Energy Stores & Transfers

• Kinetic Energy ($E_k$): This store is associated with moving objects. Any object with mass $m$ moving at a velocity $v$ possesses energy calculated by the formula $E_k = \frac{1}{2}mv^2$.

• Gravitational Potential Energy ($E_p$): Energy stored due to an object's position in a gravitational field. It depends on the object's mass, the gravitational field strength ($g$), and its height ($h$) above a reference point, expressed as $E_p = mgh$.

• Elastic Potential Energy ($E_e$): Energy stored when an object is stretched or compressed, such as a spring. For a linear elastic material with spring constant $k$ and extension $e$, the energy is $E_e = \frac{1}{2}ke^2$.

• Chemical Energy: Energy stored in the chemical bonds of compounds, such as fuels, food, or batteries. This energy is released during chemical reactions when bonds are broken and reformed.

• Thermal (Internal) Energy: The total kinetic and potential energy of the particles within a substance. As temperature increases, the particles move faster, increasing the thermal store.

• Other Stores: These include Nuclear energy (stored in atomic nuclei), Magnetic energy (stored in interacting magnets), and Electrostatic energy (stored between interacting electric charges).

• Energy Dissipation: In almost every energy transfer, some energy is transferred to 'unwanted' stores, usually the thermal store of the surroundings. This energy is described as 'dissipated' or 'wasted' because it is no longer in a useful form.

• Efficiency Calculation: Efficiency is a measure of how much input energy is successfully transferred to the intended useful store. It is calculated as a ratio or percentage: $\text{Efficiency} = \frac{\text{Useful Output Energy}}{\text{Total Input Energy}}$.

• Improving Efficiency: Systems can be optimized to reduce dissipation. For example, lubrication reduces friction (mechanical dissipation), and insulation reduces thermal energy loss to the environment.

Store vs. Transfer

• Energy Store: A way in which energy is 'kept' or 'held' within a system. It is a state of the system at a specific moment in time.
• Energy Transfer: The process or 'pathway' by which energy moves from one store to another. It describes the change occurring between states.

• Unit Consistency: Always ensure mass is in kilograms (kg), velocity in meters per second (m/s), and height in meters (m). A common exam trap is providing mass in grams or height in centimeters.

• Formula Rearrangement: Practice isolating variables in the kinetic energy formula ($v = \sqrt{\frac{2E_k}{m}}$). Many students forget to take the square root when solving for velocity.

• Conservation Logic: When a problem involves an object falling, assume $E_p$ at the top equals $E_k$ at the bottom (ignoring air resistance). This allows you to set $mgh = \frac{1}{2}mv^2$ and solve for unknown variables like final speed.

• Sanity Checks: Efficiency can never exceed 1.0 (or 100%). If your calculation results in a higher value, you have likely swapped the numerator and denominator.