A farm tractor has a rear wheel tread width of $1.50\text{ m}$. Its center of gravity is located on the longitudinal centerline at a height of $0.75\text{ m}$ above ground level. The maximum transverse slope angle (in degrees) on which the tractor can stand sideways without overturning laterally is ________ (answer in integer).
Answer Key:
45
Step-by-Step Solution & Explanation
For lateral stability of a 4-wheel vehicle on a side slope, the tipping limit occurs when the line of action of gravity through the center of gravity passes through the lower wheel contact point:
$\tan(\theta_{\text{crit}}) = \frac{\text{Half Tread Width}}{h_{cg}} = \frac{1.50 / 2}{0.75} = \frac{0.75}{0.75} = 1.0$
$\theta_{\text{crit}} = \arctan(1.0) = 45^\circ$