Final answer:
A torque wrench is mainly used to tighten a bolt to a specific torque, which is crucial for ensuring that components are properly fastened and to maintain safety in mechanical systems. The amount of torque that a mechanic is applying can be calculated using the distance from the pivot to where the force is applied and the magnitude of the perpendicular force.
Step-by-step explanation:
A torque wrench is used primarily when the exact amount of force on the bolt has to be measured. This ensures that the bolt is tightened to the manufacturer's specified torque, which is especially important in applications like cylinder head bolts in a car engine. The torque value dictates the amount of clamping force between parts and is crucial for proper assembly and safety. Torque wrenches are not typically used just because a bolt is in a hard-to-reach area or because the threads on the bolt are stripped, nor are they simply used to exert more force on a bolt—although they can provide a precise measure of the torque being applied when greater force is necessary.
For example, if a mechanic needs to apply a torque of 62.0 N.m using a wrench of length 20 cm, the perpendicular force that must be exerted at the end of the wrench can be calculated. The formula to find the torque (τ) is τ = R × F, where R is the distance from the pivot (center of the bolt) to the point where the force is applied, F is the force, and the multiplication implies a perpendicular force to the lever arm. So, with R being 20 cm (0.20 m), the force (F) required would be 62.0 N.m / 0.20 m = 310 N.
Mechanics may use a length of pipe over the handle of a wrench to increase the leverage and thus the torque they can apply to loosen a very tight bolt. This increases the effective length R of the wrench, which increases the torque since the force is applied over a longer distance. However, this is also hazardous as it can potentially break the bolt due to excessive force.
The torque has the largest value when the angle between the force and the lever arm is 90°, meaning the force is applied perpendicularly. This configuration gives the best mechanical advantage. For an applied force of 165 N at a distance of 0.140 m from the center of the bolt, the torque in newton-meters would be 165 N × 0.140 m = 23.1 N.m. To convert this to foot-pounds, you would use the conversion factor that 1 N.m is approximately equal to 0.737562 ft.lb, resulting in 23.1 N.m × 0.737562 = 17.05 ft.lb.