Energy

Table of Contents

Definition

  • the capacity to do work.
  • it is measured in Joules (J) similar to work.
  • merely describes a property of system that can be transferred but cannot be created nor destroyed.

Work-Energy Theorem

Formula: \(W_{net} = \Delta KE\)

  • when work is done \(W_{net}\) in an object, there will be a change in kinetic energy \(KE\).
  • An object in motion can do work on another object.

Types

Kinetic Energy

  • the energy while an object is in motion.
\begin{align*} E_k = \frac{mv^2}{2} \end{align*}

Potential Energy

  • Energy that could be used to do work.
  • Energy when the object is at rest.
  • an example of this is gravitational potential energy.
  • There is a relationship between force and potential energy, given the following formulas:
\begin{align*} & \displaystyle\int\vec{F}\, d\vec{r} \\ & \vec{F}(x) = \frac{du}{dx} \end{align*}

Gravitational Potential Energy

\(PE_{ gravity} = mgh\)

  • where \(m\) is mass, \(g\) is gravity, \(h\) height of the object.

Spring Potential Energy

  • also called Elastic potential energy.
\begin{align*} & F_{spring} = kx \\ & PE_{spring} = \frac{kx^2}{2} \end{align*}
  • where \(k\) is the spring constant and \(x\) is the distance.
  • This formula is known as Hooke's Law after Robert Hooke.

Non-conservative Energy

  • A system that loses energy.
  • Like when normal force loses energy when friction stops it.

Conservative Energy

  • A system that doesn't lose energy.
  • An example of this is a pendulum.
    • because the kinetic energy and potential energy is just converting between each other.

References

Date: August 18, 2023

Author: Paul Gerald D. Pare

Emacs 29.1 (Org mode 9.6.6)