Maximum angular velocity and free body diagram

[fredrogers3]

Homework Statement

I have found the question I am having trouble with here:

http://www.chegg.com/homework-help/questions-and-answers/block-mass-m-rest-surface-incline-adistance-h-10cm-base-height-incline-ish-50cm--coefficie-q218123

Homework Equations

See below

The Attempt at a Solution

After doing my free body diagram, I picked the vertical axis to be y and the horizontal axis to be r.
Force total in the r direction= Fnsinθ-Ffrcosθ= m((v^2)/r)
In the y direction, = Ffrsinθ + FnCosθ-mg=0, b/c a=0

If this box is not to be in motion, then the sum of these forces should be zero. I set the two equations = to zero, while solving for v, but it did not come out to the 1.8 that is given as a solution. Are my components at least correct? If so, where am I going wrong?

 

[haruspex]

s to be y and the horizontal axis to be r.
Force total in the r direction= Fnsinθ-Ffrcosθ= m((v^2)/r)

In which direction does each of those forces act? What is the direction of acceleration?

 

[fredrogers3]

Don't the negative and positive signs indicate the direction? This is knowing that r is positive to the right and y is positive upwards.

 

[haruspex]

Don't the negative and positive signs indicate the direction? This is knowing that r is positive to the right and y is positive upwards.

I was hinting that you have some signs wrong.

 

[fredrogers3]

I was hinting that you have some signs wrong.

I see a is negative, but I don't see anything wrong with the other signs. My rough free body diagram is attached

 

[haruspex]

I see a is negative, but I don't see anything wrong with the other signs. My rough free body diagram is attached

You diagram is fine as far as I can tell (you don't show where the axis is). I ask again, which way is the centripetal acceleration? Which of the forces you have in the equation act in that direction?

 

[fredrogers3]

You diagram is fine as far as I can tell (you don't show where the axis is). I ask again, which way is the centripetal acceleration? Which of the forces you have in the equation act in that direction?

Pointing towards the center, thus, technically it is -v^2/r. However, does that have any bearing on the sign of the components of the normal force and friction? I thought that had to do with which way the coordinate axes point

 

[haruspex]

Pointing towards the center, thus, technically it is -v^2/r. However, does that have any bearing on the sign of the components of the normal force and friction? I thought that had to do with which way the coordinate axes point

The correct equation is certainly Ffrcosθ - Fnsinθ = m((v^2)/r). But maybe you fixed it up later in your calculation somehow.
I get 1.99 rad/sec, not 1.8. What do you get? If not 1.99, please post the details of your whole calculation.