Calculating Critical Angles for Sliding Blocks on Ramps

[cellfoneguy]

Homework Statement

No specific question.
How would one find the critical angle of a ramp given the mass of the block sliding down it and the mu between ramp and block?
It's not a single question but something my teacher explained that i didn't understand.

Homework Equations

F=(mu)mg
F=ma
I'm not sure of any more

The Attempt at a Solution

I just don't get how to calculate the critical angle.
Is there a formula or a way to derive some equations?
What i know is i have to get the gravity vector that points down the ramp to exceed friction.
But how would i set up that equation?

 

[rl.bhat]

The critical angle is that angle at which component of g along the inclined plane is equal to the acceleration due to frictional force.
Can you write the expression for frictional force?

 

[cellfoneguy]

Wouldn't the vector of gravity along the ramp have to exceed the friction for it to move? If it were equal, then the block would be stationary, right?
Frictionforce=(mu)mg
Frictionforce=(mu)normalforce
Also thanks for the quick reply.

 

[Run-DMC]

Do you know what a Free Body Diagram is? Split up the components of the objects weight and set them equal to the opposite forces. Remember that cosine is horizontal while sine is vertical.

 

[rl.bhat]

Wouldn't the vector of gravity along the ramp have to exceed the friction for it to move? If it were equal, then the block would be stationary, right?
Frictionforce=(mu)mg
Frictionforce=(mu)normalforce
Also thanks for the quick reply.

The block will move with uniform velocity.
Now what is the expression for the normal force?
The component of g along the inclined plane is g*sin(θ) where θ is the critical angle of the inclined plane with the horizontal.

 

[cellfoneguy]

Now I'm confused.
The normal force is pointing perpendicular to the ramp, right?
Why would i need that?
And for the g vector along the ramp, i need to find the critical angle, so how could i use it in an equation, unless i can cancel it somehow?

 

[rl.bhat]

If you resolve g into two components, g*sinθ is along the inclined plane and g*cosθ is perpendicular to the ramp, which is thew normal force.
At critical angle g*sinθ = μ*g*cosθ.

 

[cellfoneguy]

Hmm, ok.
However, for now i only have 2 of those 3 variables, g, and mu.
If i wanted to get theta equals something, what i got from deriving is
sin(theta)/cos(theta)=mu.
So now what do i do?
I have sin and cos on one side, so would i take cos^-1(mu)/sin^-1 ?
Or what...
Also, how would the mass come into play?

 

[cellfoneguy]

Sorry, i researched a little and found that sin/cos =tan.
I got it now, thanks so much rl.bhat!
again.