- #1
minimario
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Homework Statement
A uniform pole is propped between the floor and the ceiling of a room. The height of the room is 7.80 ft, and the coefficient of static friction between the pole and the ceiling is 0.576. The coefficient of static friction between the pole and the floor is greater than that. What is the length of the longest pole that can be propped between the floor and the ceiling?
Homework Equations
Torque = F * d
The Attempt at a Solution
We consider the forces:
We first have the x-force balance: ##0.576 n_1 = \mu_2 n_2##
And the y-force balance: ##mg = n_2-n_1##
And the torque balance: ##\frac{L}{2} mg \cos \theta + L n_1 \cos \theta = L 0.576 n_1 \sin \theta ##. We can cancel the L and multiply by 2: ##mg \cos \theta + 2 n_1 \cos \theta = 1.152 n_1 \sin \theta##. (##\theta## is the bottom angle the pole makes with the ground)
But from the torque equation, we only have ##mg = n_2-n_1## so how do we make the ##n_2##s cancel?