Meriam, Kraige & Bolton — Statics of Particles: Problem 2_149

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/149 A die is being used to cut threads on a rod. If 15-lb forces are applied as shown, determine the magnitude F of the equal forces exerted on the 1/4-in. rod by each of the four cutting surfaces so that their external effect on the rod is equivalent to that of the two 15-lb forces. Problem 2/149 (a) Determination of the magnitude of the cutting force F ● Calculation Process 1. Present Final Formula: The external effect of a set of forces can be characterized by their resultant force and resultant moment. For two systems to be equivalent, their resultant moments about any point must be equal (given the resultant force is zero for both, as they form couples). The moment of the couple formed by the handle forces is: where is the applied force and is the perpendicular distance between the lines of action of the two forces. The total moment produced by the four cutting forces about the center of the rod is: where is the number of forces, is the magnitude of each force, and is the radius of the rod. Equating the two moments for equivalence: where is the diameter of the rod. 2. Substitute Values: Applied force Distance between applied forces Number of cutting forces Rod diameter M = applied P×D PD F M = cutting n×F×r nFr P×D=n×F× 2 d d P=15 lbD= 5 in+5 in=10 inn=4d= in= 4 1 0.25 in 15 lb×10 in=4×F× 2 0.25 in 3. Partial Operations: Calculate the applied moment: Calculate the total moment arm factor for the four cutting forces: 4. Fina