A mechanic working in an engine needs to tighten a bolt onto the engine block using a wrench. Assume a typical threading. Identify the lever arm in the scenario
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The direction of the force on an engine bolt is important for tightening it correctly. In this scenario, the mechanic needs to tighten the bolt onto the engine block using a wrench. The threading is typical, which means that turning the bolt clockwise (righty tighty) will tighten it, while turning it counterclockwise (lefty loosey) will loosen it. To maximize torque, the mechanic needs to apply their force at a specific angle to the lever arm. The lever arm is the distance between the axis of rotation (in this case, the bolt) and the point where the force is applied (the wrench). The angle at which the force should be applied to maximize torque depends on the specific situation and the desired outcome. The torque is applied in the direction perpendicular to the plane of rotation. In Cartesian xyz coordinates, if the bolt is in the x-y plane, the torque will be applied in the z-direction. The unit of torque is typically measured in Newton-meters (N·m) or foot-pounds (ft·lb), depending on the system of measurement used.
Stephen Z.
A bolt must be tightened with a torque 35 N.m. You use a wrench that is 25 cm long and pull at an angle of 60 degrees. How long is the lever arm and what force do you exert?
Bhushan A.
The box wrench in Fig. 5-15a is used to tighten the bolt at A. If the wrench does not turn when the load is applied to the handle, determine the torque or moment applied to the bolt and the force of the wrench on the bolt. SOLUTION Free-Body Diagram. The free-body diagram for the wrench is shown in Fig. 5-15b. Since the bolt acts as a ‐fixed support,‐ it exerts force components Ax and Ay and a moment MA on the wrench at A. Equations of Equilibrium. →+ ΣFx = 0; Ax − 52(5/13) N + 30 cos 60° N = 0 Ax = 5.00 N Ans. +↑ ΣFy = 0; Ay − 52(12/13) N − 30 sin 60° N = 0 Ay = 74.0 N Ans. ↺+ΣMA = 0; MA − [52(12/13) N] (0.3 m) − (30 sin 60° N)(0.7 m) = 0 MA = 32.6 N · m Ans. Note that MA must be included in this moment summation. This couple moment is a free vector and represents the twisting resistance of the bolt on the wrench. By Newton’s third law, the wrench exerts an equal but opposite moment or torque on the bolt. Furthermore, the resultant force on the wrench is FA = √(5.00)² + (74.0)² = 74.1 N Ans. NOTE: Although only three independent equilibrium equations can be written for a rigid body, it is a good practice to check the calculations using a fourth equilibrium equation. For example, the above computations may be verified in part by summing moments about point C: ↺+ΣMC = 0; [52(12/13) N] (0.4 m) + 32.6 N · m − 74.0 N(0.7 m) = 0 19.2 N · m + 32.6 N · m − 51.8 N · m = 0
Sri K.
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