sciPAD Physics 1.4: Energy in Physical Systems - Comprehensive Study Notes

Fundamental Principles of Energy in Physical Systems

• Definition of Energy: Scientists define energy as the ability to produce change. It is an essential part of daily life, experienced through the warmth of the sun, the motion of the wind, and the fuel provided by food. While not a visible or tangible substance, its effects are observable in the operation of electronic devices, vehicles, and industries.

• The Big Idea: Energy is transformed or transferred when things change, but the total amount of energy within a closed system always remains constant.

• The Law of Conservation of Energy: This law states that energy cannot be created or destroyed; it can only be transformed from one form to another or transferred between objects.

• Energy Forms and Descriptions:

  • Mechanical (Kinetic): The energy an object possesses by virtue of its motion ($E_{k}$). Moving objects have the ability to do work and cause environmental changes.

  • Thermal Energy: Energy derived from the vibration of atoms and molecules within substances. Increased vibration results in higher temperatures and greater thermal energy.

  • Chemical Energy: Energy released when substances, such as fuels or food, undergo chemical reactions and transform into other substances.

  • Elastic Potential Energy: Energy stored in "springy" or bouncy objects when a force causes them to be stretched or squashed.

  • Gravitational Potential Energy: Energy an object acquires due to its mass and its height above a surface ($E_{p}$). It exists within the gravitational field between the object and the Earth.

• Identifying Forms of Energy in Scenarios:

  • Spinning wind turbine: Kinetic.

  • Warm water in a pool: Thermal.

  • Fruit hanging on a tree: Gravitational.

  • Archer pulling back a string: Elastic.

  • Fully charged battery: Electrical (stored as chemical transition).

  • Digesting a burger: Chemical.

System Analysis and Energy Bar Charts

• System Definition: A system is defined as a single object or a group of objects treated together for analysis.

  • If gravitational energy is involved, the Earth must be included in the system because the energy exists in the gravitational field between the object and the Earth.

  • If friction on a surface is involved, the ground must be included in the system.

• Initial vs. Final States: Scientists compare energy at two specific instants (initial state and final state) to identify how the system has changed.

• Energy Bar Charts (LOL Diagrams): Visual representations used to track the total energy of a system across two instants.

  • Chart on the Left: Represents the initial state energy.

  • Circle in the Middle: Represents the defined system and identifies external work ($W$) entering or leaving.

  • Chart on the Right: Represents the final state energy.

  • The Conservation Equation: The total number of energy units (represented by vertical bars) in the initial state must equal the total units in the final state (accounting for any work added/removed). For a dropped ball: $E_{p} = E_{k}$.

Mass, Weight, and Gravitational Potential Energy

• Mass vs. Weight:

  • Mass ($m$): The amount of matter or "stuff" an object contains. Measured in kilograms ($kg$). Mass remains constant regardless of location (e.g., Earth vs. Moon).

  • Weight ($F_{g}$): The effect of gravity on the mass of an object. It is a force measured in Newtons ($N$).

• Strength of Earth's Gravitational Field ($g$): Approximately $10\,N\,kg^{-1}$.

• Calculating Weight:

  • $\text{Force (} F \text{)} = m \times g$

  • Example: A small dog with a mass of $7\,kg$ has a weight of $70\,N$ ($7 \times 10$).

• Calculating Gravitational Potential Energy ($E_{p}$):

  • $E_{p} = m \times g \times \Delta h$

  • $E_{p}$ is gravitational energy in Joules ($J$).

  • $m$ is mass in kilograms ($kg$).

  • $g$ is gravity ($10\,N\,kg^{-1}$).

  • $\Delta h$ is the change in height in meters ($m$).

  • Note: Since $m \times g$ equals Weight ($F$), the formula can also be expressed as $E_{p} = F \times h$.

• Key Relationships: If two objects (A and B) are lifted to the same height, the one with the larger mass gains more gravitational energy.

