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Calculate the resulting moment

Task

The forces F1 and F2 are located in the x-y plane. Calculate the resulting moment for both forces combined at the origin.

F1 = 20 N, F2 = 30 N

x1 = 1 m, x2 = 2 m, y1 = 1 m, y2 = 2 m

Two forces in the coordinate system
Two forces in the coordinate system

Solution

The following video is in german language.

Technische Mechanik 1, Übung 6 - Resultierendes Moment berechnen

We assume left-turning moments to be positive. The resulting moment is given by:

\[ \require{cancel} \] \[ \newcommand{\myvec}[1]{{\begin{pmatrix}#1\end{pmatrix}}} \]

\[\tag{1} M_0 = F_1 \cdot x_1 -- F_2 \cdot y_1 \]

\[\tag{2} M_0 = 20 N \cdot 1 m -- 30 N \cdot 1 m \]

\[\tag{3} M_0 = -10 N m \]

Annotations

The assumption of the left-turning positive moments results from the right-hand-rules. The z-axis of the coordinate system points to the viewer, this leads to left-oriented positive moments.