# Finding critical Angles

• cellfoneguy
In summary, The block will move with uniform velocity, provided the gravity vector along the ramp exceeds the friction force.f

## 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?

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?

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.

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.

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.

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?

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.

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?

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