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UAT-UK SPEC: P3MODULE: PHYSICSTOPIC ID: ARCH-P-07

Hooke's Law, Springs in Series (½k) vs. Parallel (2k) & Elastic Potential Energy (½kx²)

Master Hooke's Law, Springs in Series (½k) vs. Parallel (2k) & Elastic Potential Energy (½kx²) on the ESAT Physics paper. Traditional classroom derivations waste valuable seconds. Using the 2-step Sub-90 invariant elimination method compresses solve time to 35s, saving +105s per question.

Standard Classroom Time
140s
Textbook multi-line derivations bleed exam clock
Sub-90 Target Pace
35s
Comfortably below the 88.8s per-question limit
Time Saved for Review
+105s
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 (Compression x=L0−Lx = L_0 - L): x=12−7=5 cm=0.05 mx = 12 - 7 = 5\text{ cm} = 0.05\text{ m} and F=mg=6 NF = mg = 6\text{ N}.

Establish the structural invariant and eliminate impossible options immediately.

STEP 2 • FAST SOLVE (LINE 2)15–25s
Line 2 (Skip kk, Use 12Fx\frac{1}{2}Fx): Ee=12(6)(0.05)=0.15 JE_e = \frac{1}{2}(6)(0.05) = 0.15\text{ J} (25s).

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 #1fence_post_or_domain_trap

Substituting total stretched length L instead of extension x = L - L₀ into F = kx or E = (1/2)kx²

Forgetting to subtract the unstretched natural length L₀.

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

Using 2k for springs in series and k/2 for springs in parallel (confusing with resistor rules)

Applying series/parallel resistor formulas directly instead of stiffness rules (parallel = 2k, series = k/2).

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

Omitting 1/2 in elastic potential energy Eₑ = (1/2)kx² = (1/2)Fx

Calculating work done stretching a spring as F*x instead of average force (1/2)F*x.

Sub-90 Fix: Test invariants before expanding equations.

Try 1 Timed Question: Hooke's Law, Springs in Series (½k) vs. Parallel (2k) & Elastic Potential Energy (½kx²)

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Full Lesson All 15 Questions (ARCH-P-07)
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ARCH-P-07: Hooke's Law, Springs in Series (½k) vs. Parallel (2k) & Elastic Potential Energy (½kx²) (Sample)Physics
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SUB-90 ZONE (<40S)
0.0s40s Sub-9090s ESAT Budget150s Classroom
Question 1 of 1ARCH-P-07 (6-Card Lesson)Format: Standard 5-Option
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