A 4WD tractor has equal front and rear tread 1.25 m and CG height .85 m. It overturns while turning at 18 km/hour. Neglect tire-friction limitations and find the limiting turning radius in metres, to two decimals.
At incipient lateral overturning, moments about the outer tire-contact line balance: $(mv^2/R)h=mg(t/2)$. Therefore $R=2v^2h/(gt)$. Speed is $18/3.6=5$ m/s, giving $R=2(25)(.85)/(9.81\cdot1.25)=\mathbf{3.47}$ m. This is the geometric overturning threshold; a real tractor may skid first.
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