In-Depth Notes on Conservation of Momentum and Energy

Conservation of Momentum

• The principle that in an isolated system, the total momentum before an event (like a collision) is equal to the total momentum after the event.
• Formula: Total momentum = mass x velocity.

Conservation of Energy

Energy Stores and Transfers

• Definition of Energy: Energy is what makes everything happen; it can be transferred between stores.
• Energy Stores:
  • Kinetic Energy: Energy of moving objects.
  • Thermal Energy: Increases with temperature, related to internal energy.
  • Chemical Energy: Stored in bonds (e.g., food, fuels).
  • Gravitational Potential Energy: Energy of an object due to its height.
  • Elastic Potential Energy: Energy stored in stretched or compressed objects.
  • Electrostatic Energy: Energy between charged objects.
  • Magnetic Energy: Energy between magnets.
  • Nuclear Energy: Energy stored in atomic nuclei.

Energy Transfers

• Methods of energy transfer include:
  • Mechanically: Through forces acting on objects (e.g., pushing).
  • Electrically: Movement of electric charges (e.g., in circuits).
  • By Heating: Energy transferred from hot to cold objects.
  • By Radiation: Transferred via waves (e.g., solar energy).

Work Done

• Work done equals energy transferred.
• Equation: Work ext{ done} (E) = Force (F) imes Distance (d)
• Measured in Joules (J).

Energy Conservation Principle

• Energy can be transferred, stored, and dissipated but cannot be created or destroyed.
• In closed systems, the net change in energy is zero.

Dissipation of Energy

• Some energy is dissipated as waste (usually thermal energy) during transfers.
• Efficient systems minimize waste energy, enhancing performance.

Examples of Energy Changes

• A moving vehicle: Kinetic energy is converted to thermal energy via friction, resulting in heat.
• Heating water in a kettle: Electrical energy is converted to thermal energy, warming the water.

Calculating Energy Transfers

Kinetic Energy Equation

• KE = \frac{1}{2} mv^2
  • Where m is mass (kg) and v is velocity (m/s).

Gravitational Potential Energy Equation

• GPE = mgh
  • Where m is mass (kg), g is gravitational field strength (N/kg), and h is height (m).

Specific Heat Capacity

• The amount of energy needed to raise 1 kg of a substance by 1 °C.
• Equation: Q = mc\Delta T
  • Where Q = heat energy (J), m = mass (kg), c = specific heat capacity (J/kg°C), and \Delta T = change in temperature (°C).

Efficiency

• Efficiency measures how much of the energy input is converted into useful output.
• Formula: Efficiency = \frac{Useful ext{ Energy Output}}{Total ext{ Energy Input}}
  • Can be given as a decimal or as a percentage.

Energy Sources

Non-Renewable Sources

• Fossil Fuels: Coal, oil, natural gas - formed from organic materials - finite resources.
• Nuclear Fuels: E.g., uranium, utilized in nuclear reactions.

Renewable Sources

• Solar Energy: Solar panels convert sunlight into electricity or heat.
• Wind Energy: Wind turbines convert kinetic energy from wind into power.
• Hydro-Electric Energy: Water flow generates electricity.
• Biomass: Organic materials used for fuel.
• Geothermal Energy: Heat from beneath the Earth's surface.

Applications in Daily Life

• Energy transfer mechanisms are crucial in various applications such as cooking, heating homes, and powering vehicles. Understanding these concepts helps optimize energy usage and efficiency in various technologies.