Mechanical Work (Meaning and Explanation)

We explain what mechanical work is in physics, its characteristics and the formula to calculate it. Also, what types exist and examples.

What is mechanical work?

In physics, and more specifically in the branch of mechanics, mechanical work (or simply work) is understood to be the action of a force on a body at rest or in motion, in such a way that it produces a displacement in the body proportional to the energy invested in the force that moves it. In other words, mechanical work is the amount of energy transferred to a body by a force acting on it.

Mechanical work is a scalar magnitude, which is usually measured in the International System (SI) through joules or joules (J) and is represented with the letter W (from English work“Job”). Besides, we usually talk about positive or negative work depending on whether the force transfers energy to the object (positive work) or subtracts it (negative work). Thus, for example, whoever throws a ball does positive work, while whoever catches it does negative work.

Characteristics of mechanical work

Mechanical work is characterized by:

It is a scalar magnitude which is measured in joules (that is, kilograms per square meter per second squared) and is represented by the letter W.
It depends directly on the force that causes it so that for there to be mechanical work on a body, there must be a mechanical force applied to it along a defined path.
In common language, the term “work” is used to define that mechanical activity whose execution consumes an amount of energy.
Heat transfer (heat energy) is not considered a form of work even though it consists of an energy transfer.

Mechanical work formula

The simplest formula to calculate the work of a body that is moved by a force is usually the following:

W = F xd

where W is the work done, F the force acting on the body and D is the distance of the displacement suffered by the body.

However, force and distance are usually considered vector magnitudes, which require a specific orientation in space. Thus, the previous formula can be reformulated to include said orientation, as follows:

W = F xdx cos𝛂

where the cosine of alpha (cos𝛂) determines the angle between the direction in which the force is applied and the direction in which the object moves as a result.

Types of mechanical work

mechanical work types — Negative work occurs when the applied force resists the movement of the object.

Mechanical work can be of three types, depending on whether it adds, subtracts or maintains the energy level in the moving body. Thus, we can talk about:

Positive work (W > 0). It occurs when the force provides energy to the object in question, producing a displacement in the same direction in which the force was applied. An example of this would be a golf player who hits a ball with the club and makes it fly several meters, or a baseball player who hits a ball in motion, modifying its trajectory.
Zero work (W = 0). It occurs when the applied force does not produce any displacement in the object, even though it is consuming energy in the process. An example of this would be a person pushing a very heavy piece of furniture without making it move even a millimeter.
Negative work (W < 0). It occurs when the applied force subtracts energy from the object in question, resisting the movement that the object already had or reducing its displacement. An example of this would be a baseball player who blocks the ball thrown by another, preventing him from continuing with his trajectory; or a person who stands in front of an object that is falling down a hill and although he cannot completely stop it, he manages to slow down its fall.

Examples of mechanical work

Some examples of mechanical work are:

In a soccer game, the referee awards a penalty and Lionel Messi kicks the ball in the direction of the goal, with a force of 500N, making it travel about 15 meters without touching the ground. How much work did you put into scoring that goal?

Answer: Applying the formula W = F xd, we have that Messi performed a work of 500N x 15m, that is, a work equivalent to 7500 J.

A train is moving south at full speed, straight toward a car stuck on the tracks. A superhero, realizing the danger, decides to get in front of the locomotive and stop its progress. Considering that the train brings with it a force of 20,000 N, that the superhero is invulnerable and that the locomotive is 700 meters from the trapped car, how much work must the superhero do to stop it?

Answer: Given that stopping the locomotive requires at least 20,000 N in the opposite direction, and that the superhero would like to leave a margin of at least 2 meters between the locomotive and the trapped car, we know that he must apply a work equal to 20,000 N x 698 m , that is, a negative work of 13,960,000 J.

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