Work, Energy and Power – Class 11 Physics Chapter 5 Notes & NCERT PDF

Introduction

In everyday language "work", "energy" and "power" are used loosely. In physics each has a precise meaning. The chapter first reviews the scalar (dot) product, then defines work, links it to kinetic energy through the work-energy theorem, introduces potential energy and conservation of mechanical energy, and ends with power and collisions.

Key Concepts

5.1.1 The Scalar Product

A·B = A B cos θ — a scalar. It is commutative and distributive; in components A·B = AxBx + AyBy + AzBz. A·B = 0 when the vectors are perpendicular.

5.2 Notions of Work and Kinetic Energy

For constant acceleration, v² − u² = 2 a s; multiplying by m/2 gives ½mv² − ½mu² = F s. The quantity ½ m v² is kinetic energy and F·d is work.

Work-energy theorem: The change in kinetic energy of a particle is equal to the work done on it by the net force.

5.3 Work

W = F·d = F d cos θ. Work is zero if (i) displacement is zero (pushing a wall), (ii) force is zero (a block moving on a frictionless surface), or (iii) force ⟂ displacement (gravity on a body moving horizontally). Work can be positive or negative — friction on a sliding body does negative work. SI unit: joule (1 J = 1 N m); other units: erg (10⁻⁷ J), electron volt (1.6 × 10⁻¹⁹ J), calorie (4.186 J), kilowatt hour (3.6 × 10⁶ J).

5.4 Kinetic Energy

K = ½ m v² — a scalar measure of the work a moving body can do (flowing water turns mills, wind drives windmills). The book's table compares kinetic energies — e.g. a bullet of 50 g at 200 m s⁻¹ has 1000 J.

5.5 Work Done by a Variable Force

W = ∫ F(x) dx from xi to xf — the area under the force–displacement graph.

5.6 Work-Energy Theorem for a Variable Force

Using F = m dv/dt = m v dv/dx, integrating gives Kf − Ki = W — the theorem holds for variable forces too. It is not independent of the second law; it is the second law "integrated" over displacement.

5.7 The Concept of Potential Energy

Potential energy is stored energy of position or configuration. For gravity near the earth, V = m g h. A force is conservative if it can be written as F = −dV/dx, the work it does depends only on initial and final positions (not the path), and work around a closed path is zero. Gravity and spring force are conservative; friction is not.

5.8 Conservation of Mechanical Energy

The total mechanical energy of a system is conserved if the forces doing work on it are conservative.

K + V = constant. A ball released from height H: at the top all energy is m g H, at the ground all is ½mv², so v = √(2gH). If a non-conservative force (friction) also acts, Ki + Vi = Kf + Vf + |work done against friction|.

5.9 Potential Energy of a Spring

Spring force (Hooke's law) F = −k x, k = spring constant. Work stored = ½ k x². An oscillating mass-spring system converts K and V back and forth; at the extreme position energy is all potential, at the mean position all kinetic.

5.10 Power

Power is the time rate of doing work: average P = W/t; instantaneous P = dW/dt = F·v. SI unit watt (1 W = 1 J s⁻¹); 1 horsepower = 746 W. Electricity bills are in kWh (a unit of energy, not power).

5.11 Collisions

Momentum is conserved in all collisions; kinetic energy is conserved only in elastic collisions.

Worked Examples

Formula / Key-Facts Sheet

Exam Focus

Frequent questions: sign of work in given situations (Exercise 5.1-type), work-energy theorem numericals, energy conservation in a pendulum or roller coaster, spring compression, power of a pump or motor, and elastic/inelastic collision numericals (Exercise 5.9–5.12 types).

Key Terms

Common Mistakes