Questions
5 questions per paper
Difficulty
Medium-Hard
Importance
Core foundation for all competitive physics
Overview
Work, Energy, and Power form the foundational mechanics pillar for competitive exams, focusing on the scalar relationships between force and displacement. Understanding these concepts is essential for solving complex dynamics problems where vector analysis becomes cumbersome. The core objective is mastering energy transformation and conservation laws which simplify multi-stage physics problems.
Work-Energy Theorem
The Work-Energy theorem bridges the gap between kinetics and force, stating that the total work done by all forces equals the change in kinetic energy. This is a critical shortcut for problems involving variable forces or multiple displacements where kinematic equations fail.
- W_net = ΔK = Kf - Ki
- W = ∫F·dx
- Applicable to both conservative and non-conservative forces
- Work done by static friction can be positive, negative, or zero
- Units: Joules (J) or N·m
Conservation of Mechanical Energy
This principle applies when only conservative forces, such as gravity or spring force, do work on a system. By maintaining the sum of kinetic and potential energy as a constant, students can solve complex orbital or pendulum-based problems without calculating intermediate forces.
- Ei = Ef implies Ki + Ui = Kf + Uf
- U_gravity = mgh
- U_spring = 0.5kx^2
- Only valid if non-conservative work is zero
- Power = dW/dt = F·v
Collisions and Impulse
Collisions are classified based on the conservation of kinetic energy and linear momentum. Mastering the Coefficient of Restitution (e) is essential for predicting post-collision velocities in 1D and 2D elastic, inelastic, and perfectly inelastic scenarios.
- e = (v2 - v1) / (u1 - u2)
- Perfectly elastic: e = 1
- Perfectly inelastic: e = 0 (bodies stick together)
- Linear momentum is always conserved in isolated systems
- Impulse J = ∫Fdt = Δp
Formula Sheet
W = Fs cos(θ)
K = 0.5mv^2
P = F·v
ΔK = W_net
m1u1 + m2u2 = m1v1 + m2v2
e = |v_sep| / |v_app|
F_spring = -kx
Exam Tip
Always check if non-conservative forces like friction are doing work before applying the Conservation of Energy; if they are, use the Work-Energy Theorem instead.
Common Mistakes
- Forgetting to account for the sign of work (positive vs negative) when forces act opposite to displacement.
- Applying the conservation of mechanical energy when non-conservative forces like friction or air resistance are present.
- Confusing the coefficient of restitution (e) definitions and failing to use vector components for oblique collisions.
More Revision Notes
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