# Friction Force Homework: Calculating Normal Force & Motion

• physicos
In summary, the conversation discusses the calculation of normal force and whether or not a block on a 30.0° inclined plane is moving. The equation Fg + f + N = ma is used, along with the fact that N = mg*cos(30), to determine that the block must be moving. The conversation then delves into the understanding of static friction and how it relates to the angle of the incline, with the conclusion that if μs < tan θ, the object will start sliding.
physicos

## Homework Statement

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 ??

## Homework 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

IS IT CORRECT ?

physicos said:

## Homework Statement

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 ??

## Homework 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

## The Attempt at a Solution

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

PhanthomJay said:
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 ?

physicos said:
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.

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

physicos said:
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?

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

physicos said:
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.

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 ?

1 person
physicos said:
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 ?
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?

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

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

physicos said:
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.

## 1. How is normal force related to friction force?

The normal force is the perpendicular force exerted by a surface on an object in contact with it. This force is directly related to the friction force, as it is the force that counteracts the downward force of an object and allows for the object to stay in place or move with a constant velocity.

## 2. How do you calculate the normal force?

The normal force can be calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s^2) and the cosine of the angle between the surface and the object. This can be represented by the equation FN = mgcosθ, where FN is the normal force, m is the mass of the object, and θ is the angle between the surface and the object.

## 3. What factors affect the amount of friction force?

The amount of friction force is affected by several factors, including the type of surface the object is on, the weight of the object, and the roughness of the surfaces in contact. Additionally, the coefficient of friction, which is a measure of the interaction between the two surfaces, also plays a role in determining the amount of friction force.

## 4. How do you calculate the coefficient of friction?

The coefficient of friction can be calculated by dividing the force of friction by the normal force. This can be represented by the equation μ = Ff/FN, where μ is the coefficient of friction, Ff is the force of friction, and FN is the normal force.

## 5. What is the relationship between friction force and motion?

Friction force is always opposite to the direction of motion. This means that when an object is in motion, the direction of the friction force will be opposite to the direction of motion. Additionally, the amount of friction force can affect the acceleration of an object, as a larger friction force will result in a smaller acceleration.

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