A tractor-drawn tillage implement experiences three mutually perpendicular soil reaction forces: a horizontal longitudinal draft force $F_x = 7.2\text{ kN}$, a lateral horizontal side force $F_y = 2.1\text{ kN}$, and a downward vertical force $F_z = 3.0\text{ kN}$. The magnitude of the total resultant soil force $R$ acting on the implement in $\text{kN}$ is ________ (round off to 2 decimal places).
Answer Key:
8.08
Step-by-Step Solution & Explanation
The total resultant force $R$ acting on the tillage tool is:
$R = \sqrt{F_x^2 + F_y^2 + F_z^2}$
$R = \sqrt{7.2^2 + 2.1^2 + 3.0^2} = \sqrt{51.84 + 4.41 + 9.00} = \sqrt{65.25} \approx 8.0777\text{ kN} \approx 8.08\text{ kN}$