A 2WD tractor has a total static weight of $W = 29.43\text{ kN}$ ($3000\text{ kg}$). Its center of gravity is located at a horizontal distance of $x_1 = 1.30\text{ m}$ forward of the rear axle centerline, and the wheelbase is $L = 2.10\text{ m}$. A horizontal drawbar pull $P$ is applied at a hitch height of $h = 0.50\text{ m}$ above ground. Assuming level ground and taking moments about the rear tire-ground contact point, the critical drawbar pull $P_{\text{crit}}$ in $\text{kN}$ that causes front wheel lift-off (tipping limit) is ________ (round off to 2 decimal places).
Answer Key:
76.52
Step-by-Step Solution & Explanation
1. For front wheel lift-off, the dynamic normal reaction on the front wheels drops to zero ($R_f = 0$).
2. Taking moments about the rear wheel ground contact point:
$\Sigma M_{\text{rear}} = 0$
$P_{\text{crit}} \times h = W \times x_1$
$P_{\text{crit}} = \frac{W \times x_1}{h} = \frac{29.43\text{ kN} \times 1.30\text{ m}}{0.50\text{ m}} = \frac{38.259}{0.50} = 76.518\text{ kN} \approx 76.52\text{ kN}$