Kinetics in Nromal and Tangential coordinates - SPINING ROD W/ SPOOL

[VinnyCee]

Kinetics in Nromal and Tangential coordinates - SPINNING ROD W/ SPOOL

The 2-kg spool fits loosely on the inclined rod for which the coefficient of static friction is $\mu_s\,=\,0.2$. If the spool is located 0.25 m from A, determine the maximum speed the spool can have so that it does not slip up the rod.

http://img207.imageshack.us/img207/6962/problem13770pa.jpg

Here is what I have for this problem, but it is wrong according to the answer in the text:

$$sin\,\theta\,=\,\frac{3}{5}$$

$$\theta\,=\,36.9$$

$$\sum\,F_x\,=\,N\,cos\,53.1\,-\,f_s\,cos\,36.9\,=\,m\,a_n$$

$$\sum\,F_y\,=\,N\,sin\,53.1\,+\,f_s\,sin\,36.9\,-\,m\,g\,=\,m\,a_y$$

$$N\,=\,\frac{m\,g}{sin\,53.1\,+\,\mu_s\,sin\,36.9}$$

$$N\,=\,21.31\,N$$

Then I use another version of the $F_x$ equation to solve for $v_{max}$:

$$N\,cos53.1\,-\,N\,\mu_s\,cos\,36.9\,=\,m\,\frac{v_{max}^2}{\rho}$$

$$v_{max}^2\,=\,\frac{9.39}{10}$$

$$v_{max}\,=\,0.969\,\frac{m}{s}$$

The answer is 1.48 in the text though! Any suggestions?

 

[Doc Al]

What's the direction of the friction force on the spool?

 

[VinnyCee]

Down the rod towards point A, right?

 

[Doc Al]

Exactly. Now revise your equations accordingly.