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A wheel of mass M has radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests. The step has height h, where h < R. What minimum force F is needed?

This problem was whispering to me: "Use energy methods...". The wheel moves about the corner of the step so I could take that as my axis of rotation and calculate the torque about it. The I proceeded to calculate the work done by this torque, i.e. [itex] W = \int{\tau} d\theta[/itex], to get the wheel up the step and equate this with the negative change of potential energy (since [itex]-W = \Delta{U}[/itex]) of the center of mass so that I could solve for F. This gave me the following (assuming I didn't screw up somewhere):

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F = \frac{mgh(1-R)}{\sqrt{2hR - h^2}}

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For F to be 'valid' I must have [itex]2hR - h^2 > 0 \Rightarrow R > h/2[/itex]. This is what worries me since I was explicitly given that R > h. I know what I did is wrong then, but I don't know what to do now. Any tips?F = \frac{mgh(1-R)}{\sqrt{2hR - h^2}}

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