Meriam, Kraige & Bolton — Statics of Particles: Problem 2_69

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/69 Calculate the magnitude of the tension and the angle for which the eye bolt will be under a resultant downward force of 15 kN. Problem 2/69 ● 1. Problem Analysis and Coordinate System To solve this problem, we establish a rectangular coordinate system with the origin at the center of the eye bolt. Let the positive -axis be directed to the right and the positive -axis be directed upwards. Based on the diagram, we identify the following forces acting on the eye bolt: Force acting in the direction. Force acting at an angle of from the vertical (in the 4th quadrant). Tension acting at an angle with the horizontal (in the 3rd quadrant). The resultant force acting vertically downwards. ● 2. Expressing Forces in Vector Components We decompose each force into its and scalar components: , , , (directed into the 3rd quadrant) , ● 3. Applying Equilibrium Equations for the Resultant The sum of the force components in each direction must equal the components of the resultant force. Horizontal Equilibrium (): Tθ xy F = 1 6 kN+x F = 2 8 kN30 ∘ Tθ R=15 kN xy F = 1x 6 kNF = 1y 0 F = 2x 8sin30 kN ∘ F = 2y −8cos30 kN ∘ T = x −TcosθT = y −Tsinθ R = x 0R = y −15 kN F =∑ x R x F + 1x F + 2x T= x R x Vertical Equilibrium (): ● 4. Solving for Magnitude and Angle To find the angle , we divide (Eq. 2) by (Eq. 1): To find the magnitude , we use the Pythagorean identity: ● Final Conclusion: The magnitude of the tension is and the angle is . ✨ Final Answ