Tilting (AQA A-Level Mathematics): Flashcards

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Tilting
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Tilting in mechanics

Occurs when rigid body rotates about edge due to unbalanced moment

Moment (torque) formula

Force×Perpendicular Distance\text{Force} \times \text{Perpendicular Distance}

Centre of mass definition

Point where entire weight of body acts

Tilting condition (line of action)

Resultant force line passes outside base of support

Moment of force FF at height hh

F×hF \times h

Moment of weight for width ww

mg×w2mg \times \frac{w}{2}

Min tilting force formula (hh, ww, mm)

F≥mgw2hF \geq \frac{mgw}{2h}

Min force: 1010 kg, h=0.5h=0.5 m, w=0.3w=0.3 m

29.4 N29.4 \text{ N}

Prevent tilt: lower centre of mass

Reduces height, decreasing tilting moment

Prevent tilt: widen base

Increases stabilising moment

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