Trying To Intuit Leverage And Torque

[shozashu]

It always “feels easier” to push a door the further you are from the hinge given some perpendicular force acting on it.  From what I understand, the energy you consume over the angular sweep of the door is defined as the arc distance travelled (about the radius measured radially from the hinge to the point where the force is applied) multiplied by the magnitude of the applied force.  Thus if you have two situations, one where the force is applied at a radial distance r from the origin, and a second where the radial distance is say double that, i.e. 2r, then, for equivalent work output or energy input into the moving of the same door for the two situations, one would only have to sweep half the angle given a force applied at 2r as compared to where the force is being applied at r; in both cases however the circumferential distance or arc travelled is equal.  But I still don’t understand why it “feel easier” to push a door the further you are from the hinge?  Maybe it doesn’t, maybe if you do the experiment for both cases and make the work output same it would “feel” the same?  But I don’t think so, because it “feels harder” just to get it started to begin with, i.e. before you’ve done any travelling.  I guess this is the law of leverage at work?  My son can balance me on a see saw by sitting further from the fulcrum without moving at all; we can be static and yet we’re balanced, no arc travelled – the torques offset right? I don’t get it.  Do I just take the law of leverage as axiomatic, or am I missing something here?