# How to calculate work done by friction

**Introduction**

Friction is a force that occurs when two surfaces are in contact and oppose their relative motion. It plays a significant role in our daily lives – from the grip of our shoes on the ground to the movements of machines and vehicles. In this article, we will discuss how to calculate the work done by friction.

**Understanding Friction**

Before diving into calculations, it is essential to understand the basics of friction. There are two main types of friction: static and kinetic friction. Static friction occurs when two objects are stationary relative to each other, while kinetic friction happens when objects slide against each other.

To calculate work done by friction, we will focus on kinetic friction since it involves the motion of objects. The formula for kinetic friction is given as follows:

**F_friction = μ * F_normal**

where:

– F_friction: The force of friction

– μ: The coefficient of kinetic friction (unitless)

– F_normal: The normal force (force perpendicular to the contact surface)

**The Work-Energy Principle**

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. This principle establishes a direct relationship between work and energy, allowing us to calculate work done by various forces such as friction.

**Calculating Work Done by Friction**

To determine the work done by frictional forces, you need to follow these steps:

**1. Determine the coefficient of kinetic friction (μ):** This value depends on the materials involved and must be provided or looked up in a table.

**2. Calculate the normal force (F_normal):** This can be found using Newton’s second law if needed (F = ma) or through an understanding of other forces acting on an object, such as gravity.

**3. Apply the formula for kinetic friction:** Use F_friction = μ * F_normal to find the force of friction.

**4. Evaluate the distance over which friction acts (d):** This is the distance over which the object in motion slides against the other surface.

**5. Calculate the work done by friction:** The formula for work done is W = F * d * cos(θ), where θ is the angle between force and displacement vectors. Since friction acts in the opposite direction of displacement, θ = 180°.

By substituting the values in the formula, we get:

W_friction = F_friction * d * cos(180°)

W_friction = F_friction * d * (-1)

W_friction = – μ * F_normal * d

The negative sign indicates that the work done by friction opposes the motion of an object and reduces its kinetic energy.

**Conclusion**

Understanding how to calculate work done by friction is crucial in physics, engineering, and our daily lives. In this article, we discussed the importance of friction, introduced the work-energy principle, and provided a step-by-step approach to calculating work done by friction. By applying these steps, you can solve problems involving friction and gain a deeper understanding of its impact on motion.