Physics Final Exam Review Notes

DISPLACEMENT

• Displacement is a vector quantity that refers to an object's change in position.
• Represents the shortest distance from the initial to the final position.

MOTION AND MOTION GRAPHS

• Velocity is defined as:
  \text{velocity} = \frac{\text{displacement}}{\text{time}}
• The slope of a displacement-time graph indicates the velocity of the object.

2-D MOTION (PROJECTILES)

• For projectile motion:
  • Horizontal acceleration (11_x) is: \text{a}_x = 0 \, \text{m/s}^2
  • Vertical acceleration (55_y) is: \text{a}_y = -9.8 \, \text{m/s}^2
• Equations for projectile motion:
  • Ax = V{0x}t
  • Ay = V{0y}t + \frac{1}{2}a_y t^2
  • Vy^2 = V{0y}^2 + 2ay(Ay)

FORCES

• In a free-body diagram, all forces acting on an object are represented as vectors with their respective magnitudes and directions.
• Equations of motion involving forces:
  • When on an inclined plane:
    F = uF_n
  • Normal force: F_n = m \cdot g \cos(\theta)

UNIVERSAL GRAVITATION

• All objects attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = G \cdot \frac{m1 m2}{r^2}
  • Where G = 6.67 \times 10^{-11} \, \text{m}^2/\text{kg}^2

WORK AND ENERGY

• Work is calculated as:
  W = \text{FORCE} \times \text{DISPLACEMENT}
• Gravitational potential energy:
  U_g = mgh
• Kinetic energy:
  KE = \frac{1}{2}mv^2
• Conservation of mechanical energy states:
  U{initial} + K{initial} = U{final} + K{final}

MOMENTUM

• Momentum (p) is defined as:
  p = mv \quad \text{(mass times velocity)}
• Conservation of momentum:
  P{initial} = P{final}
• Two types of collisions:
  • Elastic: Both momentum and kinetic energy are conserved.
  • Inelastic: Only momentum is conserved; kinetic energy is not.

Buoyancy

• Buoyant force is the upward force exerted by a fluid, given by
  Fb = \text{fluid density} \cdot g \cdot V{displaced}

WAVES AND SOUND

• The speed of a wave on a string is given by:
  V = \sqrt{\frac{F}{\mu}}
  Where F is tension and \mu is linear mass density.
• Sound intensity and decibels relate as follows:
  B = 10 \log{10}(\frac{I}{I0})
• Where I_0 = 1 \times 10^{-12} \text{W/m}^2

THERMODYNAMICS

• Heat transfer during a process is represented by:
  Q = m \cdot c \cdot \Delta T
• Ideal gas law represented as:
  PV = nRT
• Thermodynamic efficiency: e = \frac{W{output}}{Q{input}}
  • Where TC is the cold temperature and TH is the hot temperature.
• Work done by gas in thermodynamic processes is calculated as:
  W = P \Delta V