Kinetic Energy and Velocity Calculations

• Kinetic Energy ($E_{k}$): The energy possessed by an object due to its motion. It depends on two factors:

  • Mass: Kinetic energy increases as mass increases (direct relationship).

  • Velocity: Kinetic energy increases with the square of the velocity.

• Formula:

  • $E_{k} = \frac{1}{2} m v^2$

• Calculating Velocity from Energy:

  • To find velocity ($v$) when energy and mass are known:

  • $v = \sqrt{\frac{2 E_{k}}{m}}$

• Real-World Application (The Skate Park):

  • A grandad ($m = 75\,kg$) dropping down a $1\,m$ ramp will have three times the gravitational energy at the top and three times the kinetic energy at the bottom compared to his granddaughter ($m = 25\,kg$).

• Air Resistance/Drag: In reality, as an object falls, some $E_{k}$ is "lost" to air friction, causing the ball to hit the ground with slightly less velocity than predicted by the idealized formula $E_{p} = E_{k}$. This energy is transformed into thermal energy.

Work, Power, and Efficiency

• Work ($W$): The transfer of energy that occurs when a force is applied to an object, causing it to move in the direction of that force ($W$ is measured in Joules, $J$).

  • $W = F \times d$

  • Work is only done if the object moves. A stationary object being held up has no work being done on it ($d = 0$).

• Power ($P$): The rate at which energy is transferred or the rate at which work is done. It is measured in Watts ($W$) or Joules per second ($J\,s^{-1}$).

  • $P = \frac{W}{t}$

  • $P = \frac{\Delta E}{t}$

  • Example: If a forklift lifts an $800\,kg$ pallet ($8\,000\,N$) to a height of $1.0\,m$ in $2.0\,s$, the power is $P = \frac{8\,000 \times 1}{2.0} = 4\,000\,W$.

• Energy Efficiency: The ratio of useful output energy to total input energy.

  • $\text{Energy efficiency (\%)} = \frac{\text{Useful energy}}{\text{Total energy}} \times 100$

  • Friction and Energy Loss: Friction transforms kinetic energy into thermal energy, which dissipates as heat. This heat is often an undesired form of energy (loss), though it is not destroyed from the universe.

  • Lubrication: Oil or grease is used in machinery to reduce friction, thereby reducing thermal energy transformation and increasing efficiency.

Thermal Energy and the Particle Theory of Matter

• Particle Theory Principles:

  1. All matter is made of particles.

  2. Particles are always moving.

  3. Temperature affects the speed of particle motion.

• States of Matter:

  • Solids: Particles pack tightly in a fixed shape, vibrating gently. Strong attractive forces. Lowest energy state.

  • Liquids: Particles are loosely packed and can slide past each other. More kinetic energy than solids.

  • Gases: Particles are far apart and move freely/rapidly. Kinetic energy exceeds attractive forces. Highest energy state.

• Temperature vs. Thermal Energy vs. Heat:

  • Temperature ($T$): A measure of the average kinetic energy of the particles. It does not depend on the amount of substance.

  • Thermal Energy: The total kinetic energy of all particles in a system. It depends on both particle speed and the total number of particles (mass).

  • Heat ($Q$): The flow of energy between systems due to a temperature difference. It always moves from a hotter object to a colder object.

• Thermal Equilibrium: The state reached when two objects in contact achieve the same temperature, and heat flow stops.

Mechanisms of Heat Transfer

• Conduction: Transfer of thermal energy through direct contact between particles without the particles moving to a new location.

  • Thermal Conductors: Materials (like metals) with free electrons and closely packed atoms that transmit vibrations quickly.

  • Thermal Insulators: Materials (like plastic, wood, polystyrene, and air) that restrict heat flow.

  • Trapped Air: Effective as an insulator (e.g., in newspaper, polar fleece, or bird feathers) because gas particles are far apart and cannot easily transfer kinetic energy.

• Convection: Transfer of thermal energy through the movement of particles in fluids (liquids and gases).

  • Process: Heating causes particles to move faster and further apart, making the fluid less dense. The warm, less dense fluid rises, while cooler, denser fluid sinks, creating a convection current.

