ARCH-P-09: Work-Energy-Power Conservation (ΔE_p = mgΔh, E_k = ½mv^2) & Resistive Drag Work

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-P-09: Why the 140s Classroom Method Fails Under the 90s Clock

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

Motor heat loss is

(1 - 0.75) \times 20 = 5\text{ kJ}

, leaving

15\text{ kJ}

of mechanical work. Useful GPE gained is

mgh = 1000\times 10\times 1.2 = 12\text{ kJ}

, so ramp friction loses

15 - 12 = 3\text{ kJ}

. Total lost to surroundings is

5 + 3 = 8\text{ kJ}

(~135s).

The Fast ShortcutTarget: 40s (Saves 100s)

Line 1 (Global Energy Box): The

75\%

motor efficiency is a distractor! Everything not stored as

mgh

goes to the surroundings.
**Line 2 (Subtract

mgh

):**

E_{\text{lost,total}} = E_{\text{in}} - mgh = 20\text{ kJ} - 12\text{ kJ} = 8\text{ kJ}

(20s).

Where Students Lose Time: In 17 past UAT-UK questions (7.3% of Physics), candidates lose 100s by omitting initial kinetic energy when the object starts with non-zero speed u. Instead, apply P3 with Maths 1 skill M1.2.

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