If the couple moment acting on the pipe has a magnitude of 400 N•m, determine the magnitude F of the vertical force applied to each wrench.

#### Solution:

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The couple moment can be found by taking the cross product between a position vector from A to B and force F.

Let us first express a position vector from A to B. The coordinates of A and B are:

B:(0.3i+0.2j+0k)\,\text{m}

The position vector is:

r_{AB}=\left\{-0.35i-0.2j+0k\right\}

We now need to express from F in Cartesian vector form. Force F is only applied in the z-axis, thus it will only have a k component.

Let us now take the cross product:

M_c=\left\{-0.2F\bold i+0.35F\bold j\right\}

The magnitude of this couple moment is:

(Remember that the question tells us the magnitude of M_c is 400 N•m)

400=\sqrt{(-0.2F)^2+(0.35F)^2}(square both sides)

160000=(-0.2F)^2+(0.35F)^2

160000=0.04F^2+0.1225F^2

160000=0.1625F^2

(divide both sides by 0.1625)

F^2=984615.38(take the square root of both sides)

F=992.28 N

#### Final Answer:

Thank you all he steps where very clear i understand how to approach those kind of questions now

You are very welcome! Best of luck with your studies 🙂