Final answer:
Torque, relevant to wrench applications in physics, provides mechanical advantage when a force is applied perpendicular to the lever arm, maximizing the efficiency of simple machines like wrenches.
Step-by-step explanation:
The topic of the question is torque, which is a concept in Physics. Torque is the measure of the force that causes an object to rotate about an axis, and it is crucial in understanding how simple machines like wrenches amplify force. The amount of torque (₹) is determined by the equation ₹ = ℝ × F, where ℝ is the distance from the pivot point to where the force is applied, and F is the force applied. Torque has the greatest value when the applied force is perpendicular to the lever arm, meaning that the sine of the angle (π) between the force vector and lever arm is 1. This occurs at a 90° angle.
The question explains that when a force of 165 N is applied perpendicularly at a distance of 0.140 m from the pivot, the torque exerted is calculated by multiplying these two values. Similarly, for a rusty nut that is loosened by applying a 20.00-N force at a 40° angle and at 0.25 m from the nut, the torque needs to be calculated taking the angle into account, which would be less efficient than when the angle is at 90 degrees.
Torque is integral to the increase in force offered by simple machines because it represents the mechanical advantage provided. When force is applied optimally, as in perpendicular to the wrench, it maximizes the torque and hence eases the process of turning a nut or bolt. The mechanical advantage is represented by the ability to apply a smaller force over a greater distance to achieve the same effect as applying a larger force over a shorter distance.