How To Find Normal Force With Mass: Several Approaches And Problem Examples


In this article, you will understand the concept and problems based on how to find normal force with mass.

As opposed to normal meaning “usual” or “expected” in common English, in mechanics the normal force is a component of a contact force that is perpendicular to the surface of an item contact.

What is the normal force acting on the mass?

There are many different types of forces in physics. The normal force is an example of one of these forces.

When we talk about a surface exerting force on another item in the plane of the surface it is operating on, we’re talking about the normal force. If an object is at rest, the net force exerted on the object equals zero, and the object is at rest.

It is a known truth that the downward force, represented by weight, must equal the upward force, represented by the normal force. This article will discuss the concept of the normal force acting on the mass as well as how to find normal force with mass along with the examples. Let’s have a look at the concepts.

How to find normal force with mass
The normal force acting on an object having mass

Image Credits: Bengt NymanNormal forceCC BY 2.0

Normal Force

The normal force can be defined as the component of a force that is vertically oriented with respect to any contact surface. It also determines the amount of force that the body exerts to the surface during a movement.

The normal force will equal the weight of the item only when the object is neither accelerating nor decelerating and vice versa. When an object is going to fall, the way in which it hits the ground will be determined by the location in which the object lands. It is symbolized by the letter FN and is expressed in newtons (N).

How to find normal force with mass
Figure illustrating how to find normal force with mass

For a body kept on a flat surface, the normal force is given by,

FN = mg

Where F= Normal force

m = mass of the object

g = acceleration due to  gravity

If the body is kept at an inclination, the normal force is given by,

FN = mg cosθ

Where, θ = angle of inclination

Read more about different approaches  for how to find the normal force on an incline


Problem based on how to find normal force with mass:

Q. A box of mass 5 kg is kept on the floor. What will be the normal force which is being exerted on the box?

Ans: Here we have mass i.e., m = 5 kg, g = 9.8 m/s2.

Normal force on the box is given by formula,

FN = mg

FN = 5 × 9.8

FN = 49 N

Therefore, the value of the normal force being exerted on the box is 49 N.

Q. A bag of wheat of mass 10 kg is resting on the table. Then how to find normal force with mass?

Ans: If you multiply provided mass by the gravitational force, which is equal to mg, we get the answer.

FN = mg

FN = 10 × 9.8

FN = 98 N

The normal force acting on a bag of wheat of mass 10 kg is 98 N.

Q. What is the amount of the normal force being exerted on a 20 kg item on a 60° inclination to the horizontal provided g = 10 m/s2?

Ans: The normal force on an inclination is given by,

FN = mg cosθ

FN = (20 kg) × (10 m/s2) × cos(60°)

FN = 200 × (1/2)

FN = 100 N

Therefore, the normal force which is being exerted on an item is 100 N.

Q. 30 degrees above horizontal, an iron slab with a mass of 10 kg rests on an inclination. How to find normal force with mass of iron slab? (g = 10 m/s2)

Ans: The larger the normal force, the lower the slope. The narrower an angle is, the bigger the value of cosine is, and thus the greater the normal force is, as a result.

The normal force on an inclination is given by,

FN = mg cosθ

FN = (10 kg) × (10 m/s2) × (cos 30°)

FN = 86.6 N

Hence, the normal force on an iron slab which being exerted is 86.6 N.

Q. A block of some mass is kept on an inclination with the angle of 60° with the horizontal. The normal force acting on the block is 20 N. Then what is the mass of the block?(Take g = 10 m/s2)

Ans: Normal force is given by, FN = mg cosθ. To find the mass we can write this formula as follow

m= FN /g cosθ

m= (20 N)/(10 m/s2) cos60°

m= 4kg

Therefore, the mass of block kept on an inclination is 4kg.

Q. An object weighing 40 N kept on a ramp at an inclination of 45°. Then what will be the normal force exerting on that object?

Ans: Here the weight of an object is given i.e., mg = 40 N.

The normal force is written as,

FN = mg cosθ

FN = (50 N) × (cos 45°)

FN = 35.36 N

Therefore, the normal force exerted on an object is 35.36 N.

So, these are some of the solved problems based on how to find normal force with mass.


Prajakta Gharat

I am Prajakta Gharat. I have completed Post Graduation in physics in 2020. Currently I am working as a Subject Matter Expert in Physics for Lambdageeks. I try to explain Physics subject easily understandable in simple way.

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