The physics of pushing

[Ether]

Originally Posted by Ken Streeter

either I'm missing something (the reason for tau being in the answer) or you made a minor mistake.

Nice catch. In my haste I labelled "h" as the vertical distance from the force to the ground. It should be the vertical distance from the force to the horizontal witness line through the center of the rear wheels.

See corrected diagram in original post.

In the corrected diagram, you get F*h + tau = W*k,

so F = (W*k -tau)/h (as originally posted).

If you then assume tau = F*r in the above equation (where "r" is wheel radius),

you get F = k*W/(h+r), where "h+r" in the new diagram is the "h" in the old one.

So yes, the formula for the original diagram should have been F = W*k/h.

For the corrected diagram, it is F=W*k/(h+r), which amounts to the same thing.

Sorry for the confusion.