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Normal Force Formula

 

The normal force is the force component vertical to any contact surface. It decides the amount of force the body applies on the ground. The normal force will be the weight of the object only if the object is not accelerating (decelerating). When a object is about to fall, it depends on which position the object falls on the ground. It is denoted by FN and is given in newtons (N).

For a body resting on the flat surface the normal force FNN is equal to the weight,

FN = mg

Where,

gravitational force is g and
mass is m,

If a force acts on a dropping body that falls at an angle of θ the normal force is greater than the weight articulated as,

FN = mg + F sin θ

 

Where,
the normal force is FN ,
the mass of the body is m,
gravitational force is g,
the angle with which body falls is θ.

If a force tugs the body in the upward direction, the normal force is less than its weight and is given by,

FN = mg – F sin θ

Where,
the normal force is FN ,
the mass of the body is m,
gravitational force is g,
the angle with which body moves up is θ

For the body placed on an inclined plane the normal force FNN is given by,

FN = mg cos θ

Where,
the normal force is FN ,
the mass of the body is m,
gravitational force is g,
the angle of the inclined surface is θ

 

Normal Force Solved Problems

 

Let’s see some examples of normal force:

Problem 1: The body drops down with a force of 200 N. If the mass of the object is 10 kg at an angle of 360. Compute the normal force being applied on the body.

Answer:

Known:

m (Mass) = 10 kg,

F (Force) = 200 N,

angle θ = 360

The normal force formula is articulated as,
FN = mg + F sin θ
FN = 10 kg × 9.8 ms-2 + 200 N × sin 360
FN = 215.55 N

Thus, the normal force being applied on the body is 215.55 N.

Problem 2: A book of mass 1.7 kg is lying on the floor. Compute the normal force being applied on the book.

Answer:

Known:

m (Mass) = 1.7 kg,

w.k.t g (gravitational force) = 9.8 ms-2

The normal force is articulated as,
FN = mg
FN = 1.7 kg × 9.8 ms-2
FN = 16.66 N.

Thus, the normal force being applied on the book is 16.66 N.