# Resolving Forces On A Particle (2D)

Find F and x

Assume that the positive X axis points to the right and the positive Y axis points to the top of your screen.

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Find:

Find F and x

Assume that the positive X axis points to the right and the positive Y axis points to the top of your screen.

Show Solution

To solve this question, we need to utilise our equation of static equilibrium:

[math]\Sigma F = 0[/math]

but before we can do that, we must resolve our forces into their individual X and Y components (we will use our 5N force is simply -5

our 10N force however is [math]\frac{10}{\sqrt{2}} \mathbf i + \frac{10}{\sqrt{2}} \mathbf j[/math]

so: [math]\Sigma F = 0 = -5\mathbf j + 7.1\mathbf i + 7.1\mathbf j + \mathbf F[/math]

[math] \mathbf F = -7.1\mathbf i - 2.1 \mathbf j[/math]

however we were required to find the magnitude and angle of the force:

F = [math]\sqrt{7.1^2 + 2.1^2}[/math] = 7.4

and x = [math]\tan^{-1}\left(\frac{-2.1}{-7.1}\right)[/math] = [math]16.5^\circ + 180^\circ = 196.5^\circ[/math]

(always be careful of which quadrant the angle you are calculating is in)

Previous Question

Force Applied To An Axially Loaded Column

Determine the force applied to an axially loaded column when only geometry and material properties are known.

Force Applied To An Axially Loaded Column

Determine the force applied to an axially loaded column when only geometry and material properties are known.