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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.

Normal Force Formula

                                                                                                                                             Source:  en.wikipedia.org

Normal Force Formula

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 which 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).

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.

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