A 2WD tractor has a total static weight of $24\text{ kN}$ with $65\%$ of the weight resting on the rear axle on level ground. The wheelbase is $2.0\text{ m}$. A horizontal pull of $8\text{ kN}$ is applied at a drawbar height of $0.45\text{ m}$ above ground. Assuming no rolling resistance on front wheels, the dynamic weight on the front wheels during pulling in $\text{kN}$ is ________ (round off to 2 decimal places).
Answer Key:
6.60
Step-by-Step Solution & Explanation
1. Static front wheel weight $W_{fs}$:
$W_{fs} = (1 - 0.65) \times 24\text{ kN} = 0.35 \times 24 = 8.40\text{ kN}$
2. Dynamic weight transfer from front to rear axle due to horizontal drawbar pull $P$:
$\Delta W = \frac{P \times h}{x_b}$
Where $P = 8\text{ kN}$, drawbar hitch height $h = 0.45\text{ m}$, wheelbase $x_b = 2.0\text{ m}$.
$\Delta W = \frac{8 \times 0.45}{2.0} = \frac{3.60}{2.0} = 1.80\text{ kN}$
3. Dynamic load on front wheels $W_{fd}$:
$W_{fd} = W_{fs} - \Delta W = 8.40 - 1.80 = 6.60\text{ kN}$