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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 (11x) is: \text{a}_x = 0 \, \text{m/s}^2
    • Vertical acceleration (55y) 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