Newton's second law:

$\overline{){\mathbf{\Sigma}}{\mathbf{F}}{\mathbf{=}}{\mathbf{m}}{\mathbf{a}}}$

Resolving 2D vector components:

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

**(A)**

Consider a standard coordinate system. Positive x points to the right while positive y points upward.

The components of the unknown force are F_{x} and F_{y}.

The figure shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. (A) How hard must you pull on the third rope to keep the knot from moving? (B) In what direction must you pull on the third rope to keep the knot from moving?

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.

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Based on our data, we think this problem is relevant for Professor Neumeister & Lewicki's class at PURDUE.