# How To Find Sliding Friction: Detailed Explanations

Friction is a force that opposes the motion between two surfaces in contact. It plays a crucial role in our everyday lives, from walking to driving a car. There are two types of friction: static friction and sliding friction. In this blog post, we will focus on sliding friction, also known as kinetic friction, and explore how to find it.

## Distinguishing Between Static and Sliding Friction

### Definition of Static Friction

Static friction is the force that prevents an object from moving when a force is applied to it. It acts in the opposite direction of the applied force and adjusts its magnitude to match the force applied. It only comes into play when the object is at rest or not moving.

### Differences Between Static and Sliding Friction

Sliding friction, on the other hand, occurs when two surfaces are sliding against each other. It is the force that opposes the motion of the object. Unlike static friction, which varies with the applied force, sliding friction remains relatively constant once the object is in motion. It is generally smaller than static friction.

### Examples of Static Friction

1. Imagine a book sitting on a table. When you try to push it, you might notice that it doesn’t move easily. The force you apply is countered by the static friction between the book and the table, preventing it from sliding.

2. Another example is when you try to slide a heavy box on the floor. Initially, it requires more force to overcome the static friction between the box and the floor. Once the box starts moving, the static friction transitions into sliding friction.

## Calculating Sliding Friction

### Formula for Calculating Sliding Friction

To calculate sliding friction, we use the following formula:

Where:
is the sliding friction force.
is the coefficient of kinetic friction, which depends on the materials in contact.
is the normal force exerted on the object due to gravity.

### How to Calculate Sliding Friction

To calculate sliding friction, follow these steps:

1. Determine the value of the coefficient of kinetic friction ) between the two surfaces in contact. This value depends on the materials involved and can be found in reference tables or through experimentation.

2. Determine the normal force ) exerted on the object. This force is equal to the weight of the object and can be calculated using the formula , where is the mass of the object and is the acceleration due to gravity ).

3. Multiply the coefficient of kinetic friction ) by the normal force ) to find the sliding friction force ).

### Worked Out Examples of Sliding Friction Calculation

Let’s work through a couple of examples to better understand how to calculate sliding friction.

#### Example 1:

A box with a mass of 10 kg is being pushed horizontally across a table. The coefficient of kinetic friction between the box and the table is 0.3. What is the sliding friction force acting on the box?

Solution:
1. Calculate the normal force:

1. Calculate the sliding friction force:

Therefore, the sliding friction force acting on the box is 29.4 N.

#### Example 2:

A car with a mass of 1500 kg is moving along a road with a coefficient of kinetic friction of 0.4. What is the sliding friction force acting on the car?

Solution:
1. Calculate the normal force:

1. Calculate the sliding friction force:

Therefore, the sliding friction force acting on the car is 5880 N.

## Exploring Factors Influencing Sliding Friction

### Does Sliding Friction Increase with Speed?

No, sliding friction does not increase with speed. The magnitude of sliding friction depends on the coefficient of kinetic friction and the normal force, but it is not affected by the speed at which the object is moving.

### Role of Mass and Force in Sliding Friction

The mass of an object does not directly affect the sliding friction force. However, the normal force, which is proportional to the mass, does influence the sliding friction force. As the normal force increases, the sliding friction force also increases.

### Impact of Inclination and Gravity on Sliding Friction

When an object is on an inclined plane, the force of gravity can be resolved into two components: one perpendicular to the surface (normal force) and one parallel to the surface (force down the incline). The sliding friction force acts in the direction opposite to the force down the incline. The steeper the incline, the greater the sliding friction force required to prevent the object from accelerating down the slope.

## Numerical Problems on how to find sliding friction

### Problem 1:

A block of mass 5 kg is placed on a horizontal surface. The coefficient of sliding friction between the block and the surface is 0.2. Calculate the force of sliding friction acting on the block if a force of 30 N is applied to push the block horizontally.

Solution:

Given:
Mass of the block, m = 5 kg
Coefficient of sliding friction, μ = 0.2
Force applied, F = 30 N

The force of sliding friction can be calculated using the formula:

The normal force can be calculated using the formula:

where g is the acceleration due to gravity.

Substituting the given values:

Finally, substituting the calculated value of the normal force:

Thus, the force of sliding friction acting on the block is calculated as .

### Problem 2:

A box weighing 50 N is being pushed along a horizontal surface with a force of 30 N. If the coefficient of sliding friction is 0.3, calculate the acceleration of the box.

Solution:

Given:
Weight of the box, W = 50 N
Applied force, F = 30 N
Coefficient of sliding friction, μ = 0.3

The net force acting on the box can be calculated using the formula:

The force of sliding friction can be calculated using the formula:

The normal force can be calculated as the weight of the box:

Substituting the given values:

Finally, substituting the calculated value of the force of sliding friction into the net force formula:

The acceleration of the box can be calculated using Newton’s second law:

Since weight is given, it can be converted to mass using the formula:

Rearranging the formula:

Substituting the given values:

Finally, substituting the calculated values of mass and net force into the acceleration formula:

Thus, the acceleration of the box is calculated as .

### Problem 3:

A crate of mass 20 kg is placed on a ramp inclined at an angle of 30° to the horizontal. The coefficient of sliding friction between the crate and the ramp is 0.4. Calculate the force of sliding friction acting on the crate if a force of 200 N is applied parallel to the incline to push the crate upwards.

Solution:

Given:
Mass of the crate, m = 20 kg
Angle of incline, θ = 30°
Coefficient of sliding friction, μ = 0.4
Force applied parallel to the incline, F = 200 N

The force of sliding friction can be calculated using the formula:

The normal force can be calculated as the component of the weight of the crate perpendicular to the incline:

where g is the acceleration due to gravity.

Substituting the given values:

Finally, substituting the calculated value of the normal force:

Thus, the force of sliding friction acting on the crate is calculated as .