Work, Energy and Power - Full Chapter Explanation & NCERT Solutions | Class 11 Physics Ch 6 (NCERT)

Work, Energy, and Power: The Scalar Quantities of Mechanics

Work, energy, and power are three closely related concepts that form the backbone of classical mechanics. In everyday language, these words are used loosely, but in physics they carry precise mathematical definitions. This chapter in the CBSE Class 11 Physics syllabus introduces the work-energy theorem as a powerful alternative to Newton's laws for solving problems involving motion, forces, and displacement. The key insight is that energy is always conserved — it changes form but is never created or destroyed — making it one of the most fundamental principles in all of physics.

In physics, work is done when a force acting on an object produces a displacement in the direction of the force. Mathematically, W = F·d·cos θ, where F is the magnitude of the force, d is the magnitude of displacement, and θ is the angle between the force vector and the displacement vector. Work is a scalar quantity measured in joules (J), where 1 joule equals 1 newton-metre. When θ = 0° (force and displacement in the same direction), maximum positive work is done. When θ = 90°, no work is done — for example, a person carrying a heavy suitcase horizontally does no work against gravity because the force (upward) is perpendicular to the displacement (horizontal). When θ = 180°, the work is negative, as in the case of friction opposing motion. The work-energy theorem states that the net work done on an object equals the change in its kinetic energy: Wnet = ½mv² − ½mu² = ΔK. This theorem is extraordinarily powerful because it connects force and displacement directly to speed without requiring detailed knowledge of the path taken or the time involved.

Energy is the capacity to do work. Kinetic energy (K = ½mv²) is the energy of motion — every moving object possesses it. Potential energy is stored energy due to position or configuration. Gravitational potential energy (U = mgh, near the Earth's surface) arises from an object's height above a reference level. Elastic potential energy (U = ½kx²) is stored in a compressed or stretched spring, where k is the spring constant. The law of conservation of mechanical energy states that in the absence of non-conservative forces like friction, the total mechanical energy (K + U) remains constant. A ball thrown upward converts kinetic energy to potential energy as it rises, and back to kinetic energy as it falls — at every point, K + U = constant. When non-conservative forces are present, the work done by them equals the change in mechanical energy. Power (P = W/t) is the rate at which work is done or energy is transferred, measured in watts (W), where 1 watt = 1 joule per second. Collisions provide important applications of energy and momentum conservation. In elastic collisions, both kinetic energy and momentum are conserved. In perfectly inelastic collisions, the colliding bodies stick together and kinetic energy is not conserved (some is converted to heat or deformation), though momentum is always conserved. The coefficient of restitution e = (relative velocity after collision)/(relative velocity before collision) quantifies the elasticity: e = 1 for perfectly elastic and e = 0 for perfectly inelastic collisions.

• Work W = Fd cos θ is positive when force aids motion, negative when it opposes, and zero when perpendicular to displacement.
• The work-energy theorem: net work = change in kinetic energy (Wnet = ΔK), connecting forces directly to speed changes.
• Conservation of energy: K + U = constant when only conservative forces act; potential energy U = mgh (gravity) or U = ½kx² (spring).
• Power P = W/t measures the rate of energy transfer; 1 watt = 1 joule per second.
• Momentum is always conserved in collisions; kinetic energy is conserved only in elastic collisions (e = 1).