# Kinetic Friction Formula

Kinetic friction is the force that opposes the relative motion of two surfaces that come into contact and move past each other. Unlike static friction, which prevents the commencement of motion between surfaces, kinetic friction occurs while the surfaces are already sliding against one another. Learn more about kinetic friction, its definition, formula and examples

## What is Kinetic Friction

Kinetic friction is a type of friction that occurs when two surfaces are in contact and moving relative to each other. It is the resistive force that opposes the motion of one surface as it slides over another.

### Key Characteristics of Kinetic Friction

Opposition to Motion: Kinetic friction acts in the direction opposite to the direction of the relative motion of the surfaces.

Constant Magnitude: For many material pairs, the kinetic friction force remains constant as long as the relative motion continues at a constant speed, regardless of the velocity.

Dependence on Normal Force: The magnitude of the kinetic friction force $$F_k$$ is proportional to the normal force $$N$$, which is the perpendicular force exerted by the surface on the object. The relationship is given by:
$F_k = \mu_k \cdot N$
where $$\mu_k$$ is the coefficient of kinetic friction.

Coefficient of Kinetic Friction ($$\mu_k$$): This dimensionless coefficient depends on the materials of the contacting surfaces and typically ranges from 0 to 1, though it can be higher for certain material combinations.

Surface Independence: The force of kinetic friction is generally independent of the contact area between the surfaces. Instead, it depends on the nature of the surfaces and the normal force.

## Formula for Kinetic Friction

The following equation provides the best definition of friction force. For the specific type of friction being considered, the friction coefficient determines the force of friction. The strength of the normal force also has a role.

Kinetic friction is the phrase used to describe the retarding force that exists between two moving planes when they come into contact. The following is the Kinetic Friction Formula:

Fk = μkFn

Additionally, Fn = mg applies if the issue involves a horizontal surface and no other vertical forces are at play.

Where,

• Fk Force of kinetic friction
• μk Coefficient of sliding friction or kinetic friction
• Fn Normal force, equal to the object’s weight
• m Object’s mass
• g Acceleration due to gravity

## Solved Examples on Kinetic Friction

Example 1: A box with a mass of 10 kg is sliding on a horizontal floor. The coefficient of kinetic friction between the box and the floor is 0.3. Calculate the kinetic friction force acting on the box.

Solution:
Calculate the normal force $$N$$:
$N = mg$
where $$m$$ is the mass of the box, and $$g$$ is the acceleration due to gravity ($$g \approx 9.8 \, \text{m/s}^2$$).

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

2. Apply the kinetic friction formula:
$F_k = \mu_k \cdot N$
$F_k = 0.3 \times 98 \, \text{N} = 29.4 \, \text{N}$

The kinetic friction force acting on the box is $$29.4 \, \text{N}$$.

Example 2: A car with a weight of 15000 N is moving on a road. The coefficient of kinetic friction between the tires and the road is 0.7. Determine the kinetic friction force when the car brakes.

Solution:
Determine the normal force $$N$$:
For a car on a horizontal road, the normal force is equal to the weight of the car.

$N = 15000 \, \text{N}$

Apply the kinetic friction formula:
$F_k = \mu_k \cdot N$
$F_k = 0.7 \times 15000 \, \text{N} = 10500 \, \text{N}$

The kinetic friction force when the car brakes is $$10500 \, \text{N}$$.

Example 3: A crate with a mass of 20 kg is being pushed up a 30° incline. The coefficient of kinetic friction between the crate and the incline is 0.4. Calculate the kinetic friction force.

Solution:
Calculate the normal force $$N$$:
The normal force on an incline is given by:
$N = mg \cos(\theta)$
where $$\theta$$ is the angle of the incline.

$N = 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times \cos(30^\circ)$
$N = 196 \, \text{N} \times \cos(30^\circ)$
$N = 196 \, \text{N} \times \frac{\sqrt{3}}{2}$
$N \approx 169.7 \, \text{N}$

Apply the kinetic friction formula:
$F_k = \mu_k \cdot N$
$F_k = 0.4 \times 169.7 \, \text{N} \approx 67.88 \, \text{N}$

The kinetic friction force acting on the crate is approximately $$67.88 \, \text{N}$$.

## FAQs (Frequently Asked Questions)

### 1. What is kinetic friction?

Kinetic friction is the force that opposes the relative motion of two surfaces that are in contact and sliding past each other. It acts in the direction opposite to the movement.

### 2. How is kinetic friction different from static friction?

• Kinetic friction acts on moving objects and opposes their motion.
• Static friction acts on objects that are not moving and prevents the start of motion.

### 3. What is the coefficient of kinetic friction?

The coefficient of kinetic friction is a dimensionless constant that depends on the materials of the two surfaces in contact. It represents how much frictional force exists between them when they are moving relative to each other.

### 4. Does the contact area affect kinetic friction?

In most cases, the contact area does not affect the magnitude of kinetic friction. Kinetic friction depends primarily on the normal force and the nature of the surfaces