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Physics Study Notes

Rolling Friction

  • Rolling Friction in Wheels
    • A wheel is needed to account for rolling friction conditions.
    • Various coefficients of friction are considered, although no wheels are present in this specific scenario.

Friction Force Overview

  • Static on Kinetic Friction

    • Definition of Friction: Friction is defined as the force that is parallel to the surface during motion.
    • Friction types are generally classified into static and kinetic friction:
    • Static Friction (Fs): This force prevents an object from moving when a force is applied until it exceeds a max limit called static friction maximum (C9s).
    • Kinetic Friction (Fk): Once the object begins to move, only kinetic friction acts, which is generally less than static friction.
  • Example of Motion

    • If a box is being pushed:
    • The force increases until it exceeds C9s (if static, denoted as Fs max).
    • Once the applied force exceeds Fs max, the box will start to move, and kinetic friction takes over.
  • Comparison of Static and Kinetic Friction

    • The value of kinetic friction, represented as Fk, is typically less than static friction maximum, indicated as Fs max:
    • Formulas for Friction Forces:
      • Fs max = C9s * N
      • Fk = C9k * N
      • Where N = normal force
    • Explanation of differences in coefficients:
      • Coefficients C9s (static) is greater than C9k (kinetic).

Fluid Dynamics and Drag Force

  • Motorcycle Example

    • While a motorcycle moves, drag force acts opposite to its direction of motion, which can usually be disregarded in simpler equations.
  • Drag Coefficient:

    • Coefficient of Drag (Cd): A dimensionless number that quantifies drag or resistance of an object in a fluid environment:
    • Example values:
      • Sphere moving through fluid: Cd = 0.5
      • Cylinder oriented in one direction: Cd = 0.8
      • Cylinder oriented in another direction: Cd = 1.1
  • Drag Force Equation:

    • The drag force (Fdrag) is determined by the formula: F{drag} = rac{1}{2}Cd
      ho A v^2
    • Where:
      • Cd = drag coefficient
      • ρ = fluid density
      • A = cross-sectional area of the object
      • v = speed of the object
  • Cross-sectional Area:

    • For different shapes:
    • Sphere: Area = ext{Area}_{circle} = ext{π} r^2
    • Cylinder (orientation):
      • Exposed circle: ext{Area}_{circle} = ext{π} r^2
      • Longitudinal view (height consideration): ext{Area} = 2rl
  • Drag Force Dependence on Speed:

    • As the speed of an object increases, the drag force increases proportionally.

Free Fall and Terminal Velocity

  • Free-Fall Scenario

    • When an object is thrown, the forces acting on the ball include gravitational force (Fg) and drag force (F_drag).
    • Fg acts downward while F_drag acts upward against the ball's motion.
  • Terminal Velocity:

    • Phenomenon occurs when F_drag equals Fg; the object ceases to accelerate and moves at a constant speed.
    • Equation for Terminal Speed:
      F{drag} = Fg
    • Rearranging provides a means to solve for terminal speed (v), involving a square root component due to inclusion of v² in drag calculations.

Newton's Third Law: Action and Reaction

  • Fundamental Concept

    • Every force exerted by one object results in a reaction force of equal magnitude but opposite direction on a second object.
    • Example: Forces on a wall and hand are separate yet need to be considered for motion dynamics.
  • Case Study

    • If a wall does not exert a reaction force on a hand, the hand would have no resistance leading to penetration.
    • Actions of objects are bound by this law, significant in object interactions.

Effect on Motion

  • Objects in Motion:

    • If an object (like a ball) is falling, the negative gravitational acceleration results in a net force reflecting mass and acceleration related through F = ma.
  • Action-Reaction Pair:

    • When considering a ball falling, the gravitational force on the ball (mass of the ball times gravitational acceleration, m_b imes g) matches an equal yet opposite force acting on the Earth, thus confirming Newton's third law in context.
  • Mass Comparisons:

    • The mass of the wall is significantly smaller than the Earth. Therefore, the wall experiences negligible acceleration relative to the mass of the Earth, resulting in almost zero effect.
  • Acceleration Values:

    • When calculated, acceleration values of the Earth due to the mass of a ball can be approximated at 2 imes 10^{-24}, effectively showing the negligible impact.

Problem Solving through Dynamic Forces

  • Understanding Forces on Multiple Objects
    • For a problem where Block A and Block B are in context together: Forces need to be analyzed distinctly per object.
    • Example frameworks:
    • Forces acting on Block A (from multiple sources) versus Block B (single force).
    • Importance of identifying forces to update F_net and understand interactions among objects for continuous or accelerated motion contexts.