FRICTION: TYPES, COEFFICIENT, CALCULATION, EXERCISES - PHYSICAL - 2024

The friction is resistance to movement of a surface being in contact with another. It is a surface phenomenon that occurs between solid, liquid and gaseous materials. The resistance force tangential to two surfaces in contact, which opposes the direction of the relative displacement between said surfaces, is also called the friction force or friction force F _r.

To displace a solid body on a surface, an external force must be applied that can overcome friction. When the body moves, the friction force acts on the body, slowing it down, and can even stop it.

Friction

The friction force can be represented graphically by the force diagram of a body in contact with a surface. In this diagram the friction force F _r is drawn opposing the component of the force applied on the body tangential to the surface.

The contact surface exerts a reaction force on the body called the normal force N. In some cases, the normal force is due only to the weight P of the body resting on the surface, and in other cases, it is due to applied forces other than the force of gravity.

Friction occurs because there are microscopic roughnesses between the surfaces in contact. When trying to move one surface over the other, friction occurs between the roughnesses that prevent free movement at the interface. In turn, energy losses occur in the form of heat that is not used to move the body.

Types of friction

There are two main types of friction: Coulomb friction or dry friction, and fluid friction.

-Coulomb friction

Coulomb friction always opposes the motion of bodies and is subdivided into two types of friction: static friction and kinetic (or dynamic) friction.

In static friction there is no movement of the body on the surface. The applied force is very low and not enough to overcome the friction force. Friction has a maximum value that is proportional to the normal force and is called the static friction force F _re.

The force of static friction is defined as the maximum force that resists the beginning of the movement of the body. When the applied force exceeds the static friction force, it stays at its maximum value.

Kinetic friction acts when the body is already in motion. The force required to keep the body moving with friction is called the kinetic friction force F _rc.

The kinetic friction force is less than or equal to the static friction force because once the body begins to move it is easier to keep moving than to try to do so while at rest.

Coulomb's Laws of Friction

1. The friction force is directly proportional to the force normal to the contact surface. The constant of proportionality is the coefficient of friction μ that exists between the surfaces in contact.
2. The friction force is independent of the size of the apparent contact area between the surfaces.
3. The kinetic friction force is independent of the sliding speed of the body.

-Fluid friction

Friction also occurs when bodies move in contact with liquid or gaseous materials. This type of friction is called fluid friction and is defined as the resistance to movement of bodies in contact with a fluid.

Fluid friction also refers to the resistance of a fluid to flow in contact with fluid layers of the same or a different material, and depends on the velocity and viscosity of the fluid. Viscosity is the measure of the resistance to movement of a fluid.

-Stokes friction

Stokes friction is a type of fluid friction in which spherical particles immersed in a viscous fluid, in laminar flow, experience a frictional force that slows their movement due to fluctuations in the fluid's molecules.

Stokes friction

The flow is laminar when the viscous forces, which oppose the movement of the fluid, are greater than the inertial forces and the fluid moves with sufficiently small speed and in a rectilinear path.

Friction coefficients

According to Coulomb's first law of friction, the friction coefficient μ is obtained from the relationship between the friction force and the force normal to the contact surface.

The coefficient μ is a dimensionless quantity, as it is a relationship between two forces, which depends on the nature and treatment of the materials in contact. Generally the value of the friction coefficient is between 0 and 1.

Static friction coefficient

The coefficient of static friction is the constant of proportionality that exists between the force that prevents the movement of a body in a state of rest on a contact surface and the force normal to the surface.

Kinetic friction coefficient

The coefficient of kinetic friction is the constant of proportionality that exists between the force that restricts the movement of a body moving on a surface and the force normal to the surface.

The coefficient of static friction is greater than the coefficient of kinetic friction.

Elastic friction coefficient

The elastic coefficient of friction is derived from the friction between contact surfaces of elastic, soft or rough materials that are deformed by applied forces. Friction opposes the relative movement between two elastic surfaces and the displacement is accompanied by an elastic deformation of the surface layers of the material.

