combined angle: Determine the tangent value: Final product: 4. Result: μ s P μ = s 0.20 P P=Wtan(α+φ ) s W α φ = s arctan(μ ) s W=100 lbα=15 ∘ μ = s 0.20 P=100⋅tan(15+ ∘ arctan(0.20)) φ = s arctan(0.20)≈11.31 ∘ α+φ = s 15+ ∘ 11.31= ∘ 26.31 ∘ tan(26.31)≈ ∘ 0.4944 P=100×0.4944=49.44 lb P≈49.4 lb ● Final Conclusion: The force required to begin raising the body when there is no friction at the ground is 49.4 lb. (b) Friction at the bottom of the wedge 1. Formula: When friction also exists at the base of the wedge, the required force must also overcome the friction at that surface. The normal force on the ground is equal to the weight . The additional f