Meriam, Kraige & Bolton — Statics of Particles: Problem 2_78

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/78 Replace the three forces acting on the bent pipe by a single equivalent force R. Specify the distance from point to the point on the -axis through which the line of action of R passes. Problem 2/78 1. Resultant Force Vector ● Calculation Process 1. Present Final Formula: The resultant force is the vector sum of all individual forces. 2. Substitute Values: Based on the diagram, we have a 40 lb force and a 60 lb force acting vertically downward ( direction) and a 50 lb force acting horizontally to the right ( direction). 3. Final Calculation: ● Final Conclusion: The equivalent resultant force is . Its magnitude is and it acts at an angle from the positive -axis. 2. Sum of Moments about Point ● Calculation Process 1. Present Final Formula: Sum the moments of all individual forces about point . Clockwise moments are considered negative according to standard convention. 2. Substitute Values: xOx R R= F= ∑F + 1 F + 2 F 3 −y +x R=(50i)+(−40j)+(−60j) lb R=50i−100j lb R=50i−100j lb R= = 50+(−100) 22 111.8 lbθ=tan = −1 ( 50 −100 ) −63.4 ∘ x O O M = ∑ O −(F ⋅ 1 d )− 1 (F ⋅ 2 d )− 2 (F ⋅ 3 d ) 3 For the 40 lb force: moment arm is For the 60 lb force: moment arm is For the 50 lb force: it acts horizontally at a height of above the -axis. Pushing to the right at this height creates a clockwise moment. The moment arm is the vertical distance 3. Partial Operations: 4. Final Calculation: ● Final Conclusion: The net moment about point is in th