Definition: Energy is a concept that describes interactions in a system; it is conserved and can neither be created nor destroyed, only transformed (mass-energy equivalence applies only in nuclear physics).
Energy Stores:
Kinetic Energy: Calculated using the formula:
E_k = \frac{1}{2} mv^2
Where:
E_k = kinetic energy (Joules)
m = mass (kg)
v = velocity (m/s)
Gravitational Potential Energy (GPE):
E_{gpe} = mgh
Thermal Energy: Change in thermal energy calculated as:
E = mc\Delta T
Where:
E = change in thermal energy (Joules)
m = mass (kg)
c = specific heat capacity (J/(kg°C))
\Delta T = change in temperature (°C)
Energy Transfer: Energy must be transferred for interactions, observable in closed systems where total energy is conserved. Example: GPE equals Kinetic Energy at different points in a roller coaster.
Power & Efficiency
Power: Rate of energy transfer, calculated using:
P = \frac{E}{T}
Where:
P = power (Watts)
E = energy (Joules)
T = time (seconds)
Efficiency:
\text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}}
Efficiency can be expressed as a ratio or percentage. Example:
If a 200W laptop provides 120W useful energy:
Efficiency:
\text{Efficiency} = \frac{120}{200} = 0.6 \text{ or } 60\%
Definition: Electric current is the flow of charge (usually electrons).
Basic Circuit Components:
Battery: Stores chemical energy, converts to electrical energy in a circuit.
Complete Loop: Necessary for charge to flow, current flows from positive to negative terminal.
Potential Difference (Voltage):
V = \frac{E}{Q}
Where:
V = potential difference (Volts)
E = energy (Joules)
Q = charge (Coulombs)
Current:
I = \frac{Q}{T}
Where:
I = current (Amperes)
Q = charge (Coulombs)
T = time (seconds)
Resistance:
V = IR
Resistance can be measured by rearranging to find R:
R = \frac{V}{I}
Series Circuits:
Current is the same; voltage is shared; total resistance is the sum.
Parallel Circuits:
Voltage is the same; current is shared; total resistance decreases with additional pathways.
Particles and States of Matter
Particle Model:
Density ($\rho$) calculated as:
\rho = \frac{m}{V}
Where:
$\rho$ = density (kg/m³)
m = mass (kg)
V = volume (m³)
States of Matter: Solids, liquids, gases; density related to particle arrangement.
Phase Changes: Occur at constant temperature, involving changes in potential energy while kinetic energy changes during temperature changes.
e.g., Melting or boiling require heat energy despite constant temperature during the phase change.
SLH Equation: E = mL
Compressing Gases: Results in a pressure increase, where pressure and volume are inversely proportional under constant temperature conditions.
P1V1 = P2V2
Atomic Structure
Models of the Atom:
Plum pudding model (JJ Thompson) to nucleus model (Ernest Rutherford) to Bohr model (electron shells).
Isotopes: Atoms of the same element differing in neutron counts.
Radioactivity: Count-rate (activity in BQ = counts per second), and half-lives, where half-life ($t_{1/2}$) is the time taken for half the radioactive nuclei to decay.
Example Calculation:
If starting counts = 96 BQ, dropping to 12 BQ, the number of half-lives is how many times to halve 96: