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# Chapter 6: Work and Energy

Difficulty Level: At Grade Created by: CK-12

Credit: Vik Walker
Source: http://www.flickr.com/photos/eidoloon/2570238282/

[Figure1]

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 $W = F_x x = (F \cos \theta)x$, the product of the component of the force along the line of motion and displacement.
• Work has units of N*m, or $(\text{kg} \cdot \text{m}^2 / \text{s}^2)$, 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: $KE = \frac{1}{2} mv^2$
• Gravitational potential energy has the form: $PE = mgh$
• The potential energy stored in a spring has the form: $PE = \frac{1}{2} kx^2$
• The relationship between the applied force and the distance a spring is stretched or compressed is: $F = kx$ (Hooke’s Law)
• The Work-Energy principle is $W = \Delta KE$
• 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: $KE_i + PE_i = KE_f +PE_f$
• In the presence of dissipative forces the conservation of energy can we written as:
• $KE_i + PE_i = KE_f + PE_f + Q_f$, where $Q_f$ is the energy that has been transformed into heat.
• In the event of an explosion, heat, $Q_i$, is added to the initial $KE$ and $PE$ energies and in the most general case, heat can also be lost, $Q_f$, after the explosive, thus:
• $KE_i + PE_i + Q_i = KE_f + PE_f + Q_f$
• The average power is the rate at which work is done or consumed or produced : $P = \frac{W}{t} = \frac{(Fx)}{t} = Fv$ and has units of Watts $(W)$

1. [1]^ Credit: Vik Walker; Source: http://www.flickr.com/photos/eidoloon/2570238282/; License: CC BY-NC 3.0

Dec 05, 2014