In previous articles, we thoroughly analyzed kinetic energy and everything related to it. In this article, we continue our exploration and move on to studying mechanical energy . This type of energy is produced by the work done by a body and can be transferred between other bodies. Mechanical energy is the sum of kinetic energy (energy of motion) and elastic and/or gravitational potential energy, generated by the interaction of bodies based on their position.
In this article we will explain how mechanical energy works, how to calculate it and some examples and applications. If you want to understand this concept in a clear and simple way, keep reading.
Explanation of mechanical energy
Let's use an example to explain mechanical energy. Imagine we throw a ball from a certain height. During the throw, the ball possesses kinetic energy due to its motion, while in the air it also acquires gravitational potential energy due to its position relative to the ground. As it rises, its potential energy increases, and as it falls, that potential energy is converted into kinetic energy.
The arm that propels the ball does work on it, transferring kinetic energy to it. If we ignore air friction, the ball will retain its total mechanical energy, which is the sum of kinetic and potential energy. In fact, the mechanical energy of a system can remain constant when there are no resisting forces such as friction.
It is important to remember that gravity is a constant force (9,8 m/s² on Earth) and always acts on objects. Thus, the calculated mechanical energy will be the result of the interaction between the velocity, mass, and height of an object. The unit of measurement for mechanical energy is the joule (J) , according to the International System of Units.
Formula for mechanical energy
Mechanical energy (Em) is the sum of kinetic energy (Ec) and potential energy (Ep) . Mathematically, it can be expressed as follows:
Em = Ec + Ep
To calculate kinetic energy (Ec), we use the formula:
- Ec = 1/2 mv²
where m is the mass of the body and v is the speed.
Regarding gravitational potential energy (Ep), the formula is:
- Ep = mgh
where m is the mass, g is the acceleration due to gravity, and h is the height.
In this way, if you know the mass of the object, its speed and the height from which it is launched, you can calculate its mechanical energy.
Principle of conservation of mechanical energy
A fundamental principle in physics states that energy is neither created nor destroyed, but rather transformed . This is known as the principle of conservation of energy . In the case of mechanical energy, this principle is valid if the system is isolated, that is, if there are no non-conservative forces such as friction.
If we throw a ball into the air, at its highest point its kinetic energy will be zero, but its gravitational potential energy will be maximum. As it descends, the potential energy is transformed into kinetic energy. Throughout this process, the total mechanical energy of the system remains constant.
The mathematical equation that describes this principle is as follows:
Em = Ec + Ep = constant
In real systems, the presence of friction and other non-conservative forces alters this equation, causing some of the energy to be dissipated as heat or other forms of energy. Even so, this principle remains useful for the analysis of many physical systems.
Examples of exercises
Let's look at some exercises to illustrate how to apply the concepts described above:
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- Select the incorrect option:
- a) Kinetic energy is the energy that a body possesses because it is in motion.
- b) Gravitational potential energy is the energy that a body possesses by being at a certain height.
- c) The total mechanical energy of a body remains constant even in the presence of friction.
- d) The energy of the universe is constant and only transforms.
- e) When a body has kinetic energy, it can do work.
- Select the incorrect option:
The incorrect option is (c) . Mechanical energy is not conserved in the presence of friction, since part of it is dissipated as heat.
- A bus with mass m descends a slope at a constant speed. The driver keeps the brakes on, limiting the speed of the bus even though it is descending from a height h. Answer whether the following statements are true or false:
- The change in kinetic energy of the bus is zero.
- The mechanical energy of the bus-Earth system is conserved.
- The total energy of the bus-Earth system is conserved, although part of it is transformed into internal energy.
In this case, the correct answer is V, F, V. Kinetic energy does not change because the speed is constant; however, mechanical energy is not conserved due to the increase in the system's internal energy caused by friction.
These examples illustrate the importance of understanding how forces and energy interact in different contexts. Mechanical energy is key in many everyday applications, from the motion of a vehicle to jumping on a diving board.
A correct understanding of mechanical energy is not only useful for passing exams, but also for understanding the phenomena of the world around us.