How to Calculate Work Done with Friction vs Without Friction

Understanding how friction affects work calculations is fundamental in physics. This guide explains the key formulas, compares results with and without friction, and provides practical examples to help you analyze work problems accurately.

Introduction

Work is a fundamental concept in physics that measures the energy transferred when a force acts upon an object to move it through a distance. When calculating work, the presence or absence of friction significantly impacts the results. Friction converts some of the applied force into heat, reducing the effective work done on the object.

This guide will help you understand:

The basic work formula
How friction modifies the work calculation
When to use each formula
Practical examples comparing results

Key Formulas

Work Without Friction

The basic formula for work done on an object is:

Work = Force × Distance W = F × d

Where:

W is work (measured in joules, J)
F is the force applied (measured in newtons, N)
d is the distance moved in the direction of the force (measured in meters, m)

Work With Friction

When friction is present, the effective force is reduced by the frictional force. The formula becomes:

Work = (Applied Force - Frictional Force) × Distance W = (F - f) × d

Where:

f is the frictional force (measured in newtons, N)
F must be greater than f for positive work to be done

Note: Friction always acts opposite to the direction of motion. If the applied force is less than the frictional force, the object won't move, and no work is done.

Comparison of Results

Let's compare the work done with and without friction using a practical example:

Scenario	Applied Force (N)	Frictional Force (N)	Distance (m)	Work Without Friction (J)	Work With Friction (J)	Difference (J)
Pushing a box	50	10	20	1000	900	100
Pulling a crate	80	5	15	1200	1175	25

The table shows that friction reduces the work done on the object. The difference becomes more significant as the frictional force increases relative to the applied force.

Worked Examples

Example 1: Pushing a Box

You push a 20 kg box across a floor with a force of 50 N. The frictional force is 10 N. How much work is done if you push it 20 meters?

Work without friction = 50 N × 20 m = 1000 J Work with friction = (50 N - 10 N) × 20 m = 900 J Difference = 100 J

Friction reduces the work done by 100 joules in this scenario.

Example 2: Pulling a Crate

A 50 kg crate is pulled 15 meters with a force of 80 N. The frictional force is 5 N. Calculate the work done.

Work without friction = 80 N × 15 m = 1200 J Work with friction = (80 N - 5 N) × 15 m = 1175 J Difference = 25 J

Here, the difference is smaller because the frictional force is much less than the applied force.

FAQ

Why does friction reduce the work done?

Friction converts some of the applied force into heat, so less energy is actually used to move the object.

When is the work done with friction equal to the work without friction?

When there is no friction (f = 0), the work done is the same as when friction is present.

Can work be done if the applied force is less than the frictional force?

No, if F < f, the object won't move, and no work is done because the net force is zero.