Physics XI - Chapter 06: Work, Energy and Power

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  • Work (W): W = F·s = Fs cosθ (Scalar quantity). SI unit: Joule (J).
  • Energy: Capacity to do work. SI unit: Joule (J).
  • Kinetic Energy (KE): KE = ½mv² (Energy due to motion).
  • Potential Energy (PE): Stored energy.
    • Gravitational PE: U = mgh
    • Elastic PE: U = ½kx² (Spring)
  • Work-Energy Theorem: Work done by net force = Change in kinetic energy (W = ΔKE).
  • Conservative Forces: Work done is path-independent (Gravity, Spring force).
  • Non-conservative Forces: Work done depends on path (Friction, Air resistance).
  • Law of Conservation of Mechanical Energy: Total mechanical energy (KE + PE) remains constant when only conservative forces act.
  • Power (P): Rate of doing work. P = W/t = F·v. SI unit: Watt (W).
  • Important Conversions:
    • 1 Joule = 1 N·m = 1 kg·m²/s²
    • 1 Watt = 1 J/s
    • 1 kWh = 3.6 × 10⁶ J
    • 1 HP ≈ 746 W
  • Spring Force: F = -kx (Hooke's Law). Work done = ½kx².
  • Relation between KE and Momentum: KE = p²/2m, where p = mv.
  • Collisions:
    • Elastic: Both momentum and kinetic energy conserved
    • Inelastic: Only momentum conserved, kinetic energy not conserved
    • Perfectly inelastic: Maximum kinetic energy loss, bodies stick together
  • Variable Force: Work done = ∫F·dx (Area under F-x graph).
  • Potential Energy and Force: F = -dU/dx.
  • Equilibrium:
    • Stable: d²U/dx² > 0 (Minimum PE)
    • Unstable: d²U/dx² < 0 (Maximum PE)
    • Neutral: d²U/dx² = 0
  • Efficiency: η = (Useful output/Total input) × 100%.

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Chapter Summary

This chapter introduces us to the fundamental concepts of Work, Energy, and Power - three interconnected physical quantities that form the basis for understanding energy transformations in physical systems. We begin by defining work as the product of force and displacement in the direction of force, emphasizing that work is a scalar quantity despite involving vectors. The concept of energy as the capacity to do work leads us to explore different forms of energy, primarily kinetic energy (energy of motion) and potential energy (stored energy).

The Work-Energy Theorem provides a powerful link between work and kinetic energy, stating that the work done by the net force equals the change in kinetic energy. We distinguish between conservative forces (like gravity and spring force) where work is path-independent, and non-conservative forces (like friction) where work depends on the path taken. The Law of Conservation of Mechanical Energy emerges as a fundamental principle when only conservative forces act, allowing us to solve complex motion problems efficiently. Power, defined as the rate of doing work, completes the triad and finds practical applications in calculating efficiency of machines and energy consumption.

Mastering this chapter is crucial as it provides the foundation for understanding energy transformations in various physical systems, from simple mechanical devices to complex engineering applications. The concepts learned here are essential for analyzing collisions, spring systems, and energy conservation in diverse scenarios. Remember to carefully identify the forces acting, apply the appropriate energy conservation principles, and pay attention to the conditions under which different theorems and laws are applicable when solving problems.

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