Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
A farm tractor has a rear wheel tread width (track width) of $1.5\text{ m}$ and its center of gravity is $0.75\text{ m}$ above ground level on flat ground. Calculate the maximum side-slope angle in $\text{degrees}$ that the tractor can negotiate statically before lateral overturn occurs.
Answer Key:
45
Step-by-Step Solution & Explanation
Static lateral overturning occurs when the line of action of gravity falls outside the downhill wheel contact line.
Maximum side slope angle $\theta$ is given by:
$\tan \theta = \frac{T/2}{h_{cg}}$
Where:
- Tread width $T = 1.5\text{ m}$, so $T/2 = 0.75\text{ m}$
- CG height $h_{cg} = 0.75\text{ m}$
$\tan \theta = \frac{0.75}{0.75} = 1.0$
$\theta = \arctan(1.0) = 45.0^\circ$