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uchicago2012
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Homework Statement
In the figure, the drawbridge has a mass of 800 kg and the hinge is rusty, producing a resistance torque of 104 Nm. What tension in the rope is necessary to raise the bridge?
See Figure 1
Homework Equations
Newton's 2nd law of rotational motion: Torquenet = I * alpha
I = rotational inertia, alpha = rotational acceleration
The Attempt at a Solution
I'm pretty lost on this question. So I said I = (1/2)MR2 for the pulley and if I did it correctly I can find the translational acceleration by
Torquenet = I * alpha
(Torquenet = R * f * sin theta, the tension in the cord, T, is tangent to R so theta = 90 and Torquenet = RT)
RT = (1/2)MR2 * alpha
T = (1/2)MR * alpha
(alpha = a/R, because the cord doesn't slip. Or it doesn't say it does.)
T = (1/2) Ma
But I'm confused where to go from here because I'm having trouble getting a force diagram for the problem. Should I just assume the center of mass of the drawbridge is in the center? But wouldn't that complicate things, because the cord is pulling on the side of the drawbridge? I also don't know how to equate something to the situation when the "bridge is raised," besides the angle being zero and I haven't figured out a use for the angle yet.
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