- What is mechanical work?
- Characteristics of mechanical work
- Mechanical work formula
- Types of mechanical work
- Examples of mechanical work
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 physical, and more specifically in the branch of the mechanics, is meant by mechanical work (or simply worked) to the action of a strength on a body at rest movement, so as to produce 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 magnitude scalar, which is usually measured in the International system (SI) through joules or joules (J) and is represented by the letter W (from the English work, "Worked"). In addition, we often 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 through joules (that is, kilograms per square meter divided by a 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 current language, the term “work” is used to define that mechanical activity whose performance consumes an amount of energy.
- The transference of heat (caloric energy) is not considered a form of work, even though it consists of a transfer of energy.
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 x d
where W is the work done, F is the force acting on the body, and D is the displacement distance 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 such orientation, as follows:
W = F x d x 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 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 contributes 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 the trajectory it had.
- 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 who pushes a very heavy piece of furniture without making it move an inch.
- Negative work (W < 0).It occurs when the applied force subtracts energy from the object in question, resisting the movement that the object already brought or reducing its displacement. An example of this would be a baseball player who catches the ball thrown by another, preventing him from following his trajectory; or a person who stands in front of an object falling down a hill and, although unable to stop it completely, manages to slow down its fall.
Examples of mechanical work
Some examples of mechanical work are:
- In a soccer game, the referee takes a penalty and Lionel Messi kicks the ball towards the goal, with a force of 500N, making it move about 15 meters without touching the ground. How much work did he put into scoring that goal?
Answer: applying the formula W = F x d, we have that Messi did a work of 500N x 15m, that is, a work equivalent to 7500 J.
- A train heads south at full speed, heading straight for a car stuck on the tracks. A superhero, realizing the danger, decides to stand 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 does the superhero have to do to stop it?
Answer: Since braking the locomotive requires at least 20,000 N in the opposite direction, and 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, that is, a negative work of 13,960,000 J.