To calculate the work done against friction, we can use the formula

where $W$ represents the work done, $F$ is the force applied, and $d$ is the distance moved.

Friction is a force that opposes motion and is directly proportional to the normal force acting on an object. The work done against friction is defined as the product of the frictional force and the distance moved in the direction opposite to the force.

For example, consider a scenario where a force of $10 \, \text{N}$ is applied to move an object a distance of $5 \, \text{m}$ against a frictional force of $5 \, \text{N}$. We can calculate the work done against friction as follows:

Substituting the values, we get:

Thus, the work done against friction in this example amounts to $25 \, \text{J}$.

In summary, to determine the work done against friction, you can utilize the formula

where $W$ is the work, $F$ is the frictional force, and $d$ is the distance moved. Simply multiply the frictional force by the distance. For instance, if you exert a force against a frictional resistance of $5 \, \text{N}$ over a distance of $5 \, \text{m}$, the total work done is $25 \, \text{J}$.