We're asked for the **tension** in each of the wires supporting the bag of cement.

This is a **2D Equilibrium **type of problem with multiple forces in different angles. As usual for equilibrium problems, we'll follow these steps:

- Draw a
**free body diagram**for each point of interest - Set up our
**equilibrium equations** - Solve for the
**target**.

In two dimensions, we use equilibrium equations in component form:

$\overline{){\mathbf{\sum}}{{\mathit{F}}}_{{\mathit{x}}}{\mathbf{=}}{\mathbf{0}}\phantom{\rule{0ex}{0ex}}{\mathbf{\sum}}{{\mathit{F}}}_{{\mathit{y}}}{\mathbf{=}}{\mathbf{0}}}$

Anytime we're working with forces that aren't at 90° angles to each other, we'll also need some of the equations to convert magnitude-angle notation to components.

Magnitude: $\overline{)\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}{\mathbf{=}}\sqrt{{{\mathit{F}}_{\mathit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathit{F}}_{\mathit{y}}}^{\mathbf{2}}}}$

Angle: $\overline{){\mathbf{tan}}{\mathbf{}}{\mathit{\theta}}{\mathbf{=}}\frac{{\mathit{F}}_{\mathit{y}}}{{\mathit{F}}_{\mathit{x}}}}$

Components of a force: $\overline{)\begin{array}{rcl}{\mathit{F}}_{\mathit{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}\mathbf{}\mathbf{cos}\mathbf{}\mathit{\theta}\\ {\mathit{F}}_{\mathit{y}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}\mathbf{}\mathbf{sin}\mathbf{}\mathit{\theta}\end{array}}$

A bag of cement weighing *F _{g}* = 325 N hangs in equilibrium from three wires as shown in the figure. Two of the wires make angles

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the 2D Equilibrium concept. You can view video lessons to learn 2D Equilibrium. Or if you need more 2D Equilibrium practice, you can also practice 2D Equilibrium practice problems.