Work–energy basics, power, kinetic & potential energy, conservative forces, work–energy theorem (JEE Main focus).
1) Work
- Work is done by a force if the point of application undergoes displacement.
- For constant force and displacement:
W = F⃗ · s⃗ = Fs cosθ
- Sign of work:
- W > 0 if 0° ≤ θ < 90°
- W < 0 if 90° < θ ≤ 180°
- W = 0 if θ = 90°
- Work by variable force (along displacement):
W = ∫(s1→s2) F ds
(Area under F–s graph)
- S.I. unit: joule (J)
| Conversion | Value |
|---|---|
| 1 joule | 10⁷ erg |
| 1 erg | 10⁻⁷ joule |
| 1 eV | 1.6 × 10⁻¹⁹ J |
| 1 kWh | 3.6 × 10⁶ J |
2) Power
- Rate of doing work:
P = dW/dt
For a particle: P = F⃗ · v⃗
- Unit: watt (W) = J s⁻¹
- 1 horsepower (hp) = 746 W
- At maximum height of a projectile, instantaneous power delivered by gravity is zero.
3) Energy
- Energy = ability to do work.
- Mechanical energy = Kinetic + Potential
Kinetic energy: K = (1/2) mv²
- Potential energy: energy due to position/configuration (stored work).
4) Conservative vs Non-conservative Forces
- Conservative: work depends only on initial & final positions (path independent). Examples: gravitational, spring, electrostatic.
- Non-conservative: work depends on path. Examples: friction, viscous/drag forces.
- Work by conservative force over a closed path (round trip) = 0.
Work by conservative force: W = −ΔU
In 1D: F(x) = − dU/dx
For x: a → b
Ub − Ua = − ∫(a→b) F(x) dx
5) Types of Potential Energy
- Gravitational potential energy (near Earth):
ΔU = +mgh (raised by height h)
ΔU = −mgh (lowered by height h)
- Elastic potential energy (spring):
U_spring = (1/2) kx²
Work done in stretching/compressing = (1/2) kx²
6) Work–Energy Theorem & Conservation of Mechanical Energy
Net work by all forces: W_net = ΔK = Kf − Ki
- If W_net > 0 ⇒ kinetic energy increases; if W_net < 0 ⇒ kinetic energy decreases.
- If only conservative forces act:
Ki + Ui = Kf + Uf (Mechanical energy conserved)
W_ext + W_nc = (Kf + Uf) − (Ki + Ui)
(change in mechanical energy)
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Last modified: December 14, 2025
