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Chapter 4 of 16 · Physics
Work, Energy and Power
Work, Energy and Power averages 2 MCQs per paper — work-energy theorem, conservation of mechanical energy, and power calculations are recurring favourites.
Work, Energy and Power is a Physics chapter on the official PMDC MDCAT 2026 syllabus, contributing roughly 2 MCQs to the 36-MCQ Physics section. Mastering the core concepts below typically secures the full chapter weightage.
Work as a dot product
Work done by a constant force is W = F·d = Fd cos θ, measured in joules (1 J = 1 N·m). Pulling a 10 kg crate 5 m along the floor with a 50 N force at 37° above the horizontal does W = 50·5·cos 37° = 200 J. Force perpendicular to displacement does zero work — this is why centripetal force does no work on a body in uniform circular motion. For a variable force, W = ∫F·dx, the area under the F-x graph.
Kinetic energy and the work-energy theorem
KE = ½mv². The work-energy theorem from HRW Chapter 7 states Wnet = ΔKE. A 2 kg block accelerated from rest to 10 m/s gains KE = ½(2)(100) = 100 J, so the net work done on it is 100 J. This theorem is dimension-independent: it works in any direction and any number of dimensions.
Potential energy and conservation
Gravitational PE near Earth: U = mgh. Elastic PE of a spring: U = ½kx². For conservative forces, total mechanical energy E = KE + PE is conserved. A pendulum of length 1 m released from 60° has h = L(1 − cos 60°) = 0.5 m, so it reaches the bottom with v = √(2gh) = √9.8 ≈ 3.13 m/s. A ball rolling down a frictionless ramp from height h reaches the bottom at the same speed regardless of ramp angle.
Power
Average power P = W/t; instantaneous power P = F·v = Fv cos θ. A 60 kg climber ascending 30 m in 60 s at constant speed develops P = mgh/t = 60·9.8·30/60 = 294 W. A car engine delivering 50 kW at constant 25 m/s exerts a forward force F = P/v = 2000 N. 1 horsepower ≈ 746 W — useful for unit-conversion MCQs.
Energy in collisions and Einstein's mass-energy
In elastic collisions both momentum and KE are conserved; in completely inelastic collisions, the bodies stick and KE loss is maximum (consistent with momentum conservation). Einstein's relation E = mc² (c = 3×10⁸ m/s) connects rest mass to rest energy; 1 kg of mass corresponds to 9×10¹⁶ J. The MDCAT often gives a mass defect of 0.1 amu and asks for the energy released — using 1 amu = 931.5 MeV is the shortcut from FSc Chapter 4 and Serway's modern-physics chapter.
Key Concepts
- Work-energy theorem
- Conservation of energy
- Conservative vs non-conservative forces
- Power
- Efficiency
Worked MCQs
Q1. A 2 kg body has its speed doubled from 5 m/s to 10 m/s. The work done is:
- A. 25 J
- B. 75 J ✓
- C. 50 J
- D. 100 J
Explanation: ΔKE = ½(2)(100 − 25) = 75 J.
Common trap: Computing ½m(v_f − v_i)² = ½(2)(25) = 25 J — the formula uses (v_f² − v_i²), not (v_f − v_i)².
Q2. A spring of constant 200 N/m is compressed 0.10 m. Stored PE is:
- A. 1 J ✓
- B. 2 J
- C. 10 J
- D. 20 J
Explanation: U = ½kx² = ½(200)(0.01) = 1 J.
Common trap: Forgetting the ½ gives 2 J.
Q3. A pump lifts 600 kg of water through 10 m in 1 minute. Its power is (g = 10 m/s²):
- A. 100 W
- B. 600 W
- C. 1000 W ✓
- D. 6000 W
Explanation: P = mgh/t = 600·10·10/60 = 1000 W.
Common trap: Forgetting to convert minutes to seconds — using t = 1 gives 60 kW.
Q4. Centripetal force does how much work on a body in uniform circular motion?
- A. ½mv²
- B. mv²/r
- C. Zero ✓
- D. 2πmv²
Explanation: Centripetal force is perpendicular to velocity, so cos 90° = 0 and W = 0.
Common trap: Confusing centripetal force with the work needed to start circular motion.
Q5. 1 atomic mass unit (1 amu) is equivalent to:
- A. 1.6×10⁻¹⁹ J
- B. 931.5 MeV ✓
- C. 9×10¹⁶ J
- D. 6.626×10⁻³⁴ J
Explanation: Standard conversion 1 amu = 1.66×10⁻²⁷ kg → E = mc² ≈ 931.5 MeV.
Common trap: Picking 1.6×10⁻¹⁹ J — that is the electronic charge in coulombs, not an energy.
Frequently Asked Questions
Is work a vector?
No. Work is the dot product of two vectors and is a scalar quantity measured in joules.
When is mechanical energy not conserved?
When non-conservative forces such as friction or air resistance act, mechanical energy decreases, with the loss appearing as heat or sound.
What is the SI unit of power?
The watt (W), equal to one joule per second.
Can kinetic energy be negative?
No. Mass is positive and v² is non-negative, so KE ≥ 0.
How is E = mc² used in nuclear reactions?
The mass defect Δm between reactants and products gives the released energy ΔE = Δm·c², commonly quoted as Δm (in amu) × 931.5 MeV.
How Work, Energy and Power Is Tested
MDCAT questions on Work, Energy and Power are a mix of recall (definitions, classifications), application (predict outcomes, interpret diagrams), and basic numerical/analytical reasoning. PMDC papers from 2020–2025 emphasized the concepts above; older UHS papers (2008–2019) tested them too, with slight variations in question framing.
Practice
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See the full MDCAT 2026 syllabus or browse all Physics chapters.