NCERT Solutions for Class 11 Physics Chapter 6 – Work, Energy, and Power
Complete solutions with kinetic energy, potential energy, work-energy theorem, collisions, and free PDF for Chapter 6.
About Chapter 6 – Work, Energy, and Power
Chapter 6, Work, Energy, and Power, introduces three of the most central concepts in all of physics. These concepts provide an alternative and often more powerful approach to solving mechanics problems than Newton's laws alone. The chapter begins by defining work in a precise scientific sense: work is done when a force causes displacement, and is calculated as W = F · d cosθ. Students learn that work is a scalar quantity and can be positive, negative, or zero depending on the angle between force and displacement.
The concept of kinetic energy (energy of motion, KE = ½mv²) and potential energy (energy stored due to position, PE = mgh for gravity; PE = ½kx² for springs) are rigorously defined. The pivotal Work-Energy Theorem states that the net work done on an object equals the change in its kinetic energy, providing a scalar alternative to vector-based force analysis. Students also encounter the principle of conservation of mechanical energy – in a system with only conservative forces, total mechanical energy (KE + PE) remains constant.
The chapter also covers power (rate of doing work, P = W/t = Fv), different types of energy, and an in-depth analysis of elastic and inelastic collisions in one and two dimensions. Collisions are particularly important for board and competitive exams. For CBSE students, the work-energy theorem and energy conservation principle are frequently tested. JEE aspirants must master variable force work calculations using integration, and the coefficient of restitution in collision problems, which are regularly asked in entrance examinations.
NCERT Solutions for Class 11 Physics Chapter 6 – Free PDF Download
NCERT Solutions – Chapter 6: Work, Energy, and Power (All Exercises)
Download solved PDF with all exercises: work done by constant and variable forces, energy conservation problems, collision numericals.
Important Formulas – Chapter 6: Work, Energy, and Power
| Concept | Formula | Description |
|---|---|---|
| Work Done (constant force) | W = F d cosθ = F⃗ · d⃗ | θ = angle between force and displacement vectors |
| Work Done (variable force) | W = ∫F dx | Area under F-x graph |
| Kinetic Energy | KE = ½mv² | Energy due to motion; always positive |
| Work-Energy Theorem | W_net = ΔKE = ½mv² − ½mu² | Net work done = change in kinetic energy |
| Gravitational PE | U = mgh | Potential energy at height h; reference at h = 0 |
| Spring (Elastic) PE | U = ½kx² | k = spring constant; x = compression/extension |
| Conservation of Mechanical Energy | KE + PE = constant | Valid only for conservative forces (no friction) |
| Power | P = W/t = F·v cosθ | Rate of doing work; unit = Watt (W) |
| Elastic Collision (1D) – velocities | v₁ = (m₁−m₂)u₁/(m₁+m₂) + 2m₂u₂/(m₁+m₂) | Both KE and momentum conserved |
| Perfectly Inelastic Collision | v = (m₁u₁ + m₂u₂)/(m₁+m₂) | Bodies stick together; only momentum conserved |
| Loss in KE (inelastic) | ΔKE = ½μ(u₁−u₂)² | μ = m₁m₂/(m₁+m₂) is reduced mass |
| Coefficient of Restitution | e = (v₂−v₁)/(u₁−u₂) | e = 1 (elastic), e = 0 (perfectly inelastic) |
Subtopics of Chapter 6 – Work, Energy, and Power
6.1 The Concept of Work
Scientific definition of work. W = Fd cosθ. Work is zero if force ⊥ displacement (e.g., centripetal force) or if there is no displacement.
6.2 Kinetic Energy
KE = ½mv². A moving body can do work. KE is always positive (scalar). It increases with velocity squared, not linearly.
6.3 Work-Energy Theorem
W_net = ΔKE. Powerful tool for problems where force varies with position or when finding speed at a point without knowing time.
6.4 Work Done by a Variable Force
W = ∫F·dx. Graphically, it is the area under the F-x curve. Applied to springs: W = ½kx².
6.5 Potential Energy
Energy stored due to position or configuration. Conservative force → definable PE. F = −dU/dx. Gravity and spring are conservative.
6.6 Conservation of Mechanical Energy
KE + PE = constant for conservative systems. Explains pendulum motion, ball drop, roller coasters.
6.7 Power
P = W/t. Average power = work/time; instantaneous power = F·v. Unit = Watt. 1 horsepower = 746 W.
6.8 Collisions – Elastic and Inelastic
Elastic: both momentum and KE conserved. Inelastic: only momentum conserved. Perfectly inelastic: bodies stick together.
Quick Reference – Types of Collisions Compared
| Type of Collision | Momentum | Kinetic Energy | Example |
|---|---|---|---|
| Elastic Collision | Conserved | Conserved (ΔKE = 0) | Billiard balls, gas molecules |
| Inelastic Collision | Conserved | Not Conserved (ΔKE > 0 lost) | Car crash, ball of clay |
| Perfectly Inelastic | Conserved | Maximum KE lost | Bullet embedding in block |
| Super-elastic Collision | Conserved | KE increases (explosive) | Bomb explosion, spring release |
| Equal mass elastic | Conserved | Conserved | v₁ and v₂ are exchanged |
| Moving body hits stationary (equal mass) | Conserved | Conserved | First body stops; second moves with u₁ |
| Very heavy body hits very light body | Conserved | Conserved | Heavy body barely changes speed; light flies off |
NCERT Solutions for Class 11 Physics Chapter 6: Work, Energy, and Power – FAQs
Work is done when a force causes displacement in the direction of the force. In physics, work depends on force, displacement, and the angle between them. Students often confuse physical work with everyday usage of the term. Understanding this distinction is essential for solving NCERT numerical problems. This concept forms the basis for studying energy and power. Mastery of work calculations helps students understand many physical processes and applications.
The Work-Energy Theorem states that the net work done on an object equals the change in its kinetic energy. This theorem simplifies many problems by avoiding direct use of motion equations. Students frequently apply it in NCERT exercises involving moving objects and varying forces. Understanding the theorem improves conceptual clarity and problem-solving efficiency. It is one of the most important results in mechanics.
Kinetic energy is the energy possessed by an object due to motion, while potential energy is stored because of position or configuration. The chapter explains gravitational and elastic potential energy in detail. Students learn how energy transforms from one form to another. Understanding this relationship helps solve numerical problems and appreciate the principle of conservation of energy. This topic has numerous real-life applications.
Conservation of mechanical energy states that the sum of kinetic and potential energy remains constant when only conservative forces act. This principle is widely used in solving motion problems involving heights, springs, and falling objects. Students often prefer this method because it reduces lengthy calculations. Understanding energy conservation develops analytical skills and provides a deeper understanding of natural processes.
Power is the rate at which work is done or energy is transferred. While work measures the total energy transferred, power indicates how quickly the transfer occurs. Two machines may perform the same work but differ in power. Students encounter numerical questions involving horsepower, efficiency, and energy consumption. Understanding power helps connect physics concepts with practical applications in engines, motors, and electrical devices.