Laws of Friction

Friction is a fundamental force that affects our everyday lives. When we slide a book across a table or walk on a slippery surface, friction comes into play. There are various laws which govern the phenomenon of friction such as Amonton’s and Columnb’s Laws. In this article, we will discuss all the laws which help us understand the concept of Friction.

What is Friction?

The force that opposes the relative motion or tendency of two surfaces in contact is known as friction.

There are several types of friction that result from the interactions between the microscopic irregularities of the surfaces i.e.,

• Static Friction
• Kinetic Friction
• Rolling Friction
• Fluid Friction
• Dry Friction

Note: The roughness, composition, and force forcing the surfaces together determine how much friction there will be.

Read More about Types of Friction.

Formula for Friction

As we know, friction is a force that opposes moving one surface in contact with another or the tendency for something to move. The formula for calculating the force of friction is:

F = μN

Where,

• F is the friction force,
• μ is the coefficient of friction, and
• N is the normal force.

What are Laws of Frictions?

The laws of friction explain how friction acts in relation to normal force and motion. There are five main laws of friction, which include:

• The First Law of Friction: Friction is proportional and perpendicular to the normal force acting on an object.
• The Second Law of Friction: The force of friction is independent of the apparent area of contact between the surfaces.
• The Third Law of Friction: The force of friction is independent of the sliding velocity between the surfaces.
• The Fourth Law of Friction: The force of friction is independent of the direction of sliding.
• The Fifth Law of Friction: The force of friction is directly proportional to the normal force acting on an object.

Amonton’s Law of Friction

Amonton’s Law of Friction are named after the French physicist Guillaume Amontons, who discovered these laws. There are two laws given by Amontons i.e.

• Amonton’s First Law
• Amonton’s Second Law

Let’s discuss these laws in detail as follows.

Amonton’s First Law

The Amontons’ First Law, sometimes known as the Amontons’ Friction Law, is one of the basic theories governing frictional forces. It states that the friction force is directly impacted by the applied normal force. In terms of math, it can be expressed as:

F ∝ N

Where:

• F = The resistive force, or friction, and
• N = is the amount of force an average person would apply to the floor or a push-up board during a push-up.

Amonton’s Second Law

Amonton also put up another important theory regarding friction, which is known as the Angle of Friction or the Second Law of Amontons. The frictional force, according to this equation, is directly determined by the normal force between the bodies rather than by the apparent area of contact between surfaces. The expression in mathematics is as follows:

F ∝ tan(θ)

Where,

• F It is friction that opposes your moving forward, and
• θ is the angle of intersection of the surfaces.

Some Other Laws

Other than these laws, there are some more laws which help us govern the concept of friction. These are:

• Coulomb’s Law of Friction
• Law of Static Friction
• Law of Kinetic Friction

Coulomb’s Law of Friction

Coulomb’s Law of Friction, formulated by Charles-Augustin de Coulomb, describes the relationship between the frictional force and the normal force acting between two surfaces in contact. It is the extension of Amontons’ First Law as it it introduces the constant of proportionality i.e., μ. Mathematically, coulomb’s law of friction is given as follows:

F_f = μ . N

Where,

• F_f is the force of friction,
• μ is the coefficient of friction, and
• N is the normal force.

Law of Static Friction

The maximum static friction force () that can exist between two stationary surfaces is directly proportional to the normal force (F_N​) acting perpendicular to the surfaces. The coefficient of static friction (μ_s​) represents the proportionality constant. Mathematically, ≤ μ_s​⋅F_N.

The static friction force opposes the impending motion or attempted motion between the surfaces. It acts tangentially to the surfaces in contact.

Law of Kinetic Friction

Kinetic friction force (​​) is directly proportional to the normal force (F_N​), which is the force perpendicular to the surfaces in contact. The coefficient of kinetic friction (μ_k​) represents the proportionality constant. Thus, =μ_k​⋅F_N.

The kinetic friction laws describe that the friction force acting against the motion of an object is dependent upon factors such as the roughness of the surface and the magnitude of the normal force.

Solved Problems on Laws of Friction

Problem 1: A boy is pulling a box of mass 10 kg. Identify the standard force. Furthermore, calculate the same force of friction if the coefficient of friction is 0.3.

Solution:

Given: Mass, m = 10 kg, where kg indicates kilogram.

Normal force, F_n =?

The mathematical expression for normal force is had by F_n = m g.

= 10 n kg × 9.8 m/ s2

= 98 N.

The Friction force is described as (μ F_n), where μ (m) is a coefficient of friction.

F = – 0.3 × 98N.

= 29.4 N.

Problem 2: Nancy who has a mass of 22lb is skating on the frost. The slider is assumed to be sliding on a frictionless floor if the kinetic coefficient of friction is 0.45. Discover the frictional force impacting her when it kisses the frost layer.

Solution:

Given: The mass m = 40 Kg, representation of the body, is the one that is subjected to the acceleration on a planet similar to ours.

The Friction coefficient μ=0.3,

The reason that F_n = mg is standard force is that it is the weight of an object which is measured by m x g.

Mr. Schumacher was accelerating with a force of 40 Kg × 9.8 m/s2.

= 392 N.

The force of Friction is demonstrated by F_f = μ Fn.

= 178 N = 0.45 × 392 N

= 176.4 N.

Practice Problems on Laws of Friction

Problem 1: The 50 kg mass block rests on a slope of an angle 30°. The static coefficient friction between the block and the inclined plane is 0.4. Determine the angle greater than which the block will slide away from the support surface.

Problem 2: A 200 N object is moving horizontally through a surface whose kinetic friction coefficient is 0.2. Find the magnitude of kinetic friction force resisting the motion of the object.

Problem 3: A mass 30 kg is placed on the rough surface. The static friction coefficient is 0.5 and the coefficient of friction rolling is 0.3. Each question will mainly have two types of forces. A force of 200 N will be applied horizontally. Thus, the object will move at constant velocity or may move and calculate the acceleration.

Problem 4: For the case of the rough inclined plane, we have a 1000 N object that is placed at a 20-degree angle. Coefficient of friction = 0.25 Make calculations about the force of friction which is the resultant of the tangential component of the normal force on the object.

Problem 5: The case that assumes there is a 500 Newtons box placed on a vertical wall is being studied now. If the lack of static friction coefficient between the wall and the box is 0.6, tell if the box will remain in place or if it will begin sliding down.

Frequently Asked Questions on Laws of Friction

What is friction?

When two surfaces hurtling against each other come into contact, their relative motion or tendency of motion is counteracted by a force termed friction. It does so due to the collisions of molecules in the surfaces of objects.

What are the laws of friction?

The laws of friction consist of principles that govern the behavior of friction between surfaces. These laws include static friction, kinetic friction, and factors influencing friction.

What is static friction?

Answer: Static friction is the force that prevents an object from moving when a force is applied to it but the object remains stationary. It is the maximum force of friction before motion occurs.

What is kinetic friction?

Kinetic friction is the force that opposes the motion of an object when it is already in motion. It is generally lower than static friction and depends on the nature of the surfaces in contact.

How does lubrication affect friction?

Lubrication reduces friction by introducing a fluid layer between surfaces, preventing direct contact and reducing wear and tear on the surfaces.

What are some characteristics of friction force?

Three characteristics of friction force include its direction opposite to the direction of motion, its dependence on the nature of surfaces in contact, and its ability to vary based on the normal force pressing the surfaces together.