Find the acceleration of the disk and the force of friction

AI Thread Summary
To find the acceleration of the disk and the force of friction, the problem involves a disk with a radius of 18 cm and mass of 9.3 kg being pulled up an incline of 37° by a tension of 20 Newtons. The relevant equation T = I(alpha) is used, where I is the mass moment of inertia, calculated as I = (1/2)mR^2. The discussion emphasizes the need to resolve forces along the incline and normal to it, considering equilibrium and moments about the disk's center. The unknowns include angular acceleration, frictional force, and normal force, with three equations available to solve for these variables. The analysis indicates that the initial approach may not correctly account for tension, requiring further examination.
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Homework Statement


In the figure, a string is used to pull a disk of radius 18 cm and mass 9.3 kg. If the incline is 37° and the tension in the string is 20 Newtons find the acceleration of the disk and the force of friction on it.


Homework Equations


T=I(alpha)


The Attempt at a Solution


T=I(alpha) --> Rmg=(1/2mR^2+mR^2)(alpha)
I moved the pivot to the contact point of the ramp.
Alpha= 2/3 g/r
a=2/3g
this can't be right though because I didn't figure the tension into it.
I'm lost. please help

[PLAIN]http://www.usi.edu/science/physics/pickett/205/16p3f1.jpg
 
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Draw the free body diagram of the disk. Resolve the components of forces along the incline (x axis) and normal to the incline (y axis). Consider equilibrium of forces along x and y
and moments about the center of disk.

The unknowns are alpha (angular acceleration), F(frictional force) , N (normal force)
and you have 3 equations.

The mass moment of inertia of disk I is = m * r^2/2
 
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