# Consider a wheel of mass `M` and radius `R` up against a ledge of height `h` , where `hltR` . What horizontal force `F` do you have to apply to the axle to roll the wheel up over the ledge?

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Expert Answers

Charlie Hooper | Certified Educator

The wheel will roll up if the torque due to the horizontal force `(tau_F)` exceeds the torque due to the force of gravity `(tau_g)` .

`tau_g=Mgsin(alpha)=Mg[sqrt(R^2-(R-h)^2)/R]`

`tau_F=Fcos(alpha)=F(R-h)/R`

`tau_Fgttau_g`

`F(R-h)/RgtMg[sqrt(R^2-(R-h)^2)/R]`

`FgtMg*sqrt(R^2-(R-h)^2)/(R-h)`

This is the solution. Notice if `h->R` Then `F ->oo` . If `h->0` ,` F->0` . This is intuitively reasonable.

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