How To Find Normal Force With Coefficient Of Friction: Several Approaches and Problem Examples

The opposing force that acts on a body is called friction. Let us understand how to find normal force with coefficient of friction.  

To know how to find normal force with coefficient of friction, we use the formula of friction. The friction is of two types, static friction and kinetic friction, and thus we have static coefficient friction and kinetic coefficient friction. Let us look at several approaches on how to find normal force with coefficient of friction. 

We are well aware of the normal mass; it acts perpendicularly on an object in the upward direction. It is the normal force that keeps objects from falling or passing through another object. 

For example, glass is kept on a shelf. We know that gravity pulls all the objects downward. So the gravitational force will act on the glass, too, and it should fall. But this does not happen. It is due to the normal force that acts on the glass in an upward direction and balances out the gravitational pull. 

The frictional force is an opposing force. It is also said to be a necessary evil. For an object which does not move, the friction is static friction. Similarly, when a body is in motion, then the friction that comes into action is kinetic. 

When we throw a ball, it rolls for some time on the ground, and gradually its speed slows down, and it stops. It is due to frictional force. Friction is the opposing force that acts on an object to restrict its motion. We can walk and write because of friction. It has much day-to-day significance in our friction. 

The coefficient of friction is the ratio of friction force and normal force. If the friction is static, then we have a static coefficient of static friction, and for kinetic friction, we have a coefficient of kinetic friction.  

The general formula of the force of friction is f=μN


f = force of friction

μ= coefficient of friction 

N = normal force. 

From this formula, we calculate normal force with the coefficient of friction. 


Now, if an object is kept on the surface and even after applying the force, it is not moving. Then the friction is static friction. In that case, the formula would be: 



For a moving object, the force of friction is kinetic; therefore, to find the normal force, the formula becomes:



How to find normal force with coefficient of friction

Problems on How To Find Normal Force With Coefficient of Friction

Problem 1) A 2 kg wooden log is being pushed from the stationary position, and 9.8 N of the force of friction acts on it with a coefficient of friction of 0.5. Calculate the normal force. 

Solution:  For the given problem we are given:

m = 2 kg

μ= 0.5

f = 9.8

Then using the formula N=f/μ and substituting the values we get:



N = 19.6 newton

Problem 2) A box kept on a horizontal table is pushed smoothly with a friction force of 7.85 N and a coefficient of friction of 0.4. Calculate the normal force.  

Solution: We are given:

μk = 0.4

fk= 7.85 N 

Then the normal force would be:


N =7.85/0.4

N = 19.625 newton

So, that was all about how to find normal force with coefficient of friction. In case of further questions read the FAQs mentioned below.

Frequently Asked Questions (FAQs)

What is friction as a force? 

The frictional force is a kind of force that tries to reduce the effect of other forces acting on a body.

In simple language, friction opposes the motion caused by the acting force. For example, when we try to push a sofa, it may not move because the friction force acting on it would be greater than the force applied by us. Another example is when we apply brakes, the friction stops the car. 

Explain the coefficient of friction. 

 The coefficient of friction gives us the amount of frictional force acting between surfaces. 

The value of friction also indicates how much force is required to overcome the friction and make the body move. The lower value of the coefficient of friction indicates that lesser friction is acting on the object. 

How are friction and normal force related? 

For a body kept on a table or moving on a horizontal surface, friction and normal force are sure to act on it.

The friction and normal force are related by the formula f∝N. When we remove the proportionality sign, we get the formula as f=μN, which relates the frictional force and the normal force; with the increase of friction, the normal force increases, and vice versa. 

What happens to friction force when a normal force is increased?

The magnitude of the force of friction varies with the normal force.  

For a given situation, the coefficient of friction remains constant throughout. Thus we get to know that friction changes with normal force. So when the normal force is increased, a greater amount of friction is required to oppose the motion. 

How to find normal force with coefficient of friction? 

We can find the normal force with a coefficient of friction using the standard formula of friction. 

The friction varies with the normal force exerted on an object. It gives us the formula of friction as f=μN . From this formula, we can find the normal force using the coefficient of friction that is N=f/μ

Why does friction depend on normal force and not the weight of the object? 

The friction does not vary with the object’s weight but with the normal force. 

This is so because it is the normal force that presses the body on the surface, so the greater the normal force, the more friction would be required. At the same time, weight tries to pull the body downwards. 

Does the coefficient of friction have a unit? 

The coefficient of friction does not hold any unit. First of all, it is a constant, and secondly, if we see the formula f=μN , from here, we get μ=f/N which is the ratio of two forces, and thus, the units get canceled out. 

Rabiya Khalid

Hi,  I am Rabiya Khalid, currently pursuing my masters in Mathematics. Article writing is my passion and I have been professionally writing for more than a year now. Being a science student, I have a knack for reading and writing about science and everything related to it. If you like what I write you can connect with me on LinkedIn: In my free time, I let out my creative side on a canvas. You can check my paintings at:

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