Final answer:
The greatest torque is achieved with a large force on a long lever arm, as torque is the product of force, lever arm length, and the sine of the angle between them, typically maximized when the force is perpendicular to the lever arm.
Step-by-step explanation:
The result in the greatest torque would be a large force on a long lever arm. Torque (τ) is calculated as the product of the force (F) applied and the lever arm's length (L) from the pivot point, with the equation τ = F × L × sin(θ), where θ is the angle between the force and the lever arm. For maximum torque, the force should be applied perpendicular to the lever arm (θ = 90 degrees), where sin(θ) equals 1.
An example of a small force exerting a large torque is using a long wrench to loosen a tight bolt; the length of the wrench acts as a long lever arm. In contrast, an example of a large force exerting a small torque would be using a short wrench to loosen the same bolt, where the short lever arm limits the torque produced despite the large force.
Mechanical advantage can be achieved by adjusting the lever arm length, where a smaller force can be used to achieve the same torque as a larger force applied with a shorter lever arm. This property forms the basis for many tools and machines, enabling the conservation of energy within a system while manipulating the output force through physical design.