Concept of Energy

Definition

Energy: in physics energy is defined as the ability to do work. For example, increasing the speed of a car or lifting a stone requires work. Energy and work are measured in the same units (J). There' re three types of energy: kinetic, potential and mechanical.

Kinetic Energy

Kinetic energy: Kinetic energy[1] is a type of energy that an object has due to its motion. We define the linear kinetic energy E k E _{k} [1]of a material point of mass m which moves with a speed v in a Galilean frame of reference by E k = 1 2 m v 2 E_{k}= {1} over {2} m v^{2}

Potential Energy

Potential energy: Potential energy[2] is the energy that exists in an object due to its position or state, it represents the work actually done and is sometimes called stored energy. The work of conservative forces is not about the path followed, it is about the starting point and the ending point. The work of these forces can be expressed by a function called potential energy E p E_{p} , for example: the gravitational potential energy is equal to E p ( z ) = mgz E_{p}(z)=mgz

Mechanical Energy

Mechanical energy: Mechanical energy is the energy resulting from movement, that is, due to the effect of force on objects.

Consider a system moving between two points A and B under the influence of conservative and non-conservative forces. The mechanical energy (total) is

E M ( B ) − E M ( A ) = ∑ W A → B F NC ⃗ → Δ E M = ∑ W A → B F NC ⃗ E_{M}( B )-E_{M}( A)= sum W_{A rightarrow B} vec F _{NC} rightarrow %DELTA E_{M}=sum W_{A rightarrow B} vec F _{NC}

With

E M = E k + E p E_{M}= E_{k}+ E_{p}

Principle of Conservation of Energy

The principle of conservation of energy is divided in two cases:

  • Case of conservative forces

E M = E k + E p = cst → Δ E M = 0 E_{M}= E_{k}+ E_{p}=cst rightarrow %DELTA E_{M}=0

This means that the change in kinetic energy is equal to the change in potential energy

Δ E k = − Δ E p %DELTA E_{k}=- %DELTA E_{p}

  • Case of non-conservative forces

E M ( B ) − E M ( A ) = ∫ W A → B ( F NC ⃗ ) → Δ E M = ∫ W A → B ( F NC ⃗ ) E_{M}( B )- E_{M}( A )= int W_{A rightarrow B} ( vec F _{NC} ) rightarrow %DELTA E_{M}=int W_{A rightarrow B} ( vec F _{NC} )

Note

We notice from here that the total energy is not constant and its variation is not non-existent, but it is equal to the work of the non-conservative forces, which represents the energy loss.

Reminder

  • Conservative forces:

Forces are said to be conservative when their work does not depend on the path followed but on the starting point and the arrival point, it is symbolized by F C ⃗ vec F _{C} . For example: Force of gravity, force of weight, spring return force.

  • Non-conservative forces:

The forces are said to be non-conservative or active forces when their work depends on the path followed, it is symbolized by F NC ⃗ vec F _{NC} . It leads to the dissipation of kinetic energy (waste or unnecessary conversion) into heat which is lost to the surrounding environment, and is considered the main consumer of the energy used. For example: Friction force.