Meriam, Kraige & Bolton — Statics of Particles: Problem 2_144

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/144 In tightening a bolt whose center is at point O, a person exerts a 40-lb force on the ratchet handle with his right hand. In addition, with his left hand he exerts a 20-lb force as shown in order to secure the socket onto the bolt head. Determine the equivalent force–couple system at O. Then find the point in the x-y plane through which the line of action of the resultant force of the wrench passes. Problem 2/144 1. Identify Given Forces and Their Positions From the problem description and the provided diagram, we can define the forces and their application points in the given coordinate system (origin at ): Left-hand force (): A force is applied at the socket to "secure" it. According to the arrow in the diagram, it acts in the positive -direction at the origin . Right-hand force (): A force is applied at the end of the handle. The handle is offset from the -axis by along the -axis, and the force is applied along the -direction from the bolt axis. The force arrow points vertically downward (negative -direction). 2. Determine the Equivalent Force-Couple System at O ● Calculation of Resultant Force () 1. Formula: 2. Substitute Values: 3. Final Calculation: O F 1 20 lb yO F = 1 20j lb r = 1 0i+0j+0k in F 2 40 lb y1.4 inx8 in y z F = 2 −40k lb r = 2 1.4i+8j in R R=F=∑F + 1 F 2 R=(20j)+(−40k) R=20j−40k lb ● Calculation of Resultant Moment () 1. Formula: 2. Substitute Values: 3. Partial Operations: Using unit vector cross product