How To Calculate Friction Force Without Mass: Detailed Explanations and Problem Examples


The frictional force is the resistive force acting against the direction of motion of the object and occurs when the two surfaces rub against each other.

The frictional force is always in the direction opposite to the direction of motion of the object. It depends upon the normal force due to the mass and the acceleration due to the gravity of the object. In this article, let us see how to calculate friction force without mass.

What is Friction Force?

The friction force is the resistive force generated due to the rubbing of two surfaces.

This follows Newton’s Third Law of motion, the frictional force is the force produced corresponding to the normal force exerting on the surface and depends upon the coefficient of friction of the surface.

If there was no coefficient of friction on the surface, that is if the surface was perfectly smooth, then the coefficient of friction would be zero and the object would have just slipped off.

Sand has more friction than metallic road; Image Credit: Pixabay

How to Calculate Friction Force?

Normally, the frictional force can be directly be calculated by knowing the normal forces exerted on the surface which is undergoing friction.

If we know the coefficient of friction and the normal force incident on the surface then we can calculate the friction force using the formula f=µ N.

The normal force is due to the mass and the acceleration is due to the gravity of the object. This force is responsible for the amount of frictional force produced on the surface of the object and the roughness of both the surfaces undergoing friction.

Let us understand how we can calculate the friction force just by knowing the normal force incident on the surface by taking a simple problem below.

What is the friction force due to the bicycle of weight 8.8 kg accelerating with normal force upon the road is 30N and coefficient of friction is 1.2?

Given: W=8.8kg

N=30 N

µ = 1.2

We have,

f = µ N

f = 1.2 * 30 = 36 N

The friction force due to bicycle is 36 N.

Now we will see how to calculate the friction force without mass step by step by taking a simple example.

Consider a driver driving a car on a steeper slope. The friction force is produced due to tires rubbing across the metallic road. How will you calculate the friction force without mass?

The friction force generated is dependent upon the normal force of the car due to the total mass of the car and its acceleration due to gravity.

how to calculate friction force without mass
Diagram of the various forces acting on the car driving the slope upward

Normal Force on the Car

The normal force on the car is equal to the product of mass and acceleration due to gravity.

N= mg

The weight of the car is exerted backward according to the center of gravity of the car align based on the position and axis of the car. The friction force and the air resistance forces are acting at the same time to resist the velocity of the car. The air resistance is very small compared to the friction force.

Coefficient of Friction

The coefficient of friction is a factor that gives us an idea about the roughness or smoothness of the surface. An object with a rough surface has a higher value of the coefficient of friction as compared to smooth surfaces.

The coefficient of friction is the ratio of the friction force to the normal force

µ =fk /N

The coefficient of friction for the dry road is 0.7 and for the wet metallic road, the coefficient of friction is 0.4.

Friction Force on the Tires

The friction force is actually given as

fk = µ N

Where µ is a coefficient of friction

Substituting eqn(1) in eqn(2), we get

fk = µ mg

Replacing Mass Aggregate in the Equation

We know that the density of the object is equal to the ratio of the mass of all the molecules constituting the volume of the object and is given by the relation,

ϱ = m/v

Where ϱ is the density of the object

M is the mass of the object and

V is the volume of the object

Hence we can rewrite the equation as m=ϱv

Substituting this equation in the above eqn (3),

fk = mu ϱ v

This equation is independent of the mass and we can calculate the friction force directly by knowing the density and volume of the object and the coefficient of friction of the surface.

Consider a man pushing a box of length, breadth, and height 1 meter each. The density of the box is 30kg/m3. What is the friction force if the coefficient of friction is 0.4?

Given: ϱ = 30 kg/m3

mu = 0.4

v = I*b*h

v = 1*1*1 = 1m3

Using the equation fk = mu ϱ v we can now find the friction force.

fk = 0.4 * 30 * 1 = 12 N

The frictional force produced as the box rubs the surface has a coefficient of friction of 0.4 is 12 Newton.

Frequently Asked Questions

What is the friction force on the balloon filled with helium gas with a volume of 30 m3 attached to the wall?

The density of a helium gas-filled balloon is 0.1785 kg/m3.

The volume of gas in balloon V=30 m3

The  coefficient of friction mu = 0.4

fk = mu ϱ v

fk = 0.4 * 0.17 * 30 = 2.142 N

The frictional force on the surface of the balloon is 2.142 N.

What is the friction force on the bicycle tires of weight 7.8kg if the coefficient of friction is 0.8?

Given: w=7.8kg

mu = 0.8

The normal force due to weight of the bicycle is

N = mg

N = 7.8 * 9.8 = 76.44

Hence the friction force on the tires of the bicycle is

fk = mu N

fk = 0.8 * 76.44 = 61.152 N

The friction force on tires is 61.152 N.

What could be the consequences if there was no existence of friction force?

The frictional force is very essential to keep the momentum of an object moving or resist the motion or keep the object stable in a place.

If there was no friction force then we could have an easy slip off while walking, running, or doing any activity, and there would have been uncontrolled motion seen in nature.

What are the demerits of friction force?

The friction force is very vital to avoid us from slipping at the same time there are some demerits of friction force too.

The frictional force generates heat energy and radiates the energy into the surrounding. The continuous friction among surfaces also radiates energy in the form of fire due to the excitation of ions.

AKSHITA MAPARI

Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess. Connect me on LinkedIn - linkedin.com/in/akshita-mapari-b38a68122

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