75-Archetype SyllabusPhysics • ARCH-P-07 • Spec P3

Full 6-Card Lesson 15-Question Timed Drill

UAT-UK SPEC CODE: P3 (Mechanics)ASSUMED MATHS 1 PREREQUISITE: M3.5FREQUENCY: MEDIUM

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

Deconstructed from 5 past UAT-UK questions (2.15% of all historical Physics papers). Students using standard A-Level classroom methods spend an average of 140s on this archetype—blowing past the 90s ESAT budget. Using the 2-line Sub-90 heuristic below compresses solve time to 35s (saving 105s per question).

Historical Frequency

5 Past Qs

2.15% of Physics

Classroom Trap Time

140s

+50s over 90s budget

Sub-90 Target Time

35s

Banks +105s on the clock

Dominant UI Format

5-Option A–E

Maths 1 Skill: M3.5

Card 1 & Card 2 Preview: The Classroom Time Trap vs. Sub-90 2-Line Rule

Excerpted from our interactive 6-Step Topic Lesson for ARCH-P-07.

Launch All 6 Active-Recall Cards

CARD 1 OF 6 • THE CLASSROOM TIME TRAP (140s)

Why Students Bleed Time:

In equilibrium, force

F = mg = 0.60\times 10 = 6\text{ N}

. Compression is

x = (12 - 7)\text{ cm} = 0.05\text{ m}

. Spring constant is

k = \frac{F}{x} = 120\text{ N m}^{-1}

, and

E_e = \frac{1}{2}kx^2 = 0.15\text{ J}

(~120s).

In 5 past UAT-UK questions (2.15% of Physics), candidates lose 105s by forgetting to subtract the unstretched natural length l₀. Instead, apply P3 with Maths 1 skill M3.5.

CARD 2 OF 6 • THE 2-LINE SUB-90 HEURISTIC (<35s)

**Line 1 (Compression

x = L_0 - L

):**

x = 12 - 7 = 5\text{ cm} = 0.05\text{ m}

and

F = mg = 6\text{ N}

**Line 2 (Skip

k

, Use

\frac{1}{2}Fx

):**

E_e = \frac{1}{2}(6)(0.05) = 0.15\text{ J}

(25s).

Sanity & Limit Check: Verify units/signs against fence_post_or_domain_trap (Substituting total stretched length L instead of extension x = L - L₀ into F = kx or E = (1/2)kx²) and sign_or_direction_flip (Using 2k for springs in series and k/2 for springs in parallel (confusing with resistor rules)).

Examiner Distractor Blueprint for ARCH-P-07

FOIL #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.

Open Fence-Post / Domain Trap Clinic

FOIL #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).

Open Sign / Direction Flip Clinic

FOIL #3factor_of_two_or_stoichiometry_trap

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

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

Open Factor-of-2 / Stoichiometry Clinic

FOIL #4subsystem_isolation_trap

Ignoring gravitational potential energy loss mgx when a vertical mass-spring system drops

Equating E_k solely to E_e without including ΔGPE = mgx.

Open Subsystem Isolation Trap Clinic

Try 1 Live Sample Question Under the 90-Second Stopwatch

Press W to open the 2-line dry-wipe scratchpad, select A–E, and lock in to reveal the Dual-View solution.

Full 6-Card Lesson Launch All 15 Questions (ARCH-P-07)

ARCH-P-07: Hooke's Law, Springs in Series (½k) vs. Parallel (2k) & Elastic Potential Energy (½kx^2) (Sample)Physics

00:00.0

SUB-90 ZONE (<35S)

0.0s35s Sub-9090s ESAT Budget150s Classroom

Question 1 of 1ARCH-P-07 (6-Card Lesson)Format: Standard 5-Option

Right-click any option to cross out • Keys A–E + Enter

Question 1 of 1 • 90s Target

Ready to Start Question 1?

The question stem, diagram, and answer options are hidden behind this pre-start gate. When you click below, the question will reveal and your 90-second split stopwatch will immediately begin ticking.

Physics•ARCH-P-07•Standard 5-Option

or press Enter to start