Physics Normal Force
What is Normal Force?
Normal Force
Definition
In physics, the normal force is the force exerted by a surface on an object in contact with it, perpendicular to the surface. It is also known as the contact force or the support force.
Characteristics
 The normal force is always perpendicular to the surface.
 The normal force is equal in magnitude to the component of the weight of the object perpendicular to the surface.
 The normal force is always positive.
Examples
 When a person is standing on the ground, the normal force is the force exerted by the ground on the person’s feet.
 When a book is resting on a table, the normal force is the force exerted by the table on the book.
 When a car is driving on a road, the normal force is the force exerted by the road on the car’s tires.
The normal force is an important concept in physics that has many applications. It is a force that is always present when two objects are in contact with each other, and it plays a role in many physical phenomena.
Normal Force Formula
The normal force is the force exerted by a surface on an object in contact with it, perpendicular to the surface. It is often denoted by the symbol $N$.
Formula
The normal force can be calculated using the following formula:
$$N = mg\cos\theta$$
where:
 $N$ is the normal force in newtons (N)
 $m$ is the mass of the object in kilograms (kg)
 $g$ is the acceleration due to gravity (9.8 m/s²)
 $\theta$ is the angle between the surface and the horizontal
Example
A 10 kg object is resting on a horizontal surface. The normal force acting on the object is:
$$N = mg\cos0\degree = (10 kg)(9.8 m/s²)(1) = 98 N$$
The normal force is an important concept in physics. It is used in a variety of applications, from calculating the friction force between two surfaces to determining the stability of objects.
Is the Normal Force a Reaction Force?
The normal force is the force exerted by a surface on an object in contact with it, perpendicular to the surface. It is often thought of as a reaction force to the force exerted by the object on the surface. However, this is not always the case.
When is the Normal Force a Reaction Force?
The normal force is a reaction force when the object is in equilibrium. This means that the net force acting on the object is zero. In this case, the normal force is equal in magnitude and opposite in direction to the force exerted by the object on the surface.
For example, consider a book resting on a table. The force of gravity pulls the book down, and the table exerts an upward force on the book. The normal force is equal to the force of gravity, and the book is in equilibrium.
When is the Normal Force Not a Reaction Force?
The normal force is not a reaction force when the object is not in equilibrium. This means that the net force acting on the object is not zero. In this case, the normal force is not equal in magnitude and opposite in direction to the force exerted by the object on the surface.
For example, consider a book sliding down a ramp. The force of gravity pulls the book down, and the ramp exerts an upward force on the book. The normal force is less than the force of gravity, and the book accelerates down the ramp.
The normal force is a reaction force when the object is in equilibrium. However, it is not a reaction force when the object is not in equilibrium.
Normal Force Examples
1. A book resting on a table
 The normal force is the force exerted by the table on the book, perpendicular to the surface of the table.
 The magnitude of the normal force is equal to the weight of the book.
2. A person standing on the ground
 The normal force is the force exerted by the ground on the person’s feet, perpendicular to the ground.
 The magnitude of the normal force is equal to the person’s weight.
3. A car driving on a road
 The normal force is the force exerted by the road on the car’s tires, perpendicular to the road.
 The magnitude of the normal force is equal to the weight of the car.
4. A boat floating in water
 The normal force is the force exerted by the water on the boat’s hull, perpendicular to the surface of the water.
 The magnitude of the normal force is equal to the weight of the water displaced by the boat.
5. A balloon floating in the air
 The normal force is the force exerted by the air on the balloon’s surface, perpendicular to the surface of the balloon.
 The magnitude of the normal force is equal to the weight of the air displaced by the balloon.
6. A person swimming in a pool
 The normal force is the force exerted by the water on the person’s body, perpendicular to the surface of the water.
 The magnitude of the normal force is equal to the weight of the water displaced by the person’s body.
7. A bird flying in the air
 The normal force is the force exerted by the air on the bird’s wings, perpendicular to the surface of the wings.
 The magnitude of the normal force is equal to the weight of the bird.
8. A fish swimming in water
 The normal force is the force exerted by the water on the fish’s body, perpendicular to the surface of the fish’s body.
 The magnitude of the normal force is equal to the weight of the water displaced by the fish’s body.
9. A submarine submerged in water
 The normal force is the force exerted by the water on the submarine’s hull, perpendicular to the surface of the submarine’s hull.
 The magnitude of the normal force is equal to the weight of the water displaced by the submarine.
10. A satellite orbiting the Earth
 The normal force is the force exerted by the Earth’s gravity on the satellite, perpendicular to the surface of the Earth.
 The magnitude of the normal force is equal to the weight of the satellite.
Relation between Friction Force and Normal Force
Friction force and normal force are two fundamental forces that act on objects in contact with each other. Understanding the relationship between these forces is crucial in various fields, including physics, engineering, and everyday life.
Friction Force
Friction force is the force that opposes the relative motion of two surfaces in contact. It arises due to the interaction of microscopic irregularities and adhesion between the surfaces. Friction force always acts in the direction opposite to the impending motion.
Normal Force
Normal force is the force exerted by a surface on an object perpendicular to the surface. It is a contact force that arises when two objects are in contact with each other. Normal force is always directed away from the surface.
Relationship between Friction Force and Normal Force
The relationship between friction force $F_f$ and normal force $N$ is given by the following equation:
$$F_f = \mu_k N$$
where $\mu_k$ is the coefficient of kinetic friction.
The coefficient of kinetic friction is a dimensionless quantity that depends on the materials in contact and the surface conditions. It represents the ratio of the friction force to the normal force.
Factors Affecting Friction Force
The magnitude of friction force is influenced by several factors, including:

