User:Egm3520.s13.Jeandona/Forces on A Plane Surface

Measured Moment:

$$ M_{meas} \mbox{ } = \mbox{ } L \cdot W$$

$$ M_{meas} \mbox{ } = \mbox{ } \frac{250 mm}{1000} \cdot \frac{50 g}{1000} \cdot 9.81 \frac{m}{s^2} \mbox{ } = \mbox{ } 0.12263 \mbox{ } N-m$$

Calculated Moment (fully submerged):

$$ M_{calc} \mbox{ } = \mbox{ } \frac{\gamma B \cos(\theta)}{3} (R_{2}^3-R_{1}^3)- \frac{\gamma B}{2} (R_{2}^2-R_{1}^2)h$$

$$ M_{calc} \mbox{ } = \mbox{ } \frac{(9.81 \frac{kN}{m^3} \cdot 1000) (\frac{75mm}{1000}) \cos(20^{\circ})}{3} ((\frac{200mm}{1000})^3-(\frac{100mm}{1000})^3) $$

$$ - \frac{(9.81 \frac{kN}{m^3} \cdot 1000) (\frac{75mm}{1000})}{2} ((\frac{200mm}{1000})^2 -(\frac{100mm}{1000})^2) \cdot \frac{90mm}{1000} \mbox{ } = \mbox{ } 0.62 \mbox{ } N-m$$

Calculated Moment (partially submerged):

$$ M_{calc} \mbox{ } = \mbox{ } \frac{\gamma B \cos(\theta)}{3} R_{2}^3- \frac{\gamma B R_{2}^2}{2}h + \frac{\gamma B \sec^2(\theta)}{6} h^3 $$

$$ M_{calc} \mbox{ } = \mbox{ } \frac{(9.81 \frac{kN}{m^3} \cdot 1000) (\frac{75mm}{1000}) \cos(20^{\circ})}{3} (\frac{200mm}{1000})^3- \frac{(9.81 \frac{kN}{m^3} \cdot 1000) (\frac{75mm}{1000})}{2} (\frac{200mm}{1000})^2 (\frac{148mm}{1000}) $$

$$ + \frac{(9.81 \frac{kN}{m^3} \cdot 1000) (\frac{75mm}{1000}) \sec^2(20^{\circ})}{6} (\frac{148mm}{1000})^3 \mbox{ } = \mbox{ } 0.116 \mbox{ } N-m $$