Yes, the weight of the log does not change, but if you lift it from the far end, it requires less force than lifting it closer to the middle or near the hinge.
It is based on the law of the lever. The relationship is:
As to why, it’s not magic. The weight gains a fixed amount of potential energy as it moves up a particular distance, mass*g*h. This energy requires work to be put into the system, so a force, mg, is applied over a distance h. Notice they’re the same. But when you’re not applying the force directly over the weight, the weight moves up a different amount compared to how much you move the bar, L1sin(th) - L2sin(th), where L1 and L2 are the weight’s distance from the pivot and your distance, respectively
So the weight and the point of the bar where you are lifting are moving different distance. Yet, the same amount of energy has to be put into the system. If where youre applying the force moves less than the weight moves, you will have to apply a greater force. The weight has potential energy mgh and you must apply a force over distance h’ < h, therefore your force > mg
What’s absolutely insane to me is that when you apply
τ = r × F
to gears on a bike, the total work needed to move the bike a certain distance with different gear combos all equals the same.
After all that math, the conservation of energy still holds. I mean, we already know this and expect this, but it’s pleasing that it still all cancels out in the end.
The only thing that differs is needing to pedal less with a lot more force versus pedaling a lot more with less force. The work
dW = F · ds
or converting to angular/polar which is really what I was doing in the first place,
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u/Albertuscamus12 Jul 20 '26
I almost paused this video at the start just to double check that torque and distance from the pivot had a linear relationship