Nature of Surfaces in Contact: Different materials have different coefficients of friction. For example, rubber on concrete has a higher coefficient of friction than ice on ice.

Roughness of Surfaces: Rougher surfaces generally have a higher coefficient of friction than smoother surfaces.

Applied Normal Force: Friction force is directly proportional to the normal force. As the normal force increases, the friction force also increases.

Relative Velocity: In some cases, friction force may also depend on the relative velocity between the surfaces in contact.
Applications of Friction Force
Friction force plays a vital role in various aspects of our daily lives and in various fields, such as:

Braking Systems: Friction between brake pads and rotors is essential for slowing down or stopping vehicles.

Walking: Friction between the soles of our shoes and the ground allows us to walk without slipping.

Holding Objects: Friction enables us to hold objects without them slipping from our grasp.

Machinery: Friction is utilized in various machines, such as gears, belts, and clutches, to transmit power and control motion.
Conclusion
Friction force and normal force are fundamental forces that interact with each other to influence the motion of objects in contact. Understanding the relationship between these forces is crucial in analyzing and predicting the behavior of objects in various situations.
Solved Examples on Normal Force
Example 1: Calculating Normal Force on a Horizontal Surface
A 10 kg block is placed on a horizontal surface. The coefficient of static friction between the block and the surface is 0.2. Calculate the normal force acting on the block.
Solution:
The normal force acting on the block is equal to the weight of the block, which is:
$$N = mg$$
$$N = (10 kg)(9.8 m/s^2) = 98 N$$
Example 2: Calculating Normal Force on an Inclined Plane
A 10 kg block is placed on an inclined plane that makes an angle of 30° with the horizontal. The coefficient of static friction between the block and the plane is 0.2. Calculate the normal force acting on the block.
Solution:
The normal force acting on the block is given by:
$$N = mgcosθ$$
$$N = (10 kg)(9.8 m/s^2)cos30° = 85.4 N$$
Example 3: Calculating Normal Force in a Dynamic Situation
A 10 kg block is moving at a constant velocity of 10 m/s on a horizontal surface. The coefficient of kinetic friction between the block and the surface is 0.2. Calculate the normal force acting on the block.
Solution:
The normal force acting on the block is given by:
$$N = mg  f_k$$
$$N = (10 kg)(9.8 m/s^2)  (0.2)(10 kg)(10 m/s)^2 = 68 N$$
Normal Force FAQs
What is the normal force?
The normal force is the force exerted by a surface on an object in contact with it, perpendicular to the surface. It is also known as the contact force or the support force.
What is the difference between the normal force and the force of gravity?
The force of gravity is the force of attraction between two objects with mass. The normal force is the force exerted by a surface on an object in contact with it, perpendicular to the surface.
What is the equation for the normal force?
The equation for the normal force is:
$$N = mg$$
Where:
 N is the normal force in newtons (N)
 m is the mass of the object in kilograms (kg)
 g is the acceleration due to gravity (9.8 m/s²)
What are some examples of normal force?
Some examples of normal force include:
 The force exerted by the ground on a person standing on it
 The force exerted by a table on a book resting on it
 The force exerted by a wall on a ball bouncing off it
What are the applications of normal force?
The normal force is used in many applications, including:
 Designing and building structures
 Analyzing the motion of objects
 Calculating the forces acting on objects
Conclusion
The normal force is an important concept in physics. It is used to describe the force exerted by a surface on an object in contact with it, perpendicular to the surface. The normal force is different from the force of gravity, and it has many applications in engineering and physics.