What is the angle at which an object on an incline plane begins to slide?

[pb23me]

1. The problem statement, all variables and g
object on an incline plane has a mass of 10 kgs and the coefficient of static friction is 0.35 at what angle does the object begin to slide.

Homework Equations

Fnet=ma Ff=sin(theta)(mg)

The Attempt at a Solution

I don't come close to the solution because i feel as though some piece of information is missing. Therefore i can't begin to solve the problem.

 

[Doc Al]

What's the maximum value of static friction for a given angle?

 

[pb23me]

isnt it Fn(Us) or normal force times static friction?

 

[pb23me]

not actuallu u that symbol that looks like a u the micro symbol

 

[pb23me]

so the normal force is equal to (mg) or in this case (10kg)*(9.86) oh ok i think I've got it now thank you very much...

 

[Doc Al]

isnt it Fn(Us) or normal force times static friction?

The maximum value for static friction equals μFn.

so the normal force is equal to (mg) or in this case (10kg)*(9.86) oh ok i think I've got it now thank you very much...

Careful! The normal force does not equal mg. (It would if the surface were horizontal, but it's not.) Hint: Find the component of the weight perpendicular to the surface.

 

[pb23me]

cos(theta)*mg

 

[Doc Al]

cos(theta)*mg

Good!

So what's the maximum static friction force?

 

[pb23me]

(.35)*cos(theta)*mg

 

[Doc Al]

(.35)*cos(theta)*mg

Good.

So what's the condition for the object to just barely start to slide?

 

[pb23me]

is this correct?

 

[pb23me]

sin(theta)mg be greater than (.35)*cos(theta)*mg

 

[Doc Al]

sin(theta)mg be greater than (.35)*cos(theta)*mg

Yes. But to solve for the point where the object is just about to slide, set them equal. That will be the critical angle.

 

[pb23me]

ok i got tan(theta)=.35 inverse tan(.35)= 19.3 deg

 

[Doc Al]

ok i got tan(theta)=.35 inverse tan(.35)= 19.3 deg

Sounds good to me.

 

[pb23me]

awsome thank you soooo much!