Friction is the force that opposes motion between surfaces in contact. It's crucial in everyday life, from walking to driving. Understanding friction helps us grasp how objects interact and move in the physical world.

Drag forces are similar to friction but occur in fluids like air or water. They affect everything from falling leaves to speeding cars. Analyzing motion with friction and drag is key to predicting object behavior in real-world situations.

Understanding Friction

Nature and effects of friction

• Friction opposes relative motion between contacting surfaces stems from electromagnetic interactions between surface atoms
• Slows moving objects prevents motion initiation converts kinetic energy to thermal energy
• Acts parallel to contact surfaces opposite motion direction
• Types include sliding friction rolling friction fluid friction (drag)

Static vs kinetic friction

• Static friction acts on stationary objects prevents motion initiation maximum value exceeds kinetic friction varies from zero to maximum
• Kinetic friction acts on moving objects opposes motion direction generally constant for given surface pair always less than maximum static friction

Calculation of friction force

• General friction force formula: $F_f = \mu F_n$ ($F_f$ friction force $\mu$ friction coefficient $F_n$ normal force)
• Static friction formula: $F_s \leq \mu_s F_n$ ($F_s$ static friction force $\mu_s$ static friction coefficient)
• Kinetic friction formula: $F_k = \mu_k F_n$ ($F_k$ kinetic friction force $\mu_k$ kinetic friction coefficient)
• Friction coefficient dimensionless depends on surface nature typically $\mu_s > \mu_k$ for same surfaces

Drag Forces and Motion Analysis

Concept of drag force

• Resistive force exerted by fluids on moving objects
• Affected by fluid density object's cross-sectional area drag coefficient (shape-dependent) relative velocity
• Low velocities: $F_d \propto v$ high velocities: $F_d \propto v^2$
• General equation: $F_d = \frac{1}{2} \rho C_d A v^2$ ($\rho$ fluid density $C_d$ drag coefficient $A$ cross-sectional area $v$ velocity)

Motion under friction and drag

• Free-body diagrams include friction and drag forces determine net force
• Newton's Second Law $\Sigma F = ma$ solves for acceleration
• Horizontal motion: Net force = Applied force - Friction force
• Objects falling through fluids: Net force = Weight - Drag force
• Terminal velocity reached when drag equals weight results in zero net force constant velocity
• Friction and drag dissipate mechanical energy work done by friction: $W = F_f d$
• Applications include vehicle brakes (disc brakes) parachutes (skydiving) lubrication (engine oil)