Work Energy Power
Key Concepts
| # | Concept | Explanation |
|---|---|---|
| 1 | Work (W) | Work is done when a force causes displacement. Scalar quantity, SI unit Joule (J). W = F·s·cosθ |
| 2 | Positive/Negative/Zero Work | θ < 90° → +ve, θ = 90° → 0, θ > 90° → –ve |
| 3 | Kinetic Energy (KE) | Energy possessed by a body due to motion. KE = ½ m v² |
| 4 | Potential Energy (PE) | Energy due to position. PE = mgh (gravitational) |
| 5 | Work–Energy Theorem | Net work = change in KE: Wnet = ΔKE |
| 6 | Power (P) | Rate of doing work. P = W/t; SI unit Watt (1 W = 1 J/s) |
| 7 | Commercial Unit | 1 kWh = 3.6 × 10⁶ J = 1 unit (electric meter) |
| 8 | Conservation Law | Total mechanical energy (KE+PE) remains constant in absence of non-conservative forces |
15 Practice MCQs
1. A 5 kg block is lifted vertically by 2 m. Work done by gravity is (g = 10 m/s²)
A) +100 J B) –100 J C) 0 J D) +50 J **Answer:** B **Solution:** W = –mgh = –5×10×2 = –100 J (force & displacement opposite) **Shortcut:** Gravity always –ve work on lifting; sign comes auto. **Tag:** Work sign convention2. A 2 kW heater runs 30 min. Energy consumed in kWh is
A) 0.5 B) 1 C) 2 D) 60 **Answer:** B **Solution:** E = P×t = 2 kW × 0.5 h = 1 kWh **Shortcut:** kW × h = kWh straight. **Tag:** Commercial unit3. A 0.1 kg stone is thrown upward at 10 m/s. Its KE at highest point is
A) 10 J B) 5 J C) 0 J D) 1 J **Answer:** C **Solution:** v = 0 at top ⇒ KE = 0 **Tag:** KE definition4. Work done by centripetal force in circular motion is
A) mv²/r B) 2πrF C) 0 D) F·r **Answer:** C **Solution:** Force ⊥ displacement ⇒ cos90° = 0 **Shortcut:** Any ⊥ force → zero work. **Tag:** Zero-work cases5. If momentum doubles, KE becomes
A) same B) double C) 3× D) 4× **Answer:** D **Solution:** KE ∝ p² ⇒ 2² = 4× **Shortcut:** p → KE square it. **Tag:** KE–momentum relation6. A 60 W bulb is used 5 h/day. Units consumed in 30 days is
A) 9 B) 18 C) 3 D) 90 **Answer:** A **Solution:** E = 0.06 kW × 5 h × 30 = 9 kWh **Tag:** kWh calculation7. A pump lifts 1000 kg water to 10 m in 5 min. Its power is (g = 10 m/s²)
A) 200 W B) 333 W C) 2 kW D) 3.33 kW **Answer:** B **Solution:** P = mgh/t = 1000×10×10 / 300 s ≈ 333 W **Tag:** Power definition8. A 4 kg body falls from 5 m; find speed just before hitting ground (no air drag)
A) 10 m/s B) 14 m/s C) 20 m/s D) 5 m/s **Answer:** A **Solution:** mgh = ½mv² ⇒ v = √(2gh) = √(2×10×5) = 10 m/s **Shortcut:** v = √(2gh) remember. **Tag:** Energy conservation9. Work done by friction is always
A) positive B) negative C) zero D) constant **Answer:** B **Solution:** Opposes motion ⇒ θ = 180° ⇒ cosθ = –1 **Tag:** Work sign10. A 50 N force acts at 60° to horizontal; moves box 4 m horizontally. Work is
A) 200 J B) 100 J C) 173 J D) 0 **Answer:** C **Solution:** W = F s cosθ = 50×4×cos60° = 50×4×0.5 = 100 J **Shortcut:** cos60° = ½ → halve F·s. **Tag:** Work formula11. 1 hp equals
A) 746 W B) 736 W C) 1000 W D) 1 kW **Answer:** A **Tag:** Power unit12. A 2 kg block slides down smooth incline 5 m long, 3 m high. Speed at bottom is
A) √60 m/s B) 10 m/s C) 5 m/s D) 6 m/s **Answer:** A **Solution:** mgh = ½mv² ⇒ v = √(2gh) = √(2×10×3) = √60 m/s **Tag:** Smooth incline13. A machine does 200 J work in 40 s. Power developed is
A) 5 W B) 8 kW C) 5 kW D) 8000 W **Answer:** A **Tag:** Basic power14. If speed halved, KE becomes
A) ½ B) ¼ C) same D) double **Answer:** B **Shortcut:** KE ∝ v² ⇒ (½)² = ¼ **Tag:** KE dependence15. Which is not a unit of energy?
A) kWh B) eV C) hp D) J **Answer:** C **Tag:** UnitsSpeed Tricks
| Situation | Shortcut | Example |
|---|---|---|
| Free fall final speed | v = √(2gh) | h = 5 m → v = 10 m/s |
| KE from momentum | KE = p²/2m | p = 10 kg·m/s, m = 2 kg → KE = 25 J |
| Work by gravity on incline | Wg = –mgh (only vertical h) | 3 m high → Wg = –m×10×3 |
| kWh to joule | 1 kWh = 3.6 × 10⁶ J | 2 kWh = 7.2 × 10⁶ J |
| Power in hp | 1 hp ≈ 746 W; quick 750 W | 3 hp ≈ 2.2 kW |
Quick Revision
| Point | Detail |
|---|---|
| 1 | Work scalar; unit J; 1 J = 1 N·m |
| 2 | KE can never be negative; minimum 0 |
| 3 | PE reference level arbitrary; only ΔPE matters |
| 4 | Work–energy theorem holds for both conservative & non-conservative forces |
| 5 | Power > 0 when work done in same direction as time flows |
| 6 | 1 W = 1 J/s; 1 kW = 1000 W |
| 7 | In circular motion, tension & weight can do zero work if ⊥ to velocity |
| 8 | Area under P–t graph gives work (energy) |
| 9 | When only gravity acts, total mechanical energy conserved |
| 10 | In exams, always check angle θ between F & s for work sign |
BETA