  • Examples: Lava lamps (wax density changes), tea bag rockets, heating a room with a radiator.

• Radiation (Infrared): Transfer of energy via electromagnetic waves. It does not require particles or matter and can travel through a vacuum.

  • Absorption and Reflection: Dull, dark objects absorb radiation well; shiny, bright surfaces reflect it.

  • Survival Blankets: Use shiny aluminum coatings to reflect emitted body radiation back to the person.

Phase Changes and Thermodynamics Calculations

• Latent Heat: The energy absorbed or released during a phase change that occurs without a change in temperature. The energy is used to break or form bonds between particles.

  • Latent Heat of Fusion ($L_{f}$): Used for changes between solid and liquid (melting/freezing). For water: $334\,000\,J\,kg^{-1}$.

  • Latent Heat of Vaporization ($L_{v}$): Used for changes between liquid and gas (boiling/condensing). For water: $2\,260\,000\,J\,kg^{-1}$.

  • Note: $L_{v}$ is always greater than $L_{f}$ because bonds must be broken completely to form a gas whereas they only loosen to form a liquid.

• Calculating Phase Change Energy:

  • $Q = m \times L$

• Specific Heat Capacity ($c$): The amount of energy needed to change the temperature of $1\,kg$ of a substance by $1\,^\circ C$.

  • Water's Specific Heat Capacity: $4\,200\,J\,kg^{-1}\,^\circ C^{-1}$.

  • Calculation Formula:

    • $Q = m \times c \times \Delta T$

• Combined Problems: To calculate the total energy to turn ice at $-10\,^\circ C$ to steam at $100\,^\circ C$, one must sum the energy to heat ice, melt ice ($L_{f}$), heat water, and vaporize water ($L_{v}$).

Electrical Energy and Circuits

• Current ($I$): The flow of electric charge, carried by electrons in metals. Measured in Amperes ($A$).

  • Current only flows in a closed circuit (complete pathway).

  • Ammeter: Measures current; must be connected in series.

• Voltage ($V$): The electrical push or potential difference that moves electrons. Measured in Volts ($V$).

  • Voltmeter: Measures potential difference; must be connected in parallel across a component.

• Circuit Rules:

  • Series Circuits:

    • Current is constant throughout the circuit ($I_{total} = I_{1} = I_{2}$).

    • Voltage is shared among components ($V_{supply} = V_{1} + V_{2}$).

    • If one component breaks, the entire circuit fails.

  • Parallel Circuits:

    • Current is shared among branches ($I_{total} = I_{branch1} + I_{branch2}$).

    • Voltage remains the same across every branch ($V_{supply} = V_{branch1} = V_{branch2}$).

    • If one component breaks, others keep functioning.

• Resistance ($R$): A quantity describing how much a component restricts current flow. Measured in Ohms ($\Omega$).

  • Ohm’s Law: $V = I \times R$

  • Electric Power ($P$): The rate of energy transformation in a circuit.

    • $P = V \times I$

  • Energy Transformed ($\Delta E$):

    • $\Delta E = P \times t$

Specialized Applications

• Dewar Flask (Vacuum Flask): Reduces heat transfer via:

  • Vacuum Gap: Prevents conduction and convection (no particles).

  • Shiny Lining: Reflects infrared radiation back into the liquid.

  • Plastic Cap: An insulator that prevents conduction and traps warm air.

• Incandescent vs. LED Lighting:

  • Incandescent Bulbs: Operate by heating a tungsten filament to $2\,500 - 3\,000\,^\circ C$. Very inefficient ($10\%$ light, $90\%$ heat). Short lifespan ($1\,000$ hours).

  • LED Bulbs: Pass electricity through a semiconductor. Highly efficient ($90\%$ light, $10\%$ heat). Long lifespan ($25\,000$ hours).

• BBQs and Efficiency: Shiny hoods reflect radiation and trap hot air (convection). Ceramic insulators separate the hotplate from the frame to prevent conduction loss to the metal structure.