Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_41

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The device shown is used to test automobile-engine valve springs. The torque wrench is directly connected to arm OB. The specification for the automotive intake-valve spring is that 83 lb of force should reduce its length from 2 in. (unstressed length) to in. What is the corresponding reading on the torque wrench, and what force exerted on the torque- wrench handle is required to produce this reading? Neglect the small effects of changes in the angular position of arm . Problem 3/41 (a) Reading on the torque wrench 1. Formula: To maintain equilibrium, the reading on the torque wrench must equal the magnitude of the moment generated by the spring force about the pivot point . where is the spring force and is the horizontal distance from pivot to the spring at . 2. Substitution: From the problem statement, the required spring force is . From the diagram, the horizontal distance is . 3. Calculation: Alternatively, converting to foot-pounds: 4. Result: (or ) ● Final Conclusion: The reading on the torque wrench is . (b) Force required on the handle 1 16 11 MF OB M M O M=ΣM = O F ⋅ s d B F s d B O B F = s 83 lb d = B 6 in. M=83 lb×6 in. M=498 lb⋅in. M= lb⋅ 12 498 ft=41.5 lb⋅ft M=498 lb⋅in.41.5 lb⋅ft 498 lb⋅in. F 1. Formula: The moment produced by the force at point about pivot must equal the required moment . Using the perpendicular component of : where is the angle between force and the normal to the handle, and is the length of the ha