In previous articles we thoroughly analyzed kinetic energy and everything related to it. In this case, we continue with the training and go on to study mechanical energy. This type of energy is produced by the work of a body and can be transferred between other bodies. Mechanical energy is the sum of kinetic energy (movement) with elastic and/or gravitational potential energy, generated by the interaction of bodies depending 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 give an example to explain mechanical energy. Imagine that we throw a ball from a certain height. During the throw, the ball has Kinetic energy due to its movement, while being in the air it also acquires gravitational potential energy by its position relative to the ground. As it rises, the potential energy increases, and when it descends, 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 the 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 speed, mass and height of a body. The unit of measurement of mechanical energy is the july (J), according to the International System of Units.
Formula for mechanical energy
Mechanical energy (Em) is the sum of the kinetic energy (Ec) and potential energy (Ep)Mathematically, it can be expressed as follows:
Em = Ec + Ep
To calculate the Kinetic energy (Ec), we use the formula:
- Ec = 1/2 mv²
where m is the mass of the body and v is the speed.
With regards to gravitational potential energy (Ep), the formula is:
- Ep = mgh
where m is the mass, g is the acceleration caused by gravity and h 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 is the one that states that Energy is neither created nor destroyed, but transformed. This is known as the principle of conservation of energyIn 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:
- 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.
The incorrect option is (C)Mechanical energy is not conserved in the presence of friction, since part of it is dissipated in the form of heat.
- 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, VKinetic energy does not vary because the speed is constant; however, mechanical energy is not conserved due to the increase in the internal energy of the system 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.