Question

a cylindrical drum has radius r and weight W. the drum is to be rolled over onto a step of height r/2 by a horizontal force F applied to the top of the drum
what is the minimum force F required for the drum to start rolling on the step?

Answer 1

$$F(r-h)=W\sqrt{r^2-(r-h)^2}$$

$$h=0.5r$$

$$F(r-0.5r)=W\sqrt{r^2-(r-0.5r)^2}$$

$$F(0.5r)=W\sqrt{0.75r^2}$$

$$F=\sqrt{3}W$$