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 as 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 (J) and is represented by the letter W (from the English Work, “Work”). In addition, it is often spoken of as positive or negative work depending on whether the force transfers energy to the object (positive work) or if it is subtracted (negative work). Thus, for example, someone who throws a ball does positive work, while someone who catches it does negative work. You must read about Tower of Babel once.
Characteristics of mechanical work
Mechanical work is characterized by:
- It is a scalar magnitude, which is measured through joules (that is, kilograms per square meter divided by square seconds) and is represented by the letter W.
- It directly depends on the force that causes it, such that for mechanical work to exist in a body, there must be a mechanical force applied to it along a defined path.
- In everyday language, the term “work” is used to define that mechanical activity whose execution consumes a quantity of energy.
- Heat transfer (caloric energy) is not considered a form of work, even though it is a transfer of energy.
Mechanical Work Formula
The simplest formula for calculating the work of a body that is moved by a force is usually the following:
W = F x d
where W is the work performed, F is the force acting on the body, and D is the distance of displacement suffered by the body.
However, force and distance are usually considered vector magnitudes, which require a certain orientation in space. Thus, the above formula can be reformulated to include said orientation, as follows:
W = F x d x cos𝛂
where the cosine of alpha (cos𝛂) determines the angle formed by the direction in which the force is applied and the direction in which the object moves as a result. Maybe you should definitely read about Aphrodite once.
Types of mechanical work
Mechanical work can be of three types, depending on whether the energy level in the moving body is added, subtracted or maintained. Thus, we can talk about:
Positive work (W > 0)
This 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 a club and makes it fly several meters, or a baseball player who hits a moving ball, modifying the trajectory it was on.
Zero work (W = 0)
This 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 who pushes a very heavy piece of furniture without managing to make it move even a millimeter.
Negative work (W < 0)
This occurs when the applied force subtracts energy from the object in question, resisting the movement that the object was already making or reducing its displacement. An example of this would be a baseball player who catches a ball thrown by another player, preventing it from continuing on its path; or a person who stands in the way of an object falling down a hill and although he is unable to stop it completely, he does manage 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 towards the goal, with a force of 500 N, causing it to travel about 15 meters without touching the ground. How much work did he do in scoring that goal?
Answer: applying the formula W = F x d, we have that Messi did a work of 500 N x 15 m, that is, work equivalent to 7500 J.
- A train is moving south at full speed, straight towards a car trapped on the tracks. A superhero, realizing the danger, decides to stand in the way of the locomotive and stop its advance. Considering that the train is carrying 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: Since 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 work equal to 20,000 N x 698 m, or negative work of 13,960,000 J.
