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Homework Statement
What is the minimum force required to hold the rod at point A?
Homework Equations
The Attempt at a Solution
If no one is holding the rod, point B would get the force mg from the rod. So the normal force from the hinge to the rod is mg, pointing up. This normal force would create a torque τ, which will cause the rod to rotate.
τ = (L/2)(mg cos θ)
The force that holds the rod in place counters this torque by having the component
Fτ = mg cos θ
that is perpendicular to the rod, in the clockwise direction. However, now the three forces acting on the rod--gravity, the normal force from the hinge, and the force from the hand--no longer sum up to zero. What is wrong?
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