Difficult problem involving friction and torque

[tjkubo]

Homework Statement

A cord connected at one end to a block which can slide on an inclined plane has its other end wrapped around a cylinder resting in a depression at the top of the plane as shown in the figure:
http://img35.imageshack.us/img35/6743/giancolich10p098.jpg
Determine the speed of the block after it has traveled 1.40 m along the plane, starting from rest.

Assume the coefficient of friction between all surfaces is μ = 3.00×10^-2. [Hint: First determine the normal force on the cylinder, and make any reasonable assumptions needed.]

Homework Equations

Newton's second law in linear and angular form

The Attempt at a Solution

The forces on the block are fairly obvious: tension T, friction f, weight mg, and normal F.
However, I am not so sure about the forces on the cylinder. First there is T and Mg. I know there is a normal force N, but I wasn't sure of the direction so I drew it pointing to the upper left, an angle θ above the horizontal. I also was not sure about the frictional force. Is it perpendicular to N? If so, I got the following 4 equations in 4 unknowns:

$$\] \\ -Ncos\theta+Tcos27+\mu Nsin\theta=0 \\ \mu Ncos\theta+Nsin\theta-Tsin27-Mg=0 \\ T-f=.5Ma \\ -T-mg cos27+mg sin27=ma \[$$

I can't seem to get the right answer from these though.

 

[Just a nobody]

From the diagram, I get the impression that the cylinder is not actually touching the triangle and is instead attached to a pivot point (which I will assume frictionless).

If this is the case, the forces on the block are the gravitational force, kinetic friction force, tension force, and normal force. The only force on the cylinder is the tension force.

You can use these to find that:
$$\Sigma F = ma = mg \sin \theta - T - \mu_k N$$
and
$$\Sigma \tau = I\alpha = R \times T$$

 

[kerimek]

Any suggestions on where I might be going wrong?

I would first commend the student for their attempt at solving the problem and for recognizing that the forces on the block are more straightforward than those on the cylinder. I would also suggest that they double check their equations and make sure they are using the correct angles and signs for each force. It may also be helpful to draw a free body diagram for the cylinder to better visualize the forces acting on it. Additionally, I would remind the student to always make reasonable assumptions when necessary and to check their final answer to see if it makes sense (e.g. is the speed of the block realistic?). If they are still having trouble, I would suggest seeking help from a peer, TA, or professor.