# Moment Arms

1. Jun 19, 2011

### AriAstronomer

1. The problem statement, all variables and given/known data
(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.

2. Relevant equations

3. 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

#### Attached Files:

• ###### diagram.jpg
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2. Jun 19, 2011

### 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.