Common Forces in Mechanics

Key Types of Forces

  • Gravitational Force: Acts between objects with mass. Always pulls objects toward Earth (e.g., weight = \(mg\)).
  • Contact Forces: Require physical touch. Examples:
    • Normal Reaction (N): Perpendicular to surfaces in contact.
    • Friction (f): Parallel to surfaces. Opposes relative motion.
    • Tension (T): Force in strings/ropes. Assumed constant if massless.
    • Spring Force: \(F = -kx\) (opposes stretching/compression).

Friction: Static, Kinetic, and Rolling

  • Static Friction (\(f_s\)):
    • Prevents stationary objects from moving.
    • Self-adjusts: \(f_s \leq \mu_s N\) (\(\mu_s\) = coefficient of static friction).
    • Example: A box on a train stays put because static friction matches the train’s acceleration.
  • Kinetic Friction (\(f_k\)):
    • Acts when surfaces slide against each other: \(f_k = \mu_k N\) (\(\mu_k < \mu_s\)).
  • Rolling Friction: Much smaller than sliding friction. Occurs due to temporary deformation (e.g., wheels use ball bearings to reduce it).

Equilibrium and Free-Body Diagrams

  • For equilibrium, net forces in all directions must cancel:
    • Example: At point P with forces \(T_1\), \(T_2\), and 50 N: \[ T_1 \cos\theta = 60\,N \quad \text{(horizontal balance)}, \\ T_1 \sin\theta = 50\,N \quad \text{(vertical balance)}, \\ \tan\theta = \frac{5}{6} \Rightarrow \theta = 40^\circ \]

Important Formulas

  • Maximum static friction: \((f_s)_{\text{max}} = \mu_s N\)
  • Kinetic friction: \(f_k = \mu_k N\)
  • Angle of repose: \(\tan\theta_{\text{max}} = \mu_s\)
  • Spring force: \(F = -kx\)

NEET High-Yield Concepts

  1. Static vs. Kinetic Friction: Know their formulas, coefficients (\(\mu_s > \mu_k\)), and real-world examples (e.g., moving a box).
  2. Equilibrium Conditions: Resolve forces into components and set net force to zero (e.g., tension problems with angles).
  3. Friction in Motion: Calculate acceleration using \(a = \frac{F – f_k}{m}\) or \(a = \mu_s g\) for maximum static cases.
  4. Normal Reaction: Always perpendicular to contact surfaces (e.g., \(N = mg\cos\theta\) on inclined planes).