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question

I'm stuck trying to find the resultant of the force system. Here it is said to find the angle θ the resultant manes with the horizontal. But θ here is narked relative to F₂. How do I find the resultant and θ

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  • $\begingroup$ It's asking for the angle of theta for which the resultant is vertical This is just a trigonometry simultaneous equation $\endgroup$ – Jonathan R Swift Mar 3 at 11:48
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In order for the Resultant force to be vertical you only need the sum of the horizontal components of $F_1$ and $F_2$ to be zero

$$F_{1x} - F_{2x} =0 $$ $$F_{1}\cos(70) - F_{2}\cos\theta =0 $$

$$\cos\theta=\frac{F_{1}}{F_{2}}\cos(70) - F_{2} $$

$$\theta=\arccos\left(\frac{F_{1}}{F_{2}}\cos(70) - F_{2}\right) $$

if you substitute you should get $$\theta=50[deg]$$

And the resultant R should be :

$$F_{1y} + F_{2y} =R $$ $$F_{1}\sin(70)+ F_{2}\sin(50) =R $$ $$R \approx 1077 [lb]$$

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  • $\begingroup$ What theory guides add the forces & equating them to zero, since it's not stated that the forces are in equilibrium $\endgroup$ – Opeolluwa Mar 3 at 12:04
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    $\begingroup$ It is stated that the resultant of the two forces is vertical, which indicates that the horizontal portion of the forces is in equilibrium. $\endgroup$ – Jonathan R Swift Mar 3 at 12:05
  • $\begingroup$ The question is about the resultant of the forces. If you are thinking about the reaction from the bracket, then this will be determined by the load. $\endgroup$ – NMech Mar 3 at 12:08
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I don't have time to type this up nicely - thought it would be quicker to write out by hand but in hindsight my handwriting is terrible. Let me know if you can't read anything!

enter image description here

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  • $\begingroup$ There seem to be an error in the resultant R $\endgroup$ – Opeolluwa Mar 3 at 12:12
  • $\begingroup$ You're totally right - I must have mashed the buttons on my calculator weirdly. Hopefully you can work out the correct value from the addition before it! $\endgroup$ – Jonathan R Swift Mar 3 at 12:19
  • $\begingroup$ I have done a quick photoshop update to correct the final value or R! $\endgroup$ – Jonathan R Swift Mar 3 at 12:22
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A problem with meaningful solution must have a key with enough conditions/constraints, that make it soluble. As a problem solver, we need to find/identify the key and the associated conditions/constraints. Sometimes work a problem in the backward manner can be helpful. The steps are as follows:

  1. Expand the unknown (R = ?) to a more detailed expression. That is, in an orthogonal grid system,

R = (Fx^2 + Fy^2)^1/2; in which, Fx = F1cos70 + F2cos(\theta), and Fy = F1sin70 + F2sin(\theta)

  1. Identify/find the key. In this problem, the angle (\theta) is the key, and the statement that says "Determine the angle (\theta) which makes the resultant (R) of the two forces vertical, is the furnished condition/restraint. Laterally the statement tells us to find the angle (\theta) that will result in: sum Fx (horizontal resultant force) = 0, so the relationship can be expressed as,

Fx = F1cos70 + F2cos(\theta) = 0

Now you have the key to solve the problem. Hope this helps.

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