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Chapter 6: Work and Energy

Difficulty Level: At Grade Created by: CK-12
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Energy is a common concept in the modern world.  A key to understanding energy in detail is how different kinds of energy transform from one to the other, such as circular motion being changed into electrical power. 

Chapter Outline

Chapter Summary

  • Work is defined as \begin{align*}W = F_x x = (F \cos \theta)x\end{align*}, the product of the component of the force along the line of motion and displacement.
  • Work has units of N*m, or \begin{align*}(\text{kg} \cdot \text{m}^2 / \text{s}^2)\end{align*}, also known as Joules (J).
  • Energy comes in two forms: kinetic and potential

Kinetic energy is the energy of motion and potential energy is the energy of position. Potential energy can also have many forms. For example: gravitational potential energy, elastic potential energy, chemical potential energy, and nuclear potential energy to name a few.

  • Energy is the ability to do work and has units of joules, J.
  • Kinetic energy has the form: \begin{align*}KE = \frac{1}{2} mv^2\end{align*}
  • Gravitational potential energy has the form: \begin{align*}PE = mgh\end{align*}
  • The potential energy stored in a spring has the form: \begin{align*}PE = \frac{1}{2} kx^2\end{align*}
  • The relationship between the applied force and the distance a spring is stretched or compressed is: \begin{align*}F = kx\end{align*} (Hooke’s Law)
  • The Work-Energy principle is \begin{align*}W = \Delta KE\end{align*}
  • Dissipative forces such as friction are considered non-conservative forces. Mechanical energy is not conserved in the presence of non-conservative forces.
  • The conservation of mechanical energy can be written as: \begin{align*}KE_i + PE_i = KE_f +PE_f\end{align*}
  • In the presence of dissipative forces the conservation of energy can we written as:
  • \begin{align*}KE_i + PE_i = KE_f + PE_f + Q_f\end{align*}, where \begin{align*}Q_f\end{align*} is the energy that has been transformed into heat.
  • In the event of an explosion, heat, \begin{align*}Q_i\end{align*}, is added to the initial \begin{align*}KE\end{align*} and \begin{align*}PE\end{align*} energies and in the most general case, heat can also be lost, \begin{align*}Q_f\end{align*}, after the explosive, thus:
  • \begin{align*}KE_i + PE_i + Q_i = KE_f + PE_f + Q_f\end{align*}
  • The average power is the rate at which work is done or consumed or produced : \begin{align*}P = \frac{W}{t} = \frac{(Fx)}{t} = Fv\end{align*} and has units of Watts \begin{align*}(W)\end{align*}

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Difficulty Level:
At Grade
Date Created:
Jun 10, 2014
Last Modified:
Oct 20, 2016
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