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henryli78
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Homework Statement
A 8.0-cm radius disk with a rotational inertia of 0.12 kg*m^2 is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end. The mass is raised by a using a crank to apply a 9.0-N*m torque to the disk. The acceleration of the mass is:
A. 0.50 m/s^2
B. 1.7 m/s^2
C. 6.2 m/s^2
D. 12 m/s^2
E. 20 m/s^2
Answer: A
Homework Equations
∑[itex]\tau[/itex] = I[itex]\alpha[/itex]
∑F = ma
a = [itex]\alpha[/itex]r
The Attempt at a Solution
The net torque of the system is:
I*[itex]\alpha[/itex] = I*a/r = 9.0 N*m - [itex]F_{T}[/itex]*r
Thus, [itex]F_{T}[/itex] = (Ia/r-9)/(-r)
By N2L:
ma = [itex]F_{T}[/itex] - mg = (Ia/r-9)/(-r) - mg
Rearranging gives:
a = (mg)/((I/r-9/(-r))-m) and substituting in values gives me an answer of about 1.17 m/s^2.
Can someone direct me on where I have gone wrong in my calculations? I would very much appreciate it :)
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