7.6 Conservation of Energy

Energy conservation is a fundamental principle in physics. It states that energy can't be created or destroyed, only converted between forms like kinetic, potential, thermal, electrical, and chemical. This concept helps us understand and predict energy transfers in various processes.

The law of energy conservation applies to different forms of energy, including kinetic, potential, thermal, electrical, and chemical. It also relates to work, power, and force. Understanding these concepts helps us analyze energy efficiency and transformations in real-world situations.

Conservation of Energy

Conservation of energy law

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• Energy cannot be created or destroyed, only converted from one form to another (kinetic, potential, thermal, electrical, chemical)
• Total energy of an isolated system remains constant over time
• Energy transforms between various forms, but total amount remains the same
  • Dropped ball: potential energy converts to kinetic energy as it falls, then to thermal and sound energy upon impact with ground
• Allows analysis of energy transfer and transformation in various processes
• Helps predict outcome of energy-related phenomena (collisions, oscillations, thermodynamic processes)

Forms of energy in conservation

• Kinetic energy ($[KE](https://www.fiveableKeyTerm:KE)$): energy associated with motion of an object
  • $KE = \frac{1}{2}mv^2$, $m$ = mass, $v$ = velocity
• Potential energy ($PE$): energy stored in an object due to position or configuration
  • Gravitational potential energy: $[PE_g](https://www.fiveableKeyTerm:PE_g) = mgh$, $m$ = mass, $g$ = acceleration due to gravity, $h$ = height above reference point
  • Elastic potential energy: $[PE_e](https://www.fiveableKeyTerm:PE_e) = \frac{1}{2}kx^2$, $k$ = spring constant, $x$ = displacement from equilibrium position
• Thermal energy: energy associated with random motion of particles in a substance
  • Related to temperature of substance
• Electrical energy: energy associated with movement of electric charges
  • Stored in electric fields or transferred through electric currents
• Chemical energy: energy stored in bonds between atoms in molecules
  • Released or absorbed during chemical reactions

Efficiency of energy conversions

• Efficiency: measure of how effectively energy converts from one form to another
  • Efficiency = \frac{\text{[Useful work](https://www.fiveableKeyTerm:useful_work) output}}{\text{Total energy input}} \times 100\%
• Useful work: energy successfully converted into desired form and used for intended purpose
• Energy losses: occur due to friction, heat dissipation, and other irreversible processes
  • Reduce amount of useful work obtained from total energy input
• Calculating efficiency:
  1. Identify useful work output and total energy input
  2. Divide useful work output by total energy input
  3. Multiply result by 100% to express as percentage
• Example: Electric motor supplied with 100 J electrical energy, performs 70 J mechanical work
  • Efficiency = $\frac{70 \text{ J}}{100 \text{ J}} \times 100\% = 70\%$
• Higher efficiency indicates more effective energy conversion with minimal losses

Work, Power, and Force in Energy Conservation

• Work: transfer of energy when a force acts on an object, causing displacement
  • $W = F \cdot d \cdot \cos\theta$, where $F$ is force, $d$ is displacement, and $\theta$ is angle between force and displacement
• Power: rate at which work is done or energy is transferred
  • $P = \frac{W}{t}$, where $W$ is work and $t$ is time
• Force: any interaction that, when unopposed, changes the motion of an object
  • Related to work and energy through the work-energy theorem
• Momentum: product of an object's mass and velocity, conserved in closed systems
  • $p = mv$, where $m$ is mass and $v$ is velocity
• Energy conservation principle: total energy of an isolated system remains constant, encompassing all forms of energy and their transformations