Meriam, Kraige & Bolton — Statics of Particles: Problem 2_18

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/18 Determine the resultant R of the two forces applied to the bracket. Write R in terms of unit vectors along the - and -axes shown. Problem 2/18 ● Calculation Process To find the resultant force , we first decompose each applied force into its scalar components along the given - and -axes. From the diagram, the -axis is directed along the bottom edge of the bracket, and the -axis is perpendicular to it. 1. Decompose the 150 N force (): The force has a magnitude of and is oriented at an angle of from the positive -axis towards the negative -axis. 2. Decompose the 200 N force (): The force has a magnitude of and is oriented at an angle of from the positive -axis towards the positive -axis. 3. Sum the components to find the resultant : The components of the resultant force are the algebraic sums of the components of the individual forces. 4. Express the resultant in vector form: Using the unit vectors and along the and axes respectively: xy R xyx y F 1 F 1 150 N30 ∘ yx F = 1x −150sin30= ∘ −150×0.5=−75.0 N F = 1y 150cos30= ∘ 150×0.86603≈129.90 N F 2 F 2 200 N35 ∘ xy F = 2x 200cos35= ∘ 200×0.81915≈163.83 N F = 2y 200sin35= ∘ 200×0.57358≈114.72 N R R = x F =∑ x F + 1x F = 2x −75.0+163.83=88.83 N R = y F =∑ y F + 1y F = 2y 129.90+114.72=244.62 N ijxy R=R i+ x R j= y 88.83i+244.62j N ● Final Conclusion: Rounding the results to three significant figures, the resultant force is expressed as: ✨ Final Answer Summary Resultant Force: Mecade