How to Solve for the Angle of Incline in a Sliding Block Problem

[NaZer]

Homework Statement

A 5.0-kg wooden block is placed on an adjustable inclined plane. [ U(mu)k=0.25 and U(mu)s=0.45]
a.) What is the angle of inclined above which the block will start to slide down the plane?
b.) At what angle of incline will the block slide down the plane at a constant speed.


~Now I know how to set up the problem (i think), but I haven't the slightest clue how to approach this. If someone wouldn't necessarily give me the answer but tell my how to tackle it. Or explain it to me, that would be ideal. Now since you have to show kind of poking at the problem, here you go.

Homework Equations

The Attempt at a Solution

http://img401.imageshack.us/img401/276/physics311ua2.th.jpg

 

[Mathgician]

Hint: Trigonometry

read the question carefully, it says when it starts sliding. What does that tell you?

 

[NaZer]

How would you use Trig.? Isn't there too many unkowns. In order to use Trig, i would need some sides or angles.

 

[Mathgician]

relate the directions of the arrows you just drew with trig and the angle of the incline. try to make the sum of force equations for the Y and the X direction

 

[Mathgician]

You know the Earth's force and the mu(it effects the force that is related to the mu), your mass does not effect your angle(but, write everything down in your sum of force equations because it may throw you off), and relate that to the trig representation of your directional arrows. Imagine your arrows as x and y-axis of a graph, the x-axis is rotated to make the incline parallel to the horizontal axis(think about your normal force). When you get to the end of the problem you will see that a simple trig identity will help you find your angle. Your arrows are all the force involved on your little block, name them(what kind of force are each one of them?) by labeling them with the assistance of trigonometry. This is a very general, non specific problem, so you need to be patient and not focus on finding numeric known and unknowns, you need to solve by a deduction by trigonometry. In other words, its a good problem

 

[sc86]

Just a little hint my old instructor gave me: On your drawing do not make the angel beta = 45 degres. If you make it bigger or smaller, then I believe it is much easier to see which angels there are alike.