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Physics.fisikastudycenter.com,- Physics Olympiads Problems and Solutions Examples, Problem 8 for senior high school. Basic concepts needed in this problem are mechanics, forces, torque, equilibrium and phytagorean.

Problem 8
In figure below, what magnitude of force F should be applied on the wheel is necessary to raise the wheel over an obstacle of height h, the radius of the wheel is R , it's mass is m and the accelaration due to gravity is g, show the answer in g, R and h.

Solution Problem 8
Sketch the problem, include the necessary forces acting on the system. The sample shown below, you might have your own sketch or free-body diagram.

The forces are the weight of the wheel (W) where W = mg, the force F, the normal force acting at point B, named N_B. Actually there is a normal force acting on point A, we neglect it because point A will be our pivot point.

The additional data that will we need are d_F (perpendicular distance of force F to the pivot point)), and d_W (perpendicular distance of W to the pivot point). Without any difficulties d_F = 2R-h and apply phytagorean for AOC triangle to get d_W :



Applying equilibrium conditions, calculate Σ τ = 0, use point A as a pivot, and take the magnitude of N_B is zero. (As it raises, no normal force acting on B)



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Literature: Problem #21, Equilibrium and Elasticity, Fundamentals of Physics 8 Ed, Halliday.Resnick