A 2WD tractor has a total weight $W = 25\text{ kN}$ with a wheelbase $L = 2.0\text{ m}$. The center of gravity is located $0.7\text{ m}$ ahead of the rear axle and $0.8\text{ m}$ above ground level. The tractor is pulling a horizontal drawbar load $P = 10\text{ kN}$ attached at a hitch height of $0.45\text{ m}$ on level ground. The dynamic vertical load on the front wheels is ________ $\text{kN}$ (round off to two decimal places).
Answer Key:
6.50
Step-by-Step Solution & Explanation
Taking moments about the rear wheel ground contact point under static and dynamic equilibrium:
$\sum M_{\text{rear}} = 0$
$R_f \times L + P \times h - W \times x_r = 0$
where:
- $L = 2.0\text{ m}$ (wheelbase)
- $W = 25\text{ kN}$
- $x_r = 0.7\text{ m}$ (distance from rear axle to CG)
- $P = 10\text{ kN}$
- $h = 0.45\text{ m}$ (hitch height)
Substituting values:
$R_f (2.0) + (10)(0.45) - (25)(0.7) = 0$
$2.0 R_f + 4.5 - 17.5 = 0$
$2.0 R_f = 13.0 \implies R_f = 6.5\text{ kN}$
Thus, dynamic load on front wheels $= 6.50\text{ kN}$.