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UAT-UK SPEC: P3MODULE: PHYSICSTOPIC ID: ARCH-P-09

Work-Energy-Power Conservation (ΔEₚ = mgΔh, Eₖ = ½mv²) & Resistive Drag Work

Master Work-Energy-Power Conservation (ΔEₚ = mgΔh, Eₖ = ½mv²) & Resistive Drag Work on the ESAT Physics paper. Traditional classroom derivations waste valuable seconds. Using the 2-step Sub-90 invariant elimination method compresses solve time to 40s, saving +100s per question.

Standard Classroom Time
140s
Textbook multi-line derivations bleed exam clock
Sub-90 Target Pace
40s
Comfortably below the 88.8s per-question limit
Time Saved for Review
+100s
Banks clock buffer across 27 questions

2-Step Sub-90 Shortcut Formula

How to eliminate intermediate algebra and solve under 45 seconds.

Launch Interactive Lesson
STEP 1 • SETUP INVARIANT (LINE 1)10–15s
Line 1 (Global Energy Box): The 75%75\% motor efficiency is a distractor! Everything not stored as mghmgh goes to the surroundings.

Establish the structural invariant and eliminate impossible options immediately.

STEP 2 • FAST SOLVE (LINE 2)15–25s
Line 2 (Subtract mghmgh): Elost,total=Ein−mgh=20 kJ−12 kJ=8 kJE_{\text{lost,total}} = E_{\text{in}} - mgh = 20\text{ kJ} - 12\text{ kJ} = 8\text{ kJ} (20s).

Evaluate the simplified expression using integer factoring or unit elimination.

Distractor Trap Forensics

The predictable cognitive traps engineered by examiners into the wrong options.

TRAP #1subsystem_isolation_trap

Equating work against drag to mgh only, ignoring initial kinetic energy (1/2)mu² (e.g. parachutist leaving a moving plane)

Omitting initial kinetic energy when the object starts with non-zero speed u.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #2factor_of_two_or_stoichiometry_trap

Omitting 1/2 in Eₖ = (1/2)mv² or forgetting to square velocity v

Arithmetic slip in kinetic energy evaluation.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #3fence_post_or_domain_trap

Using slope length d instead of vertical height h in ΔGPE = mgh

Multiplying weight mg by inclined ramp distance instead of vertical elevation change.

Sub-90 Fix: Test invariants before expanding equations.

Try 1 Timed Question: Work-Energy-Power Conservation (ΔEₚ = mgΔh, Eₖ = ½mv²) & Resistive Drag Work

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Full Lesson All 15 Questions (ARCH-P-09)
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ARCH-P-09: Work-Energy-Power Conservation (ΔEₚ = mgΔh, Eₖ = ½mv²) & Resistive Drag Work (Sample)Physics
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SUB-90 ZONE (<35S)
0.0s35s Sub-9090s ESAT Budget150s Classroom
Question 1 of 1ARCH-P-09 (6-Card Lesson)Format: Standard 5-Option
1-5Choose•FFlag•SScratchpad•EnterNext
Question 1 of 1 • 90s Target

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