work, energy, and power

Components of a Physical System

• Identify and define the components, boundaries, and initial/final states of a physical system.

Types of Systems

• Distinguish between open, closed, and isolated systems based on the exchange of matter and energy:
    - Open System: Exchanges both matter and energy with its surroundings.
    - Closed System: Exchanges energy but not matter with its surroundings.
    - Isolated System: Does not exchange matter or energy with its surroundings.

Visual Modeling

• Construct a visual model (system map) that uses arrows to represent the direction and type of energy flow across a boundary.

Energy Definitions

• Kinetic Energy (KE): A property of a system related to the motion of an object.
    - Formula: $KE = rac{1}{2}mv^2$

• Potential Energy (PE): A property of a system related to the relative positions of objects interacting through a field (specifically gravity).
    - Formula: $PE = mgh$

Total Mechanical Energy

• Use computational simulations (like PhET) to provide evidence that the total energy in a frictionless system (Total Mechanical Energy, TME) remains constant:
    - $TME = KE + PE$

Energy Calculations

• Calculate Gravitational Potential Energy (GPE) using $mgh$ and Kinetic Energy (KE) using $rac{1}{2}mv^2$ with correct SI units:
    - Energy Unit: Joules (J)
    - Mass Unit: Kilograms (kg)
    - Velocity Unit: Meters per second (m/s)

• Mathematically derive a prediction for an unknown variable (such as final velocity) by setting initial energy equal to final energy:
    - Principle: Initial Energy = Final Energy

Real-World Applications

• Analyze experimental data to explain why "real-world" results often deviate from theoretical mathematical models due to energy transfers to the surroundings (e.g., friction, air resistance).

Temperature and Kinetic Energy

• Relate the temperature of a gas to the average kinetic energy of its molecules:
    - Formula: $KE = rac{1}{2}mv^2$

• Visualize how a distribution of speeds exists within a substance, even at a constant temperature.

• Predict the change in particle collision frequency and force when thermal energy is added to a closed container.

Particle Motion

• Contrast the motion of particles in solids, liquids, and gases at the same temperature:
    - Solids: Particles vibrate in fixed positions.
    - Liquids: Particles move past one another with more freedom.
    - Gases: Particles move freely and rapidly.

• Explain that thermal energy always flows from a higher temperature object to a lower temperature object until equilibrium is reached.

Conservation of Energy

• Apply the Law of Conservation of Energy to show that energy lost by one substance is gained by another:
    - Equation: $Q_{lost} = Q_{gained}$

• Calculate the theoretical final temperature of a mixture using the method of mixtures:
    - Method: Heat gained = Heat lost

Equilibrium and Specific Heat Capacity

• Identify the point of equilibrium on a temperature-vs-time graph.

• Define Specific Heat Capacity as the energy required to raise 1 kg of a substance by 1°C:
    - Formula: $c = rac{Q}{m imes riangle T}$

• Execute a calorimetry experiment to find the unknown specific heat of a metal.

• Graph processed data from the specific heat capacity investigation.

% Error and R² Value

• Calculate the percentage error and relate it to the validity of the investigation:
    - Formula: $Percentage ext{ error} = rac{| ext{Theoretical} - ext{Experimental}|}{ ext{Theoretical}} imes 100$

• Consider the R² value to determine the reliability of the data collected in a scientific investigation.

Rearranging Equations

• Rearrange the equation $Q = mc riangle T$ to solve for any variable:
    - Rearranged forms include:
      - $c = rac{Q}{m imes riangle T}$
      - $riangle T = rac{Q}{mc}$

Thermal Conductivity

• Evaluate materials based on their thermal conductivity properties.

Energy Transfer Prototypes

• Design and build a prototype container that minimizes energy transfer via conduction, convection, and radiation.

Work Done

• Define Work Done (W) as the product of a force and the distance moved in the direction of that force:
    - Formula: $W = F imes d$

• Identify Force as a pull or a push measured in Newtons (N) and distinguish it from mass (kg):
    - Units of Force: Newtons (N)
    - Units of Mass: Kilograms (kg)

• Calculate work done in Joules (J) and recognize that no work is done if the distance moved is zero.

Friction and Power

• Identify static friction as a boundary interaction that must be overcome by applying a force to initiate motion.

• Define Power (P) as the work done per unit of time:
    - Formula: $P = rac{W}{t}$

• Calculate power using the units Watts (W):
    - Definition: 1 Watt = 1 Joule per second.

• Relate power to the speed at which a task is completed:
    - More power is required to complete a task faster.

• Identify power as a property of a system's output across a boundary.

Efficiency

• Define Efficiency as the ratio of useful energy output to total energy input:
    - Formula: $ext{Efficiency} = rac{ ext{Useful Output}}{ ext{Total Input}} imes 100$

• Explain that no system is 100% efficient because energy is often transformed into non-useful thermal energy (friction, heat).

Energy Flow

• Analyze energy flow using Sankey Diagrams to visualize "wasted" vs. "useful" energy crossing a boundary.