Academia Aeternum
तमसो मा ज्योतिर्गमय
NCERT | Class 11 | Physics
Energy is the currency of the universe. Every process from nuclear reactions to muscle contractions is governed by the principle of energy conservation.
Conceptual Framework
Quick Reference
| Quantity | Formula | Remarks |
|---|---|---|
| Work | \(W = Fd\cos\theta\) | θ = angle between F and d |
| Kinetic Energy | \(KE = \tfrac{1}{2}mv^2\) | Always ≥ 0 |
| Work-Energy Theorem | \(W_{\text{net}} = \Delta KE\) | Net work = ΔKE |
| Spring PE | \(U = \tfrac{1}{2}kx^2\) | x = extension/compression |
| Power | \(P = \vec{F}\cdot\vec{v} = W/t\) | Instantaneous power |
| Elastic Collision (1D) | \(v_1'=\dfrac{(m_1-m_2)u_1+2m_2u_2}{m_1+m_2}\) | Final velocity of m₁ |
| Coefficient of Restitution | \(e = \dfrac{v_2-v_1}{u_1-u_2}\) | e=1 elastic; e=0 perfectly inelastic |
| 1 kWh | \(1\text{ kWh} = 3.6\times10^6\text{ J}\) | Electrical energy unit |
Study Material
Exam-Ready Insights
Work is a scalar. Work done by friction is always negative (force opposite to displacement).
Work done = 0 when: F⊥d (tension in circular motion), d = 0 (static friction on stationary body), or F = 0.
Conservative forces (gravity, spring) have associated PE. Non-conservative forces (friction) dissipate energy as heat.
In elastic collision: kinetic energy is conserved. In inelastic: KE is not conserved (converted to heat, sound, deformation).
At maximum compression in elastic collision on a spring: both bodies have the same velocity (not zero!).
Power = Fv: this form is crucial for problems involving vehicles and engines at constant speed.
Momentum is always conserved in all collisions (elastic, inelastic) if net external force = 0.
Competitive Exams
Work, Energy & Power is tested across all major competitive examinations. Here are the most frequently tested topics:
Jump into the MCQ bank or the True–False quiz to gauge how well you've understood Work, Energy & Power.
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