# Homework Help: Friction force

1. Mar 29, 2014

### physicos

1. The problem statement, all variables and given/known data

A 3 kg block is on a plane inclined at 30.0° with respect to horizontal.Coefficient of static friction Csfbetween block and plane is 0.60.
What is normal force , and is the block moving ??

2. Relevant equations
Using second low of Newton (vectors):
Fg +f+N=ma.
So N=mg*Cos(30)
and we know that f=Csf *N = mg cos(30)* Csf
but considering the object not moving f= m*g*sin(30)
so the object must be moving
3. The attempt at a solution
IS IT CORRECT ?

2. Mar 29, 2014

### PhanthomJay

no. recall the formula for static friction force. . Is it always equal to C_sf*N?

3. Apr 5, 2014

### physicos

yes it is ! I used a different method , as the object is given a static friction coefficient , I thought a=0 , and I calculated C-sf to see whether it is the same as given by the statement : It wasn't so I concluded the object was not static , is it correct ?

4. Apr 5, 2014

### PhanthomJay

No. Think about it. If the static friction force acting up the plane was greater than the component of the weight force acting down the plane, then the object would accelerate up the plane! Does that make any sense? Static friction force is not always the same as the limiting (C_sf)N. For example, if a block of mass m was sitting on a rough table with a static friction coefficient of C_sf, and the block was not moving, what would be the friction force?
You are missing a very important fact about the static friction force. Look it up . Then report back, please. Thanks.

5. Apr 5, 2014

### physicos

I can't find any helpful link and the teacher was not clear enough ! Do you mean that if f (Friction force ) is greater than a weight (Gravitational force) the object is moving ??

Because we know that f = Csf * N and N= mg*sin(30) which means that f>Wg and thus the object is moving

6. Apr 5, 2014

### PhanthomJay

No. Check this out
http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html
Static friction is only equal to C_sf (N) when the object is just at the threshold of pending motion. Is the block moving?

7. Apr 6, 2014

### physicos

The question is to know whether it is moving or not !

8. Apr 6, 2014

### PhanthomJay

Physics is science, not magic. If you place a block on an inclined plane, and it starts moving up the plane due to friction, that is magic. The block either stays at rest or moves down the plane. Note that friction always opposes the direction of motion or pending motion relative to the contact surface.

9. Apr 6, 2014

### physicos

I have an idea : if the object was not moving , it means that :
vectors f+Fg+N=0 so mg sinθ = μs *N
and N = mg cosθ
so
Sinθ = μs *mg cosθ

so μs = tan θ = 0.57 , but μs= 0.60 <tan θ

So the object started sliding.
Is it correct now ?

10. Apr 6, 2014

### PhanthomJay

No, you are not catching onto the fact that the static friction force is often less than uN.
In this case , it is just enough to maintain the equilibrium condition. In fact, regarding the question I posed earlier about the block placed on a level table with a friction coefficient of u , the friction force in that case is not uN, it is 0. Is this at all clear to you?

11. Apr 6, 2014

### physicos

yeah, cause there is no kinetic friction ! only static one

12. Apr 6, 2014

### physicos

all I want to know now is that is it true that if μs<tan θ the object will start sliding ?

13. Apr 6, 2014

### PhanthomJay

Yes! Then it starts to slide down the plane and kinetic friction comes Ito play.