When we attempt to move an object across a surface, the movement is impeded by a connection between the object and the surface. This connection is due to the electromagnetic forces between the charged particles present at the surface and the object's surface that is in contact with it. This opposition is denoted by a force called friction. The focus of our discussion is specifically on 'kinetic friction.' As we delve deeper into this topic, we will explore the definition of kinetic friction, the work accomplished by friction, the distinction between static and kinetic friction, and the three types of kinetic friction. In addition, we will provide visual aids to aid in comprehending each concept thoroughly.
What is Kinetic Friction?
Kinetic friction, also known as dynamic friction, is the force that opposes the movement of an object relative to a surface. When an object slides, rolls, or moves in any other way over a surface, kinetic friction acts in the direction opposite to the motion of the object, making it harder to move. This force is caused by the irregularities in the surfaces of both the object and the surface it's in contact with, which create interlocking points and prevent the object from sliding smoothly. Kinetic friction depends on the type of surfaces in contact, their roughness, and the force pressing them together. It can be calculated by multiplying the coefficient of kinetic friction, which represents the interaction between the surfaces, by the normal force, which is the force pressing the object and surface together.
What is the formula of Kinetic Friction?
The formula for kinetic friction can be expressed as:
Fk = μk * N
where Fk is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force, which is the force perpendicular to the surface that the object is in contact with. The coefficient of kinetic friction is a constant that depends on the type of surfaces in contact and their roughness. It is a dimensionless quantity that ranges between 0 and 1, where 0 represents no friction, and 1 represents a strong frictional force. The unit of kinetic friction is the same as that of force, which is Newtons (N).
Derivation of Kinetic Friction Formula
The force of kinetic friction is given by:
Fk = ma
where m is the mass of the object and a is the acceleration of the object. Since the object is moving with constant velocity, a = 0.
Therefore, we can write:
Fk = 0
However, this does not mean that there is no force acting on the object. There is a force of kinetic friction acting in the opposite direction to the motion of the object.
Therefore, we can modify the equation as follows:
F - Fk = 0
where F is the external force applied to the object.
Rearranging this equation, we get:
Fk = F
Now, we can substitute the value of F from Newton's second law of motion, which states that:
F = ma
Substituting this in the above equation, we get:
Fk = ma
But, we also know that the force of kinetic friction is given by:
Fk = μkN
Substituting this in the above equation, we get:
μkN = ma
Rearranging this equation, we get:
a = μk (N/m)
where N/m is the force per unit mass, which is equal to the acceleration due to gravity, g.
Therefore, we get:
a = μk g
This is the derivation of the formula for kinetic friction, which relates the acceleration of an object to the coefficient of kinetic friction and the acceleration due to gravity.
How many types of Kinetic Friction are there?
There are three types of kinetic friction:
Sliding Friction: This type of friction occurs when an object slides over a surface. For example, when a box is dragged across the floor, sliding friction opposes its motion.
Rolling Friction: This type of friction happens when an object rolls over a surface. For example, when a wheel rolls on a road, rolling friction acts against its motion.
Fluid Friction: This type of friction occurs when an object moves through a fluid, such as air or water. The resistance to the object's motion is due to the viscosity of the fluid, which causes the fluid to stick to the object's surface and create drag. For example, when a swimmer moves through water, the fluid friction of the water opposes their motion.
The type and magnitude of kinetic friction depend on the properties of the surfaces in contact and the speed and direction of the object's motion.
Applications of Kinetic Friction
Kinetic friction has many practical applications in our daily lives, some of which are:
Brakes: The braking systems in vehicles use kinetic friction to stop the motion of the vehicle. The brake pads press against the wheels, creating friction and reducing the speed of the vehicle.
Tires: The tires of vehicles use rolling friction to provide traction and enable the vehicle to move forward.
Walking: When we walk, the soles of our shoes experience kinetic friction with the ground, allowing us to move forward and maintain balance.
Sports: In sports like soccer, basketball, and tennis, the ball experiences kinetic friction when it rolls or bounces on the ground, which affects its speed and trajectory.
Manufacturing: The production of many goods, such as sandpaper, adhesive tapes, and grinding wheels, requires the use of abrasive materials that generate kinetic friction to shape or polish surfaces.
Energy conversion: Kinetic friction is also used in many energy conversion devices, such as generators and wind turbines, where mechanical energy is converted into electrical energy by inducing a rotating motion that experiences kinetic friction with the surrounding surfaces.
Understanding the properties and behavior of kinetic friction is essential in designing and optimizing these applications.
