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
- The drag force (Fdrag) is determined by the formula:
F{drag} = rac{1}{2}Cd
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.