Friction Force Homework: Calculating Normal Force & Motion

[physicos]

Homework Statement

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

Homework Equations

Using second low of Newton (vectors):
F_g +f+N=ma.
So N=mg*Cos(30)
and we know that f=C_sf *N = mg cos(30)* C_sf
but considering the object not moving f= m*g*sin(30)
so the object must be moving

The Attempt at a Solution

IS IT CORRECT ?

 

[PhanthomJay]

Homework Statement

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

Homework Equations

Using second low of Newton (vectors):
F_g +f+N=ma.
So N=mg*Cos(30)
and we know that f=C_sf *N = mg cos(30)* C_sf
but considering the object not moving f= m*g*sin(30)
so the object must be moving

The Attempt at a Solution

IS IT CORRECT ?

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

 

[physicos]

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

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 ?

 

[PhanthomJay]

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 ?

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.

 

[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

 

[PhanthomJay]

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

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?

 

[physicos]

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

 

[PhanthomJay]

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

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.

 

[physicos]

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

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

So the object started sliding.
Is it correct now ?

 

[PhanthomJay]

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

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

So the object started sliding.
Is it correct now ?

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?

 

[physicos]

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

 

[physicos]

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

 

[PhanthomJay]

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

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