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
-
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 convention -
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 unit -
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 definition -
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 cases -
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 relation -
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 calculation -
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 definition -
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 conservation -
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 sign -
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 formula -
1 hp equals A) 746 W
B) 736 W
C) 1000 W
D) 1 kW
Answer: A
Tag: Power unit -
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 incline -
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 power -
If speed halved, KE becomes A) ½
B) ¼
C) same
D) double
Answer: B
Shortcut: KE ∝ v² ⇒ (½)² = ¼
Tag: KE dependence -
Which is not a unit of energy? A) kWh
B) eV
C) hp
D) J
Answer: C
Tag: Units
Speed 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
