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.
• On an inclined plane with no other forces acting perpendicular to the surface, the normal force equals the component of the weight perpendicular to the surface ($N = mg\cos\theta$). However, if additional forces act on the object (e.g., a push or pull), the normal force adjusts accordingly.
• The normal force is zero or positive. It can be zero when surfaces are about to separate (e.g., at the top of a hill if a car moves fast enough).

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

When an object rests on an inclined plane with no other forces acting perpendicular to the surface, the normal force can be calculated using:

$$N = mg\cos\theta$$

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

Important: This formula only applies when gravity is the only force with a component perpendicular to the surface. If additional forces act on the object (e.g., someone pushing down on it, or vertical acceleration), the normal force must be found using Newton’s second law applied perpendicular to the surface.

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 block on an inclined plane

• The normal force is the force exerted by the inclined surface on the block, perpendicular to the surface.
• The magnitude of the normal force is equal to $mg\cos\theta$, where $\theta$ is the angle of inclination (assuming no other perpendicular forces).

5. A person in an elevator

• The normal force is the force exerted by the elevator floor on the person’s feet, perpendicular to the floor.
• If the elevator accelerates upward with acceleration $a$, the normal force is $N = m(g + a)$. If it accelerates downward, $N = m(g - a)$.

Note on common misconceptions: The following are NOT examples of normal force:

• A boat floating in water experiences buoyant force (an upward force from the displaced fluid), not normal force.
• A balloon in air experiences buoyant force from the surrounding air.
• A bird flying experiences lift (an aerodynamic force), not normal force.
• A fish swimming experiences buoyant force from the surrounding water.
• A satellite orbiting Earth experiences gravitational force only; there is no contact surface, so there is no normal force.

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 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:

On a horizontal surface with no vertical acceleration and no other vertical forces, the normal force equals the weight of the block:

$$N = mg$$

$$N = (10 \text{ kg})(9.8 \text{ m/s}^2) = 98 \text{ N}$$

Note: Friction acts horizontally (opposing the motion) and does not affect the normal force in the vertical direction. The kinetic friction force is $f_k = \mu_k N = (0.2)(98) = 19.6 \text{ N}$, acting horizontally.

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.