In our daily experience we understand and use the word energy as something always related to movement. For example, for a car to work it needs fuel, for human beings to work and carry out their daily tasks they have to eat. Here we associate both fuel and food with energy. From now on we will move towards a more precise definition of energy.
The movement of a car, a person or any object has energy, this energy related to movement is called kinetic energy. A moving body, possessing kinetic energy, can do work by coming into contact with another body or object and transferring energy to it.
However, an object at rest can also have energy, which makes it insufficient just to relate the concept of energy to movement. For example, an object at rest at a certain height from the ground has energy. This object, when abandoned, starts a movement and increases in speed over time, this occurs because the weight force does a job and makes it go into motion, that is, it acquires energy kinetics. An object at rest is said to have an energy called gravitational potential energy, which varies according to its height in relation to the ground.
Another form of energy is elastic potential energy, present in a compressed or stretched spring. When we compress or stretch a spring, we perform work to achieve the deformation and we can observe that, after released, the spring acquires movement - kinetic energy - and returns to its initial position where it was not stretched or compressed.
So, more specifically, we can say that kinetic energy is the energy or ability to perform work due to movement and that potential energy is the energy or ability to do work due to position.
In mechanics, there are two forms of potential energy: one associated with weight work, called energy gravitational potential, and another related to the work of the elastic force, which is the potential energy elastic. Now let's study these two forms of potential energy in more detail.
1. Gravitational Potential Energy
It is the energy associated with the position in which the body is. Look at figure 1 and consider the body of mass m initially at rest at point b. The body is at a height h in relation to the ground a. When abandoned from rest, due to its mass, the weight force performs work on the body and it acquires kinetic energy, that is, it starts to move.
The work that the weight of the sphere does allows us to measure the gravitational potential energy, so let's calculate work.
Considering point a as the reference point, the displacement from b to a is given by h, the modulus of force weight being given by P = m.g and o angle between the direction of application of the force weight and the displacement α = 0º, as both are in the same direction, just apply the definition of work (τ):
τ=F.d.cosα
If F is equal to the force weight P=mg, the displacement d = h and α = 0º (cos 0º = 1), substituting in equation 1, we will have:
τ=F.d.cosα
τ=m.g.h.cos 00
τ=m.g.h
Thus, the energy that relates the position of an object to the ground, Gravitational Potential Energy, is calculated by:
ANDP= m.g.h
Equation 2: Gravitational Potential Energy
On what:
Ep: gravitational potential energy;
g: gravitational acceleration;
m: body mass.
2. Elastic Potential Energy
Consider the spring-mass system in figure 2, where we have a body with mass m attached to a spring of elastic constant k. To deform the spring we must do a job, as we have to push or stretch it. When we do this, the spring acquires elastic potential energy and, when released, moves back to its initial position, where there was no deformation.
In order to obtain the mathematical expression of the elastic potential energy, we must proceed in the same way as we did for the gravitational potential energy. Then, we will obtain the expression of the elastic potential energy stored in a mass-spring system by the work that the elastic force exerts on the block.
When the mass-spring system is at point A, there is no deformation in the spring, that is, it is neither stretched nor compressed. Thus, when we stretch it to B, a force appears, called elastic force, which causes it to return to A, its initial position, when abandoned. The modulus of the elastic force exerted by the spring on the block is given by Hooke's Law:
Fel = k.x
Where Fel indicates the elastic force, k is the elastic constant of the spring and x is the value of the contraction or elongation of the spring.
The work of the elastic force for a displacement d = x is given by:
Thus, the energy associated with the work of elastic force, Elastic Potential Energy, is also given by:
On what:
Eel: elastic potential energy;
k: spring constant;
x: spring deformation.
It is observed that the sphere with mass m suspended in relation to the ground and the spring-mass system, when stretched or compressed, have the ability to do work, as they have stored energy due to their position. This energy stored due to position is called Potential Energy.
By Nathan Augusto
Graduated in Physics
Source: Brazil School - https://brasilescola.uol.com.br/fisica/energia-potencial-gravitacional-elastica.htm
