#
**Problem**: Two snowcats in Antarctica are towing a housing unit to a new location, as shown in the figure. The sum of the forces FA and FB exerted on the unit by the horizontal cables is parallel to the line L, and FA = 4600 N .(a) Determine FB.(b) Determine the magnitude of FA + FB.

###### FREE Expert Solution

###### FREE Expert Solution

We're asked to determine **F**_{B} and the **magnitude** of the sum of the two forces.

This problem involves __2D Horizontal Forces__. Like with any forces problems, we'll follow the same series of steps:

- Draw a
**free body diagram (FBD)**, making sure to include and label coordinate axes - Set up Newton's Second Law equation (
**∑***F*=)**ma** **Solve**for the target variable

The equations to convert between components and magnitude-angle notation will always be useful when we're dealing with forces at different angles

Calculating components:

$\overline{)\begin{array}{rcl}{\mathit{F}}_{\mathit{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathbf{}\mathit{\theta}\\ {\mathit{F}}_{\mathit{y}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{\theta}\end{array}}$

Looking at the nature of our problem, these equations will be:

$\overline{)\begin{array}{rcl}{\mathbf{F}}_{\mathit{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{F}}\mathbf{\right|}\mathbf{sin}\mathbf{}\mathbf{\theta}\\ {{\mathbf{F}}}_{{\mathbf{y}}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{F}}\mathbf{\right|}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{}}{\mathbf{\theta}}\end{array}}$

This is because for the **x-direction**, we have **opposite** and **hypotenuse** and for **y-direction**, we have **adjacent** and **hypotenuse** to the angles.

Calculating magnitude:

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

**Step 1:** Draw a free body diagram (FBD)

We'll simplify our problem by presenting it in an FBD.

We'll use a **standard **coordinate system where forces to the **right** will be considered to be in positive **x-direction** and forces **upwards** will be in the positive **y-direction**.

Remember, **F _{Ax} **is towards the left, hence negative (

**- F**

_{Ax})

###### Problem Details

Two snowcats in Antarctica are towing a housing unit to a new location, as shown in the figure. The sum of the forces **F**_{A} and **F**_{B} exerted on the unit by the horizontal cables is parallel to the line L, and F_{A }= 4600 N .

**(a) **Determine F_{B}.**(b) **Determine the magnitude of **F**_{A} + **F**_{B}.

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 Forces in 2D concept. You can view video lessons to learn Forces in 2D Or if you need more Forces in 2D practice, you can also practice Forces in 2D practice problems .

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Jerousek's class at UCF.