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46. Problem 13.29P (HRW) A force F is applied horizontally at the axle of a wheel for raising the wheel over an obstacle of height h. We have to find the force F necessary for raising the wheel over the obstacle. We can take r as the radius of the wheel and W as its weight.
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Solution: Click For PDF Version
When the wheel is just about to rise over the obstacle there will be no normal force from the ground it. In addition to the weight W and force F the wheel will experience a normal force T exerted by the edge of the obstacle, indicated by O in the free-body diagram of the wheel. Let x be the moment arm of the force W about the point O. From geometry we have the relation
We calculate the torque about the point O. Condition for equilibrium is that net torque has to be zero. This gives the condition
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