problem 3.7 - 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 $M$ of two equal and opposite parallel forces $F$ separated by a perpendicular distance $d$ is given by $M = F\times d$.

Step2: Calculate moment about point A

The perpendicular distance between the two 50 - N forces from point A is $d_A=1 + 2+1.5=4.5$ m. Using the formula $M = F\times d$, with $F = 50$ N and $d = d_A$, we have $M_A=50\times4.5 = 225$ N·m.

Step3: Calculate moment about point B

The perpendicular distance between the two 50 - N forces from point B is $d_B=1.5$ m. Using the formula $M = F\times d$, with $F = 50$ N and $d = d_B$, we get $M_B=50\times1.5 = 75$ N·m.

Step4: Calculate moment about point C

The perpendicular distance between the two 50 - N forces from point C is $d_C=2 + 1=3$ m. Using the formula $M = F\times d$, with $F = 50$ N and $d = d_C$, we obtain $M_C=50\times3 = 150$ N·m.

Answer:

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