Meriam, Kraige & Bolton — Statics of Particles: Problem 2_24

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/24 At what angle must the 400-lb force be applied in order that the resultant of the two forces have a magnitude of 1000 lb? For this condition what will be the angle between and the horizontal? Problem 2/24 ● Solution Strategy We are given two forces acting at a common point . Let's define a coordinate system where the positive -axis points to the left (along the 700-lb force) and the positive -axis points upwards. This choice simplifies the components because the 700-lb force is entirely horizontal. Force 1: directed along the positive -axis. Force 2: directed at an angle relative to the -axis. The magnitude of the resultant is specified as . We will use the law of cosines for vector addition to find , and then use the components or the law of sines to find . (a) Determination of angle ● Calculation Process 1. Present Final Formula: Using the law of cosines for the magnitude of the resultant of two forces and with an angle between them: 2. Substitute Values: 3. Partial Operations: θR βR O xy F = 1 700 lbx F = 2 400 lbθx R=F + 1 F 2 R=1000 lb θ β θ F 1 F 2 θ R= 2 F + 1 2 F + 2 2 2F F cosθ 12 1000= 2 700+ 2 400+ 2 2(700)(400)cosθ 1,000,000=490,000+160,000+560,000cosθ 1,000,000=650,000+560,000cosθ 4. Final Calculation: ● Final Conclusion: The angle must be . (b) Determination of angle ● Calculation Process 1. Present Final Formula: The resultant vector's components in our coordinate system (where horizontal is the -axis) are: The