Chapter 1: Conservation and Dissipation of Energy - Comprehensive Study Guide

Key Terminology for Conservation and Dissipation of Energy

• Chemical: Energy that can be transferred through chemical reactions involving foods, fuels, and the chemicals found in batteries.
• Closed System: A system where no energy can escape to or enter from the surroundings. The total energy in a closed system never changes.
• Dissipated: Energy that is wasted; it is transferred to less useful stores, specifically the thermal energy store of the surroundings.
• Efficiency: A measure of how much energy is transferred usefully. It can be expressed as a decimal or a percentage.
• Elastic Potential: The energy an elastic object possesses when it is stretched or compressed.
• Electrostatic: The energy a charged object has when it is near another charged object.
• Gravitational Potential: The energy an object has because of its height above the ground.
• Kinetic: The energy an object possesses because it is moving.
• Lubrication: A method used to reduce unwanted energy transfer resulting from friction.
• Magnetic: The energy a magnetic object has when it is located near a magnet or within a magnetic field.
• Nuclear: The energy stored specifically within the nucleus of an atom.
• Power: The rate at which work is done or energy is transferred per second. Measured in Watts ($W$).
• Streamlining: A method used to reduce energy wasted due to air resistance or drag in water.
• System: An object or a group of objects defined for study.
• Thermal (or Internal): The energy an object has because of its temperature, representing the total kinetic and potential energy of the particles within the object.
• Work Done: The energy transferred when a force moves or changes the state of an object.

Defining Systems and Energy Stores

• The Concept of a System:     * A system is defined as an object or group of objects.     * Whenever a change occurs within a system, energy is transferred between different stores or to the surroundings.
• Closed Systems:     * In a closed system, energy cannot leave or enter from the outside environment (surroundings).     * The total energy within a closed system remains constant (never changes).
• Specific Energy Stores:     * Kinetic Energy Store: Energy an object has due to its motion.     * Gravitational Potential Store: Energy an object has due to its height above the ground.     * Elastic Potential Store: Energy an elastic object has when it is stretched or squashed.     * Thermal (Internal) Store: Energy due to the object's temperature, composed of the total kinetic and potential energy of the particles in the object.     * Chemical Store: Energy transferable by chemical reactions (e.g., in foods, fuels, and batteries).     * Nuclear Store: Energy stored in the nucleus of an atom.     * Magnetic Store: Energy held by a magnetic object when near a magnet or in a magnetic field.     * Electrostatic Store: Energy held by a charged object when near another charged object.

Mechanisms and Examples of Energy Transfer

• Methods of Transfer:     * Heating: Energy transferred from one object to another due to a difference in temperature.     * Waves: Energy transferred via light waves or sound waves.     * Electricity: Energy transferred by an electric current.     * Forces (Mechanical Work): Energy transferred when a force moves or changes the state of an object.
• Contextual Examples of Transfers:     * Stretching a Rubber Band: Energy is transferred from the chemical store (of the person stretching it) to the rubber band’s elastic potential store.     * Dropping a Block from a Height: Energy is mechanically transferred by the force of gravity from the block’s gravitational potential store to its kinetic store.     * Block Impacting the Ground: Energy from its kinetic store is transferred mechanically and by sound waves to the thermal energy store of the surroundings.     * Electric Kettle: Electric current transfers energy to the heating element's thermal energy store. This energy is then transferred by heating from the element to the water's thermal energy store.     * Slowing Down Due to Friction: Energy is mechanically transferred from the object’s kinetic store to its own thermal store, the thermal store of the surface it is rubbing against, and the general thermal store of the surroundings.

Quantitative Energy Equations

• Work Done: When an object is moved by a force, work is done. The force transfers energy to the object. The energy transferred is equal to the work done.     * Formula: $\text{work done (J)} = \text{force (N)} \times \text{distance (m)}$
• Gravitational Potential Energy ($E_p$): Depends on height, gravitational field strength, and mass.     * Formula: $\text{gravitational potential energy (J)} = \text{mass (kg)} \times \text{gravitational field strength (N/kg)} \times \text{height (m)}$     * Symbolic: $E_p = m \times g \times h$
• Kinetic Energy ($E_k$): Depends on mass and speed.     * Formula: $\text{kinetic energy (J)} = \frac{1}{2} \times \text{mass (kg)} \times (\text{speed (m/s)})^2$     * Symbolic: $E_k = \frac{1}{2} \times m \times v^2$
• Elastic Potential Energy ($E_e$): For a stretched spring (assuming the limit of proportionality is not exceeded).     * Formula: $\text{elastic potential energy (J)} = \frac{1}{2} \times \text{spring constant (N/m)} \times (\text{extension (m)})^2$     * Symbolic: $E_e = \frac{1}{2} \times k \times e^2$
• Power ($P$): The rate of work done or energy transfer per second.     * Unit: Watt ($W$). $1\text{ watt} = 1\text{ joule}$ transferred per second.     * Formulas: $P = \frac{E}{t}$ or $P = \frac{W}{t}$     * Terms: $\text{power (W)} = \frac{\text{energy (J)}}{\text{time (s)}}$ or $\text{power (W)} = \frac{\text{work (J)}}{\text{time (s)}}$

Conservation, Dissipation, and Efficiency

• The Law of Conservation of Energy: Energy cannot be created or destroyed. It can only be transferred usefully, stored, or dissipated (wasted).
• Energy Dissipation:     * Energy is never transferred 100% usefully; some is always dissipated to less useful stores.     * Ultimately, all energy is eventually transferred to the thermal energy store of the surroundings.
• Energy Loss in Machines:     * Work done against friction typically causes energy to be wasted, increasing the thermal store of the machine and the surroundings.
• Methods of Reducing Unwanted Energy Transfers:     * Lubrication: Reduces energy loss caused by friction.     * Streamlining: Reduces energy loss caused by air resistance or water drag.     * Thermal Insulation: Reduces energy loss dissipated as heat to the surroundings.
• Calculating Efficiency:     * As a Decimal: $\text{efficiency} = \frac{\text{useful output energy transfer (J)}}{\text{total input energy transfer (J)}}$     * Using Power: $\text{efficiency} = \frac{\text{useful power output (W)}}{\text{total power input (W)}}$     * As a Percentage: Multiply the decimal result by $100$ and add the $\%$ sign.

Retrieval Questions

• 1. Name the five energy stores. (Note: The text actually lists eight stores: kinetic, gravitational potential, elastic potential, thermal/internal, chemical, nuclear, magnetic, and electrostatic).
• 2. Name the four ways in which energy can be transferred.
• 3. What is a system?
• 4. What is a closed system?
• 5. What is work done?
• 6. What is the unit for energy?
• 7. What is one joule of work?
• 8. Describe the energy transfer when a moving car slows down.
• 9. Describe the energy transfer when an electric kettle is used to heat water.
• 10. Describe the energy transfer when a ball is fired using an elastic band.
• 11. Describe the energy transfer when a battery powered toy car is used.
• 12. Describe the energy transfer when a falling apple hits the ground.
• 13. Name the unit that represents one joule transferred per second.
• 14. A motor is 30% efficient. What does that mean?