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Playbook

Work, Energy and Power

23 q · 9% HARD. KE=½mv², PE=mgh, W=Fd cosθ, P=W/t. Conservation between KE↔PE in free-fall and on inclined planes. Simple Machines (lever class identification) is the recall corner.

questions in the bank
23
tagged HARD
9%
subtopic(s)
4
worked examples
2

When you’ll see it

A KE↔PE conversion in free-fall, a W = F·d·cosθ angle calculation, a constant-power machine v(t), or a Simple Machines lever-class identification.

How this chapter is tested

23 q in 10 years · 9% HARD. The chapter splits four ways: Energy and Conservation (10 q — free fall, inclined plane), Work-Energy Theorem and Power (6 q — P = Fv, constant-P), Work and Work Done (5 q — definition and the cosθ trap), Simple Machines (2 q — lever class identification).

Mechanical energy conservation in a frictionless system: ½mv₀² + mgh₀ = ½mv² + mgh. Equivalently: KE gained = PE lost. The 320-g ball dropped from height h with 625 J of PE problem: v = √(2gh) using mgh = ½mv² ⟹ v = √(2 × 625 / 0.320) = √3906 ≈ 62.5 m/s. Always check units (g in grams vs kg).

Constant-power machine on smooth surface: P = Fv = const. Combined with F = ma = m(dv/dt) gives v dv = (P/m) dt ⟹ v ∝ √t (NOT v ∝ t). This is the recurring HARD shape: 'constant power, find v vs t' — the linear answer is the trap.

The sub-skills

The rules and habits that decide whether you get a question right.

  • Conservation of mechanical energy

    KE + PE = const in frictionless system. ½mv₀² + mgh₀ = ½mv² + mgh. Set the reference point for PE (usually ground = 0). Subtract.

  • Work = F·d·cosθ

    Angle between force and displacement. Perpendicular (θ=90°) ⟹ zero work. Centripetal force on circular motion does zero work; magnetic force on charged particle does zero work.

  • Power forms

    P = W/t (average). P = F·v (instantaneous). For constant power on smooth surface, F decreases as v grows: F = P/v.

  • Simple machine lever classes

    Class 1: fulcrum BETWEEN load and effort (seesaw, crowbar). Class 2: load between fulcrum and effort (wheelbarrow, bottle opener). Class 3: effort between fulcrum and load (tongs, human arm, broom).

2 worked examples from the bank

Real past-year questions illustrating the playbook. Click to reveal options + solution.

Example 1Work, Energy and PowerMODERATE
A constant power machine pulls a block on a smooth horizontal surface. Which one correctly describes the relation between speed (v)(v) and time (t)(t)?

[Q60 · Apr · 2026]

Example 2Work, Energy and PowerMODERATE
A ball of mass 320 g has 625 J potential energy when released from a height. The speed with which it will hit the ground is

[Q97 · Sep · 2024]

Traps to expect

Distractor shapes specific to this chapter. The page-wide Traps section covers the bank-level patterns.

  • Zero work when force perpendicular to motion

    A waiter carrying a tray walks horizontally — gravity is vertical, motion horizontal, so gravity does ZERO work on the tray. Wrong option uses W = mgh = 0 only when h=0; right reasoning uses cos 90° = 0.

  • Constant-power: v ∝ t trap

    If you naively assume constant force from a constant-power machine, you get v ∝ t (constant a). Wrong. P = Fv constant means F decreases as v grows; integrating gives v ∝ √t.

Drill every work, energy and power question

23 questions from the bank, scoped to 4 bundled subtopics.

Drill the 23 questions

Related playbooks

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