Meriam, Kraige & Bolton — Statics of Particles: Problem 2_131

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/131 Three forces act at point O. If it is known that the y-component of the resultant R is -5 kN and that the z-component is 6 kN, determine F3, θ, and R. Given from the diagram for PROBLEM 2/131: Force is directed along the positive -axis. Force is directed along the positive -axis. Force is the third force with unknown magnitude and orientation . The resultant has a -component and a -component . Problem 2/131 1. Vector Representation of the Forces Based on the coordinate system in the diagram: The force of is directed along the positive -axis: The force of is directed along the positive -axis: The third force has unknown components: The resultant force is the vector sum of these three forces: 2. Determine Components of We are given the and components of the resultant : y-component: F = 1 4 kNy F = 2 7 kNx F 3 F 3 θ RyR = y −5 kNzR = z 6 kN 4 kNy F = 1 0i+4j+0k kN 7 kNx F = 2 7i+0j+0k kN F 3 F = 3 F i+ 3x F j+ 3y F k 3z R R=F + 1 F + 2 F = 3 (7+F )i+ 3x (4+F )j+ 3y F k 3z F 3 yzR R = y 4+F = 3y −5⟹F = 3y −5−4=−9 kN z-component: To determine , we refer to the diagram for force . The dashed lines indicate that lies in the plane (meaning its -component should be zero). However, this contradicts the given if and are purely axial as drawn. Re- interpreting the diagram, is the angle between the -axis and the projection of in the plane. A common implicit constraint in such problems for a complete solution is that the resultant has a z