Finding critical Angles

  • #1

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?
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
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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?
 
  • #3
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.
 
  • #4
1
0
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.
 
  • #5
rl.bhat
Homework Helper
4,433
8
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.
 
  • #6
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?
 
  • #7
rl.bhat
Homework Helper
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If you resolve g in to 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.
 
  • #8
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?
 
  • #9
Sorry, i researched a little and found that sin/cos =tan.
I got it now, thanks so much rl.bhat!
again.
 

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