How To Find Sliding Friction: Detailed Explanations

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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

how to find sliding friction
Image by Maxmath12 – Wikimedia Commons, Wikimedia Commons, Licensed under CC0.

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:

F_{text{friction}} = mu_k times F_{text{normal}}

Where:
F_{text{friction}} is the sliding friction force.
mu_k is the coefficient of kinetic friction, which depends on the materials in contact.
F_{text{normal}} 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 (mu_k) 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 (mu_k) by the normal force (F_{text{normal}}) to find the sliding friction force (F_{text{friction}}).

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:
F_{text{normal}} = m times g = 10 text{ kg} times 9.8 text{ m/s}^2 = 98 text{ N}

  1. Calculate the sliding friction force:
    F_{text{friction}} = mu_k times F_{text{normal}} = 0.3 times 98 text{ N} = 29.4 text{ N}

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:
F_{text{normal}} = m times g = 1500 text{ kg} times 9.8 text{ m/s}^2 = 14700 text{ N}

  1. Calculate the sliding friction force:
    F_{text{friction}} = mu_k times F_{text{normal}} = 0.4 times 14700 text{ N} = 5880 text{ N}

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

Exploring Factors Influencing Sliding Friction

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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

how to find sliding friction
Image by Hanjin Deviasse – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 3.0.
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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:

[ text{Force of sliding friction} = mu times text{Normal force} ]

The normal force can be calculated using the formula:

[ text{Normal force} = m times g ]

where g is the acceleration due to gravity.

Substituting the given values:

[ text{Normal force} = 5 , text{kg} times 9.8 , text{m/s}^2 ]

[ text{Force of sliding friction} = 0.2 times text{Normal force} ]

Finally, substituting the calculated value of the normal force:

[ text{Force of sliding friction} = 0.2 times (5 , text{kg} times 9.8 , text{m/s}^2) ]

Thus, the force of sliding friction acting on the block is calculated as  text{Force of sliding friction} = 9.8 , text{N} .

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:

 [ text{Net force} = text{Applied force} - text{Force of sliding friction} ]

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

 [ text{Force of sliding friction} = mu times text{Normal force} ]

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

 [ text{Normal force} = W ] 

Substituting the given values:

 [ text{Force of sliding friction} = 0.3 times 50 , text{N} ]

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

[ text{Net force} = 30 , text{N} - (0.3 times 50 , text{N}) ]

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

[text{Net force} = text{mass} times text{acceleration} ]

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

 [ text{Weight} = text{mass} times text{acceleration due to gravity} ]

Rearranging the formula:

 [ text{mass} = frac{text{Weight}}{text{acceleration due to gravity}} ]

Substituting the given values:

 [ text{mass} = frac{50 , text{N}}{9.8 , text{m/s}^2} ]

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

[ text{acceleration} = frac{text{Net force}}{text{mass}} ]

Thus, the acceleration of the box is calculated as  text{acceleration} = 0.612 , text{m/s}^2 .

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:

 [ text{Force of sliding friction} = mu times text{Normal force} ]

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

 [ text{Normal force} = m times g times cos(theta) ]

where g is the acceleration due to gravity.

Substituting the given values:

 [ text{Normal force} = 20 , text{kg} times 9.8 , text{m/s}^2 times cos(30°) ]

 [ text{Force of sliding friction} = 0.4 times text{Normal force} ]

Finally, substituting the calculated value of the normal force:

 [ text{Force of sliding friction} = 0.4 times (20 , text{kg} times 9.8 , text{m/s}^2 times cos(30°)) ]

Thus, the force of sliding friction acting on the crate is calculated as  text{Force of sliding friction} = 153.96 , text{N} .

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