What Force Is Needed to Roll a Wheelchair Over a Curb?

[AriAstronomer]

Homework Statement

(a) Estimate the magnitude of the force F a person must apply
to a wheelchair’s main wheel to roll up over a sidewalk
curb (Fig. 12.11a). This main wheel, which is the one that
comes in contact with the curb, has a radius r, and the height
of the curb is h.

Homework Equations

The Attempt at a Solution

The solution is given in the book. The thing I am stuck on is understanding the moment arm. A diagram is attached.

Apparently the moment arm to from P to O is the x component - d = [r^2 - (r-h)^2]^1/2, why wasn't it just the radius r??
Same thing goes for F - I would have thought it would just a direct line connecting P to C (the Force), but instead they say it's just the y component, or 2r - h. Why?

Ari

 

[PhanthomJay]

The moment of a force about a point is the force times the perpendicular distance from the line of action of the force to that point. When the wheel jumps the curve, the wheel at point Q leaves the ground, and thus there is no force there from the ground. All the forces required from equilibrium , required to balance the wheels weight and the applied force F, are are at P, both vertically and horizontally. Try summing moments about P instead of 0.