The coefficient of friction that is obtained under these conditions depends on the degree of surface roughness, the physical properties of the materials in contact, and the magnitude of the tangential component of the shear force at the interface of the materials.

Molecular friction coefficient

The molecular coefficient of friction is obtained from the force that restricts the movement of a particle that slides on a smooth surface or through a fluid.

How is friction calculated?

The friction force on solid interfaces is calculated using the equation F _r = μN

Substituting the weight equation in the friction force equation gives:

Characteristics of the normal

When an object is at rest on a flat surface, the normal force is the one exerted by the surface on the body, and it opposes the force due to gravity, according to Newton's law of action and reaction.

The normal force always acts perpendicular to the surface. On an inclined surface, the normal decreases as the lean angle increases and points in a perpendicular direction away from the surface, while the weight points vertically downward. The equation of the normal force on an inclined surface is:

θ = angle of inclination of the contact surface.

Inclined plane friction

The component of the force acting on the body to slide it is:

As the applied force increases it approaches the maximum value of the friction force, this value is the one corresponding to the static friction force. When F = F _re, the static friction force is:

And the coefficient of static friction is obtained by the tangent of the angle of inclination θ.

Solved exercises

-Friction force of an object resting on a horizontal surface

A 15Kg box placed on a horizontal surface is pushed by a person who applies a force of 50 Newton along a surface to make it move and then applies a force of 25 N to keep the box moving at a constant speed. Determine the coefficients of static and kinetic friction.

Box moving on horizontal surface

Solution: With the value of the force applied to move the box, the coefficient of static friction μ _{e is obtained}.

The normal force N to the surface is equal to the weight of the box, so N = mg

In this case, μ _e = 50New / 147New

The force applied to keep the speed of the box constant is the kinetic friction force which is equal to 25New.

The coefficient of kinetic friction is obtained with the equation μ _c = F _rc / N

-Friction force of an object under the action of a force with an angle of inclination

A man applies a force to a 20Kg box, with an angle of application of 30 ° in relation to the surface where it rests. What is the magnitude of the force applied to move the box if the coefficient of friction between the box and the surface is 0.5?

Solution: The free-body diagram represents the applied force and its vertical and horizontal components.

Free-Body diagram

The applied force makes an angle of 30 ° with the horizontal surface. The vertical component of the force adds to the normal force affecting the force of static friction. The box moves when the horizontal component of the applied force exceeds the maximum value of the friction force F _re. Equating the horizontal component of the force with that of static friction gives:

Normal strength

The normal force is no longer the weight of the body due to the vertical component of the force.

According to Newton's second law, the sum of the forces acting on the box on the vertical axis is zero, therefore the vertical component of acceleration is a _y = 0. The normal force is obtained from the sum

By substituting the equation into the equation, the following is obtained:

-Friction in a moving vehicle

A 1.5-ton vehicle is traveling on a straight and horizontal road at a speed of 70 km / h. The driver sees obstacles on the road at a certain distance that force him to brake sharply. After braking, the vehicle skids for a short time until it comes to a stop. If the coefficient of friction between the tires and the road is 0.7; determine the following:

1. What is the value of friction while the vehicle is skidding?
2. Vehicle deceleration
3. The distance traveled by the vehicle from when it brakes to when it stops.

The friction force of the vehicle when it skids is:

= 10290 New

Section b

The friction force influences the slowdown of the vehicle when it skids.

By applying Newton's second law the value of the deceleration is obtained by solving for the equation F = ma

Section c

The initial speed of the vehicle is v ₀ = 70Km / h = 19.44m / s

When the vehicle stops its final speed is v _f = 0 and the deceleration is a = - 6.86m / s ²

The distance traveled by the vehicle, from when it brakes to when it stops, is obtained by solving for d from the following equation:

The vehicle travels 27.54m of distance before stopping.

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