Work, Energy & Power

Concept overview

Work-energy methods offer an alternative to Newton's-laws force analysis. Instead of computing forces and integrating F = ma, you compute the work done by each force and use energy conservation to relate initial and final states.

Work by a constant force is W = F·d = Fd cosθ, where θ is the angle between force and displacement. For a variable force, W = ∫F·dx. Kinetic energy is ½mv². The work-energy theorem states that the total work done on a body equals its change in kinetic energy: W_net = ΔKE.

Potential energy is defined only for conservative forces — gravity, spring force, electric force. For gravity near Earth's surface, U = mgh. For a spring, U = ½kx². The mechanical energy E = KE + U is conserved when only conservative forces act; friction and other non-conservative forces reduce E by the amount of energy dissipated as heat.

Power is the rate of doing work: P = dW/dt = F·v. Instantaneous power in linear motion is Fv cosθ. This chapter is a favourite for JEE because a well-chosen energy method can bypass three pages of force analysis. Learn to identify when energy conservation is the shorter path.

Key formulas & concepts

• Work (constant force): W = F d cosθ
• Work (variable force): W = ∫ F · dx
• Kinetic energy: KE = ½mv²
• Work-energy theorem: W_net = ΔKE
• Gravitational PE (near Earth): U = mgh
• Spring PE: U = ½kx²
• Power: P = F·v = dW/dt
• Conservation of energy: KE_i + U_i = KE_f + U_f + W_nc

Common mistakes to avoid

• Applying energy conservation when non-conservative forces (friction) act — you must include the dissipated energy or account for W_friction explicitly.
• Using U = mgh at large altitudes where g varies — for Earth-satellite problems, use U = −GMm/r.
• Confusing average power (W/t) with instantaneous power (F·v).
• Forgetting that work done by internal forces of a rigid body is zero — only external forces do net work on the body.

JEE Main relevance

JEE Main asks 1–2 energy problems every paper — usually one work-energy theorem numerical and one power/efficiency question. Spring-block problems are also standard.

JEE Advanced relevance

Advanced problems combine energy methods with rotational motion, spring dynamics or variable-mass systems. Problems asking for the power output of a vehicle climbing a slope with drag are also common.

Previous-year questions (PYQ)

Filter the PYQ bank by 'Work, Energy & Power'. Spring-block and inclined-plane problems dominate the year-to-year archetypes.