Work, Energy and Power – Complete JEE Revision
This chapter connects force and motion through energy. JEE loves testing signs, reference frames, variable forces, and conservation traps.
1. Work
(a) Work by Constant Force
$W = \vec{F}\cdot\vec{s} = Fs\cos\theta$
Work depends on the component of force along displacement.
- $\theta=0^\circ$ → Maximum work
- $\theta=90^\circ$ → Zero work (centripetal force)
- $\theta=180^\circ$ → Negative work
(b) Variable Force
$W = \int \vec{F}\cdot d\vec{r}$
Work equals area under F–x graph.
2. Special Forces & Work
- Gravity: Conservative → path independent
- Friction: Non-conservative → path dependent
- Normal force: Usually zero work
- Centripetal force: Always zero work
3. Kinetic Energy (KE)
$K = \frac{1}{2}mv^2$
Work–Energy Theorem
Net work done = Change in kinetic energy
$W_{\text{net}} = \Delta K$
Applies even when forces are complicated.
4. Potential Energy (PE)
(a) Gravitational PE (Near Earth)
$U = mgh$
(b) Spring Potential Energy
$U = \frac{1}{2}kx^2$
Valid only within elastic limit.
5. Conservative vs Non-Conservative Forces
| Conservative | Non-Conservative |
|---|---|
| Gravity | Friction |
| PE definable | PE not definable |
| Path independent | Path dependent |
6. Mechanical Energy
$E = K + U$
Law of Conservation of Energy
If only conservative forces act:
$K_i + U_i = K_f + U_f$
7. Power
(a) Average Power
$P_{\text{avg}} = \frac{W}{t}$
(b) Instantaneous Power
$P = \vec{F}\cdot\vec{v}$
Zero when force ⟂ velocity.
9. Impulse & Momentum Connection
$J = \int F\,dt = \Delta p$
Impulse is crucial in short-time collisions and force–time graphs.
10. Work Done by Friction (JEE Favorite)
Horizontal: $W = -\mu mg\,s$
Incline: $W = -\mu mg\cos\theta \cdot s$
Incline: $W = -\mu mg\cos\theta \cdot s$
Negative sign indicates energy dissipation.
11. Stopping Distance & Retardation
$s = \frac{u^2}{2\mu g}$
- Independent of mass
- Derived using work–energy theorem
12. Spring–Block Energy Exchange
Without friction: $\frac{1}{2}mu^2 = \frac{1}{2}kx^2$
With friction: $\frac{1}{2}mu^2 = \frac{1}{2}kx^2 + \mu mgx$
13. Power – Complete View
$P = \frac{dW}{dt} = \vec F \cdot \vec v$
Used heavily in lift, engine, and belt–pulley questions.
14. Force–Potential Energy Relation
$F = -\frac{dU}{dx}$
Slope of $U$–$x$ graph gives force direction and magnitude.
15. Escape Velocity (Energy Approach)
$v_e = \sqrt{\frac{2GM}{R}}$
Final JEE Reality Check
- Energy method fails when friction dominates
- Normal force can do work in accelerating frames
- Always choose reference level wisely
- Graphs hide most traps
8. Classical JEE Traps
- Assuming friction always does negative work
- Forgetting reference level for PE
- Using $mgh$ for large heights
- Ignoring variable force work integration
- Applying energy conservation when friction exists
- Wrong sign in power formula
Exam Insight:
JEE tests whether you choose:
JEE tests whether you choose:
- Newton’s laws
- Work–Energy theorem
- Energy conservation
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