Normal Force Formula

In physics, various kinds of forces exist. One of them is the normal force. The normal force is defined as the force that any surface exerts on any other object. If that object is at rest, then the net force acting on the object is equal to zero. It is a fact that the downward force i.e. weight must be equal to the upward force i.e. the normal force. In this article, we will discuss the concept of Normal force and normal force formula with example. Let us learn the concepts.

                                                                                                                                                                 Source:  en.wikipedia.org

Normal Force Formula

What is Normal Force?

 The normal force is defined as the force that any surface exerts on any other object. If that object is at rest, then the net force acting on the object is equal to zero. It is a fact that the downward force i.e. weight must be equal to the upward force i.e. the normal force.

Concept of Normal Force

The normal force is thoroughly defined as the force component vertical to any contact surface. It also decides the amount of force that the body applies on the ground.

The normal force will be equivalent to the weight of the object only if the object is not accelerating i.e. decelerating. When an object is about to fall, then it will depend on which position the object falls on the ground. It is denoted by \(F_N\) and is given in newton (N).

Normal Force Examples

• When a female stands on a level surface, she is subjected to one perpendicular force. A Normal Force is defined as a force that acts perpendicular to a female.
• When a book is put on a table, it is subjected to a perpendicular force. A Normal Force is defined as a force that acts perpendicular to the surface of a book.

 How do inanimate surfaces “know” to exert a normal force?

Most people understand that while holding a hefty bag of dog food, a person must apply upward power with their hands.

However, some individuals find it difficult to accept that an inanimate object, such as a table, can exert an upward normal force on a bag of dog food. Some people feel that the table is just “getting in the way” of the dog food going down, rather than exerting an upward force. Newton’s laws, on the other hand, do not function in this way. The dog food would have to speed downhill if there was simply a downward force of gravity acting on it. More than “getting in the game” is required of the table.

The formula for normal force:

• For a body resting on a given flat surface, then the normal force \(F_N\) is equal to the weight,

\(F_N = mg\)

Where,

\(F_N\)	Normal Force
m	Mass
g	Acceleration due to gravity

 

• If a force acts on a dropping body that falls at an angle of \Theta, the normal force is greater than the weight computed as,

\(F_N = mg + F sin\;\theta\)

Where,

\(F_N\)	Normal Force
M	Mass
G	Acceleration due to gravity
\(\theta\)	Angle with which body falls

 

• If a force acts on the body in the upward direction, then the normal force is less than its weight and is given by,

\(F_N = mg – F sin\;\theta\)

Where,

\(F_N\)	Normal Force
M	Mass
G	Acceleration due to gravity
\(\theta\)	Angle with which body falls

 

• For the body placed on a plane which is inclined at an angle \(\theta\) the normal force \(F_N\) is given by,

\(F_N = mg cos\;\theta\)

Where,

\(F_N\)	Normal Force
M	Mass
G	Acceleration due to gravity
\(\theta\)	Angle with which body falls

Solved Examples

Q.1: The body drops down with a force of 300 N. If the mass of the object is 20 kg at an angle of 30\degree. Then compute the normal force being applied to the body.

Answer:

Known parameters are:

Mass, m = 20 kg,

Force, F = 300 N,

Angle \(\theta = 30°\)

Sin \(30° = \frac{1}{2}\)

The normal force formula is articulated as,

\(F_N = mg + F sin\;\theta\)

\(F_N = 20 \times 9.8 + 300 \times sin\;30\)

\(F_N = 196 + 150\)

\(F_N = 246 N.\)

Thus, the normal force is applied to the body is 246 N.

Q.2: A book of mass 2 kg is lying on the floor. Calculate the normal force being applied to the book.

Answer:

Known values:

m = 2 kg,

g = \(9.8 ms^{-2}\)

The normal force is computed as,

\(F_N = mg\)

Substituting the values, we get

\(F_N = 2 \times 9.8\)

\(F_N = 19.6 N\)

Thus, the normal force is applied to the book is 19.6 N.

FAQs on Equations of Motion

Q.1 Normal Force arises from which force?

Ans: The electromagnetic force generates the normal force; precisely, the electrons in the book push against the electrons in the table.

Q.2 Write down the formula of normal force when the body is at rest.

Ans: For a body resting on a given flat surface, then the normal force  is

𝐹_𝑁 =𝑚𝑔

Where,

𝐹_𝑁 =Normal Force

M =Mass

g =Acceleration due to gravity