Question:
The height of the CG of a 4WD tractor with equal tread (1.25 m) in front and rear is 0.85 m. The tractor overturns during turning at a speed of 18 km.h\(^{-1}\). Neglecting the frictional forces on the tractor wheels, the turning radius is _________ m. (Rounded off to 2 decimal places)
The height of the CG of a 4WD tractor with equal tread (1.25 m) in front and rear is 0.85 m. The tractor overturns during turning at a speed of 18 km.h\(^{-1}\). Neglecting the frictional forces on the tractor wheels, the turning radius is _________ m. (Rounded off to 2 decimal places)
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The turning radius for a tractor can be calculated by considering the speed, the height of the center of gravity, and the tread. Make sure the units are consistent when performing the calculations.
Updated On: Apr 14, 2025
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Solution and Explanation
Given:
Tread width, $b = 1.25$ m
Height of CG, $h = 0.85$ m
Speed, $V = 18$ km/h = $5$ m/s
Acceleration due to gravity, $g = 9.81$ m/s2
Overturning Condition:
Height of CG, $h = 0.85$ m
Speed, $V = 18$ km/h = $5$ m/s
Acceleration due to gravity, $g = 9.81$ m/s2
Overturning Condition:
\[ \frac{V^2}{gR} = \frac{b}{2h} \quad \Rightarrow \quad R = \frac{V^2 \cdot 2h}{g \cdot b} \]
Substitute the values:\[ R = \frac{(5)^2 \cdot 2 \cdot 0.85}{9.81 \cdot 1.25} = \frac{42.5}{12.2625} \approx \boxed{3.47 \, {m}} \]
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