How To Find Normal Force On An Incline:Several Approaches And Problem Examples

In order to calculate the net force exerted on a body positioned on an inclined plane, it is important to know how to find normal force on an incline.

A slanted surface is referred to as an inclined plane in physics. Objects are capable of accelerating down inclined planes as a result of an imbalanced force. It is necessary to evaluate the forces operating on an item on an inclined plane in order to truly understand this form of motion.

The gravitational and normal forces are always acting on everything placed on an inclined plane. It is gravity that acts downward, and normal force that operates perpendicularly to the surface (in fact, normal means “perpendicular”).

Herein, we will see how to find normal force on an incline plane.

What is the normal force of a box on an incline plane?

Whenever a box is placed on slant surface, its weight causes an angle theta with the normal, which must be resolved along the horizontal and vertical directions by drawing perpendicular to the corresponding axes.

As long as the box remains stationary, there is no way for the box to move on an inclined plane, which means that there must be a force balancing it and can be given as mgcosθ. The force between the box and the inclined plane will be referred to as the Normal Force. Therefore, we can write the equation as N=mgcosθ.

How To Find Normal Force On An Incline
Figure illustrating normal force on an incline

How to find acceleration on an inclined plane without friction.

The net force of a body on an inclined plane is difficult to calculate because the two forces acting on it are not in opposite directions.

To simplify, it is necessary to break down one of the object’s forces into perpendicular components. Gravitational force is divided into two components as a result of the inclining surface: one component will be parallel to the inclined surface and the other will be perpendicular to the inclined surface. The inclining surface is responsible for this division.

A parallel component and a perpendicular component are depicted in the picture below, which demonstrate that the gravitational force has been replaced by two force components.

Components of Gravitaional Force

The normal force is balanced by the perpendicular component of gravitational force, which is depicted in the picture to point in the opposite direction as the normal force. There is no other force capable of balancing the gravitational force’s parallel component.

Because of the presence of an imbalanced force, the object will accelerate down the inclined plane as it approaches the bottom. This acceleration is caused by the parallel component of the gravitational force, which is accountable for its existence. It is the component of gravity’s force that is parallel to the direction of gravity’s force that is referred to as “net force.”

To calculate the magnitudes of the components of Fg i.e., gravitational force, following equations are used

When there is no friction and other forces, then the acceleration of an object is given by the parallel component value divided by the mass of the object. It can be written as follow:

Is normal force equal to weight on an incline?

The weight of the item, mg, is divided into components that go down the ramp and along the ramps normal. These two components are referred to as mgsinθ and mgcosθ, in that order.

An inclined plane’s normal force is never equal to the object’s weight. (Except for the limiting case of flat ground or surface). It’s calculated by multiplying the object’s weight by the cosine of the angle created by the inclined plane with the horizontal.

How to find normal force without an angle.

Normal force without an angle can be calculated by using the formula of gravitational force.

The gravitational force is equivalent to the normal force on a horizontal plane. The object’s gravitational force is given by, Fg = mg

To understand this let us consider an example where an object is kept on a table which is at rest. Then what is the normal force operating on the object if it has a mass of 22 kg?

As we know that the object’s gravitational force is given by,

Fg = mg = (22.0 kg) * (9.8 m/s2) = 215.6 N

Frequently Asked Questions (FAQs):

Q. What exactly is an inclined plane?

Ans: An inclined plane is simply a flat supporting surface that has one end that is higher than the other and is sloping at an angle.

Q. What effect does friction have on inclined planes?

Ans: When we see the object is gliding over the surface is the result of absence of friction.

In the case of an incline, the gravitational force does not act perpendicular to the surface. The normal force decreases with increasing slope, reducing frictional force.

One can raise the inclination until the thing starts to slide.

Q. Assume you have a slab of ice on a 40-degree incline that glides down. What is the rate of acceleration?

Ans: Acceleration is the component of g that acts parallel to the ramp. Take note that this finding is mass-independent.

F = ma

a = F/m

a = gsinθ

a = 9.8 [sin(40°)] m/s2

a = 9.8 (0.6428) m/s2

a = 6.299

[latex]a\approx 6.3\ m/s^{2}[/latex]

Q. A box weighing 22.0 kg is situated on a ramp that is 30 degrees above the horizontal. What is the magnitude of the weight component that is parallel to the ramp’s surface?

Ans: By using the formulas of force of gravity.

Fg = mg = (22.0 kg) * (9.8 m/s2) = 215.6 N

F|| = Fg sinθ = (251.6 N) * [sin(30°)] = 107.8 N

It is positive since it is pointing down the incline to the right.

Q. A wooden cube is sitting on a piece of furniture The cube weighs a total of 100 kg. Is it possible to determine the magnitude and direction of the normal force? (Here take g = 10 m/s2)

Ans: Normal force can be determined by looking at the magnitude and direction of the normal force.

The normal force of the table is exerted on the block of wood. If the block is being pushed downward by gravity, then the normal force must push straight up to maintain the block stationary. In order to create zero net force, these two forces must be equal and inversely proportional to each other.

FN = Fg = mg

FN = (100 kg) * (10 m/s2)

FN = 1000 N

Due to the fact that normal force is pushing upward, the result will be positive. (The gravitational force would be in the negative direction.)

Q. A box is placed on a ramp that has a 30° inclination to it. Suppose a box has a weight of 50N. Then how to find normal force on an incline plane?

Ans:  We are provided the weight of box i.e., mg = 50N


FN = mgcosθ  = (50N) * [cos(30°)]

FN = 43N

So, here in this article you have learned the different approaches on how to find normal force on an incline along with the examples.

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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