In physics, the term work is used when we talk about work done by a force, that is, mechanical work. A force applied to a body does a job when it produces a displacement in the body.

We use the lowercase Greek letter tau () to express work.

The unit of work in the IS is Joule (J)

When a force has the same direction of movement the work done is positive: >0;

When a force has a direction opposite to the movement the work done is negative: <0.

The resulting work is obtained by summing the work of each force applied to the body, or by calculating the resulting force in the body.

Force parallel to displacement

When the force is parallel to the displacement, that is, the displacement vector and the force do not angle each other, we calculate the work:


What work is done by a force applied to a 5kg body mass that causes an acceleration of 1.5m / s² and travels for a distance of 100m?

Force not parallel to displacement

Whenever the force is not parallel to the displacement, we must decompose the vector into its parallel and perpendicular components:

Whereas the perpendicular component of the Force and the parallel component of the force.

That is:

When the furniture moves horizontally, only the forces parallel to the movement produce work. Soon:


A force of intensity 30N is applied to a block forming an angle of 60 ° with the displacement vector, which has an absolute value of 3m. What is the work done by this force?

We can always consider this case, where the cosine of the angle appears, since when the force is parallel to the displacement, its angle is 0 ° and cos0 ° = 1, this may help to understand why when the force is contrary to the displacement the work is negative since:

The cosine of an angle between 90 ° and 180 ° is negative, with cos180 ° = -1.

Work of a variable force

To calculate the work of a varying force we must employ integration techniques, which is a mathematical technique studied at the higher level, but to simplify this calculation, we can calculate this work by calculating the area under the curve in the diagram.

Calculating the area under the curve is a valid technique for forces that do not vary as well.

Strength work Weight

To calculate the work of the weight force, we must consider the trajectory as the height between the body and the point of origin, and the force to be employed, the weight force.