ARCH-P-05: 1D Coupled Multi-Body Resultant Force (F_net = ma), Lifts & Internal Tension

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-P-05: Why the 150s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~150s (Blows 90s Clock)

Apply

F_{\text{net}} = (m_1 + m_2)a

5000 - (600 + 400) = (1200 + 800)a \implies a = \frac{4000}{2000} = 2\text{ m s}^{-2}

. Then isolate the trailer:

T - 400 = 800 \times 2 = 1600 \implies T = 2000\text{ N}

(~135s).

The Fast ShortcutTarget: 40s (Saves 110s)

Line 1 (Proportional Drag Check): Since

\frac{600}{1200} = \frac{400}{800}

, resistive drag is proportional to mass and cancels from the internal tension split!
Line 2 (Mass Fraction):

T = F_{\text{drive}} \times \frac{m_2}{m_1 + m_2} = 5000 \times \frac{800}{2000} = 2000\text{ N}

(25s).

Where Students Lose Time: In 11 past UAT-UK questions (4.72% of Physics), candidates lose 110s by failing to treat the coupled blocks/train as a single system of mass (m₁ + m₂) when finding common acceleration a. Instead, apply P3 with Maths 1 skill M4.4.

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