Overview
This lecture covers the fundamental concepts of Work, Energy, and Power (Chapter 6, Class 11 Physics), including definitions, formulas, types of energies, and the mechanics of collisions, with a focus on key principles and example problems.
Work: Definition & Calculation
- Work is done when a force causes displacement; sitting still does not count as "work" in physics.
- Work is the dot product of force and displacement: W = F · s or W = Fs cos θ.
- Work is a scalar quantity measured in Joules (J = Newton·meter).
- If force and displacement are in the same direction, work is positive; if perpendicular, it's zero; if opposite, it's negative.
- For variable forces, work done is found by integrating: W = ∫ F · dr.
- Area under the Force vs Displacement graph gives work done.
Energy: Types & Properties
- Energy is the capacity to do work; measured in Joules, same as work.
- Types include mechanical (kinetic + potential energy), thermal, solar, wind, nuclear, chemical, electrical, etc.
- Kinetic Energy (KE): Energy of motion, KE = ½mv² or KE = p²/2m.
- Potential Energy (PE): Energy by virtue of position (e.g., gravitational PE = mgh).
- Both KE and PE are scalar, frame-dependent, and always positive.
Work-Energy Theorem & Conservation
- Work done by all forces equals change in kinetic energy: W = ΔKE.
- Derivation for both constant and variable forces links work to kinetic energy change.
- Conservation of Mechanical Energy: In absence of non-conservative forces, total mechanical energy (KE + PE) is constant: KE₁ + PE₁ = KE₂ + PE₂.
Conservative vs Non-Conservative Forces
- Conservative forces: work done is path-independent (e.g., gravity, spring force).
- Non-conservative forces: work done depends on path; energy dissipates (e.g., friction).
- For conservative forces, work done in a closed loop is zero.
Power: Definition & Calculation
- Power is the rate of doing work: P = W/t (average), or P = F · v (instantaneous).
- SI unit is Watt (W), where 1 W = 1 J/s.
- Horsepower is another unit: 1 hp = 746 W.
Collisions: Types & Principles
- Collisions involve impulsive forces and changes in momentum.
- Elastic Collision: Both momentum and kinetic energy are conserved.
- Inelastic Collision: Momentum is conserved, some KE lost.
- Perfectly Inelastic Collision: Objects stick together; maximum KE loss.
- Coefficient of Restitution (e): Ratio of velocity of separation to approach (0 ≤ e ≤ 1), e=1 (elastic), e=0 (perfectly inelastic).
- Principle of Conservation of Linear Momentum (PCLM) applies to all collisions.
Key Terms & Definitions
- Work — Product of force and displacement in the direction of force.
- Kinetic Energy (KE) — Energy due to motion, KE = ½mv².
- Potential Energy (PE) — Stored energy due to position, PE = mgh.
- Dot Product — Scalar product of two vectors: a·b = ab cos θ.
- Conservative Force — Work done independent of path, recoverable energy.
- Non-Conservative Force — Work depends on path, energy dissipated.
- Power — Rate at which work is done, P = W/t.
- Coefficient of Restitution (e) — e = (velocity of separation)/(velocity of approach).
- Momentum — Product of mass and velocity, conserved in collisions.
Action Items / Next Steps
- Complete NCERT example 5.2 and example 8 (work-energy/collisions).
- Answer all posed homework/comment box questions on calculation, concepts, and collision outcomes.
- Review problems on conservative/non-conservative forces and vertical circular motion.
- Practice applying work, energy, power, and collision formulas to new scenarios.