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Physics · Unit 3

Work and Energy: MDCAT Notes and MCQs

Work

  • W = F · d = Fd cos θ (scalar; joule = N m). Positive (θ < 90°), zero (θ = 90°, e.g. centripetal force, carrying a bag horizontally), negative (θ > 90°, friction).
  • Work done = area under force–displacement graph. Work by gravity is independent of path (conservative force); work against friction depends on path.

Energy

  • Energy = ability to do work (joule). 1 eV = 1.6 × 10−19 J; 1 kWh = 3.6 × 106 J.
  • Kinetic energy KE = ½mv² = p²/2m. Doubling speed → 4 × KE. Work–energy theorem: net work = ΔKE.
  • Potential energy: energy due to position/configuration (elastic PE = ½kx², electric PE…). Gravitational PE is the special case due to gravity: PE = mgh near the earth's surface.
  • GPE is measured from a chosen reference level: positive above it, negative below it. Absolute PE takes infinity as zero: U = −GMm/r (always negative — bound system).

Power

  • P = W/t = F · v (watt = J/s). 1 horsepower = 746 W.

Friction & efficiency

  • Body sliding down a rough incline: mgh = ½mv² + fh — work against friction is dissipated as heat to the environment.
  • Efficiency = (useful output / total input) × 100% — always < 100% in real devices (losses as heat, sound, friction). Implications: wasted fuel/cost, heating of machines (need cooling, lubrication), pollution; improved by lubrication, streamlining, insulation.
PMDC learning outcomes for this unit
  • Work, energy, power: 3.1 Describe the concept of work in terms of the product of force F and displacement d in the direction of force
  • Work, energy, power: 3.2 Describe energy
  • Work, energy, power: 3.3 Explain kinetic energy
  • Work, energy, power: 3.4 Explain the difference between potential energy and gravitational potential energy.
  • Work, energy, power: 3.5 Describe that gravitational potential energy is measured from a reference level and can be positive or negative.
  • Work, energy, power: 3.6 Express power as scalar product of force and velocity.
  • Work, energy, power: 3.7 Explain that work done against friction is dissipated as heat in the environment.
  • Work, energy, power: 3.8 State the implications of energy losses in practical devices

Work and Energy MCQs with answers

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Q1
No work is done when the angle between force and displacement is:
A45°
B90°
C180°
D0°
Show answer
Answer: B (90°). W = Fd cos 90° = 0.
Q2
If the speed of a body is doubled, its kinetic energy becomes:
ADouble
BFour times
CHalf
DSame
Show answer
Answer: B (Four times). KE ∝ v², so it becomes 4 times.
Q3
Power can be expressed as:
AF × d
BF × t
CF · v
Dm × v
Show answer
Answer: C (F · v). P = W/t = F·d/t = F·v.
Q4
Absolute gravitational potential energy of a body at distance r from earth's centre is:
A−GMm/r
BGMm/r
Cmgh
DZero
Show answer
Answer: A (−GMm/r). Taking zero at infinity, U = −GMm/r.
Q5
A body slides down a rough incline from height h. The correct energy equation is:
Amgh = ½mv²
Bmgh = fh
C½mv² = mgh + fh
Dmgh = ½mv² + fh
Show answer
Answer: D (mgh = ½mv² + fh). Part of the PE becomes KE and part is used against friction (heat).
Q6
1 horsepower is equal to:
A550 W
B100 W
C746 W
D1000 W
Show answer
Answer: C (746 W). 1 hp = 746 W.
Q7
A machine has input 500 J and useful output 400 J. Its efficiency is:
A40%
B125%
C20%
D80%
Show answer
Answer: D (80%). Efficiency = 400/500 × 100 = 80%.
Q8
A 2 kg body is raised 5 m. Its gain in PE is (g = 10 m/s²):
A100 J
B50 J
C10 J
D25 J
Show answer
Answer: A (100 J). PE = mgh = 2 × 10 × 5 = 100 J.
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