Pushing on a wrench with the exact same amount of force produces very different results depending on where along the handle you push, and how long the handle is in the first place. That's because what actually loosens a bolt isn't force by itself — it's torque, the rotational equivalent of force, which depends just as much on distance from the pivot point as it does on how hard you push.
Torque is force times distance from the pivot
Torque is defined as the applied force multiplied by the perpendicular distance from the pivot, or axis of rotation, to the point where that force is applied — a quantity sometimes called the lever arm or moment arm. Doubling the length of that lever arm while applying the exact same force doubles the resulting torque, which is precisely why a mechanic reaches for a longer wrench, or slides a length of pipe over a stuck wrench handle to extend it, when a bolt won't budge with a shorter tool: the force being applied by hand hasn't necessarily changed at all, but the torque it produces has increased in direct proportion to how much farther from the pivot that force is now being applied.
The same principle behind seesaws, doors, and screwdrivers
This same relationship explains why pushing a door open near its hinge takes noticeably more force than pushing it open near the handle, on the far edge from the hinge — the handle side has a much longer lever arm, so the same applied force produces far more torque there, which is exactly why door handles are placed as far from the hinge as practical rather than close to it. It also explains why a wide-diameter screwdriver handle is easier to turn than a narrow one for the same wrist force, and why long-handled bolt cutters can shear through metal that hand strength alone, applied directly, never could: in every case, the physical force involved hasn't necessarily grown at all, but positioning that force farther from the pivot multiplies the resulting torque, letting a comparatively modest force produce a rotational effect a much larger direct force, applied close to the pivot, wouldn't achieve.
What we're still unsure about
The definition of torque as force multiplied by lever-arm distance, and its consequences for tools like wrenches, doors, and levers, is fundamental, extremely well-established classical mechanics with no serious scientific dispute. Where genuine engineering judgement is still required is applying this principle to real, non-idealised situations — accounting for friction, material strength limits, and the geometry of an actual mechanical system introduces complications that the clean textbook torque formula doesn't capture on its own, which is why mechanical and structural engineers still rely on detailed calculation and testing specific to each real design, rather than the basic torque formula alone, when it matters that a mechanism perform reliably under real load.
This sits inside Rotational Motion & Torque, one of eight topics in Mechanics, one of five domains in Physics, one of seventeen subjects the app can quiz you on.