Chapter 6: Work and Energy
Difficulty Level: At Grade
Created by: CK12
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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*}
W=Fxx=(Fcosθ)x , 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*}
(kg⋅m2/s2) , 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*}
KE=12mv2
 Gravitational potential energy has the form: \begin{align*}PE = mgh\end{align*}
PE=mgh
 The potential energy stored in a spring has the form: \begin{align*}PE = \frac{1}{2} kx^2\end{align*}
PE=12kx2
 The relationship between the applied force and the distance a spring is stretched or compressed is: \begin{align*}F = kx\end{align*}
F=kx (Hooke’s Law)
 The WorkEnergy principle is \begin{align*}W = \Delta KE\end{align*}
W=ΔKE
 Dissipative forces such as friction are considered nonconservative forces. Mechanical energy is not conserved in the presence of nonconservative forces.
 The conservation of mechanical energy can be written as: \begin{align*}KE_i + PE_i = KE_f +PE_f\end{align*}
KEi+PEi=KEf+PEf
 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*}
KEi+PEi=KEf+PEf+Qf , where \begin{align*}Q_f\end{align*}Qf is the energy that has been transformed into heat.
 In the event of an explosion, heat, \begin{align*}Q_i\end{align*}
Qi , is added to the initial \begin{align*}KE\end{align*}KE and \begin{align*}PE\end{align*}PE energies and in the most general case, heat can also be lost, \begin{align*}Q_f\end{align*}Qf , after the explosive, thus:

\begin{align*}KE_i + PE_i + Q_i = KE_f + PE_f + Q_f\end{align*}
KEi+PEi+Qi=KEf+PEf+Qf
 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*}
P=Wt=(Fx)t=Fv and has units of Watts \begin{align*}(W)\end{align*}(W)
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Covers potential and kinetic energy, work, conservation of energy, the WorkEnergy Principle, power, and various energy and power problems.
Difficulty Level:
At Grade
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Date Created:
Jun 27, 2013
Last Modified:
Jun 07, 2016
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