Laws of Kinetic Friction
There are actually four laws of kinetic friction:
The force of kinetic friction is proportional to the normal force: As the normal force increases, the force of kinetic friction also increases proportionally.
The force of kinetic friction is independent of the velocity: The force of kinetic friction is generally assumed to be independent of the velocity of the object. However, in reality, the force of kinetic friction can sometimes vary with the speed of the object.
The force of kinetic friction is dependent on the nature of the surfaces in contact: The coefficient of kinetic friction, which determines the magnitude of the force of kinetic friction, depends on the nature of the surfaces in contact and their roughness.
The force of kinetic friction is independent of the contact area: The force of kinetic friction is independent of the contact area between the object and the surface, as long as the normal force and coefficient of kinetic friction remain constant.
These four laws describe the basic behavior of kinetic friction and can be used to calculate the force of kinetic friction in different situations. However, it is important to note that the force of kinetic friction can vary depending on several other factors, such as the temperature, the presence of lubricants, and the surface quality, among others.
Types of Friction
There are four main types of friction:
Kinetic Friction: This is the force that opposes the motion of an object that is already in motion. It is the force that needs to be overcome to keep an object moving at a constant velocity.
Static Friction: This is the force that resists the motion of an object that is at rest and prevents it from moving. It is the force that needs to be overcome to start the motion of an object.
Rolling Friction: This is the force that resists the motion of an object that is rolling along a surface. It is typically lower than kinetic friction, allowing objects such as wheels to roll smoothly.
Fluid Friction: This is the force that resists the motion of an object through a fluid (e.g. air or water). It is also known as drag and can be either laminar or turbulent depending on the speed of the object and the properties of the fluid.
Type of Friction | Definition | Example | Direction of Force |
Static Friction | Force that resists the motion of an object that is at rest and prevents it from moving | Trying to push a heavy box that won't budge | Opposes the direction of the applied force |
Kinetic Friction | Force that opposes the motion of an object that is already in motion | Sliding a box across a surface | Opposes the direction of motion |
Rolling Friction | Force that resists the motion of an object that is rolling along a surface | Rolling a ball across a surface | Opposes the direction of motion |
Fluid Friction | Force that resists the motion of an object through a fluid | Swimming through water | Opposes the direction of motion |
Solved Examples of Kinetic Friction
Some solved examples of Kinetic Friction are listed below:
Question: A block of wood is being dragged along a rough surface at a constant speed of 2 meters per second. If the coefficient of kinetic friction between the wood and the surface is 0.5, what is the force of kinetic friction acting on the block?
Solution: The formula for kinetic friction is Fk = μkN, where Fk is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force. Since the block is moving at a constant speed, the force of kinetic friction is equal and opposite to the applied force, which is the force needed to overcome the friction. Therefore, Fk = ma = 0, and the force of kinetic friction is:
Fk = μkN = 0.5 x (mg) = 0.5 x (10 kg x 9.81 m/s^2) = 49.05 N
Question: A car with a mass of 1200 kg is traveling at a constant speed of 20 meters per second on a flat road. If the coefficient of kinetic friction between the tires and the road is 0.4, what is the force of kinetic friction acting on the car?
Solution: The force of kinetic friction is equal to the force needed to overcome the resistance of the tires and keep the car moving at a constant speed. Therefore, the force of kinetic friction is:
Fk = μkN = 0.4 x (mg) = 0.4 x (1200 kg x 9.81 m/s^2) = 4704 N
Question: A box of mass 10 kg is being pushed along a surface with a force of 40 N. If the coefficient of kinetic friction between the box and the surface is 0.3, what is the acceleration of the box?
Solution: The net force acting on the box is the applied force minus the force of kinetic friction. Therefore, the net force is:
Fnet = Fa - Fk = 40 N - (0.3 x 10 kg x 9.81 m/s^2) = 7.53 N
Using F = ma, the acceleration of the box is:
a = F/m = 7.53 N / 10 kg = 0.753 m/s^2
Question: A crate of mass 50 kg is being pulled across a floor with a force of 200 N. If the coefficient of kinetic friction between the crate and the floor is 0.2, what is the acceleration of the crate?
Solution: The net force acting on the crate is the applied force minus the force of kinetic friction. Therefore, the net force is:
Fnet = Fa - Fk = 200 N - (0.2 x 50 kg x 9.81 m/s^2) = 98.1 N
Using F = ma, the acceleration of the crate is:
a = F/m = 98.1 N / 50 kg = 1.96 m/s^2