A 2WD agricultural tractor has a total static mass of $2500\text{ kg}$ with $35\%$ of its static weight on the front wheels on level ground. The wheelbase is $L = 2.0\text{ m}$. A horizontal drawbar pull of $P = 12\text{ kN}$ is exerted at a hitch height of $h = 0.40\text{ m}$ above the ground. Taking $g = 9.81\text{ m/s}^2$, the dynamic normal reaction on the front wheels ($R_f$) during pulling in $\text{kN}$ is ________ (round off to 2 decimal places).
Answer Key:
6.18
Step-by-Step Solution & Explanation
```
Dynamic Weight Transfer During Pulling:
Static Weight W = 2500 * 9.81 = 24.525 kN
Static Front Weight W_fs = 0.35 * 24.525 = 8.584 kN
Drawbar Pull P = 12 kN at height h = 0.40 m
Wheelbase L = 2.0 m
```
**Step-by-step Calculation:**
1. Static front wheel reaction ($W_{fs}$):
$W = 2500 \times 9.81 = 24525\text{ N} = 24.525\text{ kN}$
$W_{fs} = 0.35 \times 24.525 = 8.58375\text{ kN}$
2. Dynamic weight transfer from front to rear axle ($\Delta W$):
Taking moment about the rear wheel ground contact line:
$\Delta W = \frac{P \times h}{L} = \frac{12\text{ kN} \times 0.40\text{ m}}{2.0\text{ m}} = \frac{4.80}{2.0} = 2.40\text{ kN}$
3. Dynamic normal reaction on front axle ($R_f$):
$R_f = W_{fs} - \Delta W = 8.58375 - 2.40 = 6.18375\text{ kN} \approx 6.18\text{ kN}$