If there is a 23lb. block on a plank and the static friction is .6 and the sliding friction is .35. What angle must the plank be raised to just allow the box to slide?

4 answers

You don't need the sliding friction coefficeint to answer this; you need the maximum friction force possible without sliding, which is calculated with the static coefficient, Us. You also do not need the weignt (23 lb); it will cancel out.
Let W be the weight and A be the maximum angle without slipping.

W sin A = W cos A Us
Divide both sides by W cos A and you will have an equation for the tangent of the maximum angle A.
So to figure out maximum friction force possible without sliding, that's the product of the 23lb block and the static friction of .6. that will be A?
Then I'm not sure what to do next
You must have not read or understand what I wrote. You don't use the weight AT ALL.

If you do the last step that I suggested, you end up with
tan A = Us = 0.6
Therefore A is the angle with a tangent of 0.6. That is written

A = arctan 0.6

Use a hand calculator or trig table to get A.
Than you for your help