Question

Find the force F which when applied at an horizontal angle of 15 degrees to the center of a wheel of radius R and weight W will pull it over a step of height y <r

Answer 1

We assume that force applied at an horizontal angle of 15 degrees up, otherwise it wouldn't pull the wheel over a step, it would pull it down. This is a torque problem, with the pivot point being at the corner of the step that the wheel will rotate around to get on top of the step. The applied force must provide a torque greater than the torque provided by the weight.
So the torque provided by force
F: F*cos(15)*r &gt; mg*r - the torque provided by the weight when when center of the wheel is at distance r from the vertical
edge of the step
F &gt; mg/cos(15), mg = W
F &gt; W/cos(15)
F_min = W/cos(15)