Discussion
A two wheel drive tractor, weighing 15.84 kN with a wheel base of 2160 mm, has the static weight divided between the front and rear axles in the ratio of 30 : 70 on a horizontal level surface. The hitch point is at a height of 700 mm from the ground and at a horizontal distance of 120 mm to the rear side from the center of the rear axle. Pull acts at an angle of 12° downwards from the horizontal. The maximum pull in kN, when the front wheels would just start rising from the ground is
Answer: B
The maximum pull is about 14.46 kN.
The front wheels lift when the moment of the pull about the rear wheel contact point equals the restoring moment of the weight. The centre of gravity lies 0.30 × 2160 = 648 mm ahead of the rear axle. The pull acts 12° below the horizontal: its horizontal part acts at the hitch height of 0.70 m, and its downward part acts 0.12 m behind the rear axle, so both tend to tip the tractor backwards:
\[ \begin{aligned} P(0.70\cos 12^{\circ} + 0.12\sin 12^{\circ}) &= 15.84 \times 0.648 \\ P(0.6847 + 0.0249) &= 10.264 \\ P &= 10.264 / 0.7097 \\ &= 14.46\ \text{kN} \end{aligned} \]
1.48 kN is far too small to lift the front of a 15.84 kN tractor through a 0.7 m hitch, and 39.04 or 85.54 kN are several times the tractor's own weight. Note that the downward component helps tip the tractor here only because the hitch is behind the rear axle.
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