problem 1.9 - given the shown forces acting on a boat. determine the couple moment about a) point a on the…

Explanation:

Step1: Recall couple - moment formula

The couple - moment $\vec{M}=\vec{r}\times\vec{F}$, and for two parallel forces $F_1 = F_2=F$, the magnitude of the couple - moment $M = Fd$, where $d$ is the perpendicular distance between the two forces. Here, $F = 50\ N$.

Step2: Calculate distance for point A

The perpendicular distance between the two 50 - N forces with respect to point A: $d_A=1 + 2+1.5=4.5\ m$. Then the couple - moment about point A, $M_A=Fd_A$. Substituting $F = 50\ N$ and $d_A = 4.5\ m$, we get $M_A=50\times4.5 = 225\ N\cdot m$.

Step3: Calculate distance for point B

The perpendicular distance between the two 50 - N forces with respect to point B: $d_B=1.5\ m$. Then the couple - moment about point B, $M_B=Fd_B$. Substituting $F = 50\ N$ and $d_B = 1.5\ m$, we get $M_B=50\times1.5 = 75\ N\cdot m$.

Step4: Calculate distance for point C

The perpendicular distance between the two 50 - N forces with respect to point C: $d_C=2 + 1=3\ m$. Then the couple - moment about point C, $M_C=Fd_C$. Substituting $F = 50\ N$ and $d_C = 3\ m$, we get $M_C=50\times3 = 150\ N\cdot m$.

Answer:

a) $M_A = 225\ N\cdot m$ b) $M_B = 75\ N\cdot m$ c) $M_C = 150\ N\cdot m$