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

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-P-07: Why the 140s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~140s (Blows 90s Clock)

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).

The Fast ShortcutTarget: 35s (Saves 105s)

**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).

Where Students Lose Time: 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.

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