If F_2 (cos(60*)/cos(20*))*sin(20*) + F_2 sin(60*) - 600 = 0, then F_2 = ....

[slow_engineer]

Hey guys

. . . . .\(\displaystyle F_2\, \dfrac{\cos(60^{\circ})}{\cos(20^{\circ})}\, \sin(20^{\circ})\, +\, F_2\, \sin(60^{\circ})\, -\, 600\, =\, 0\)

. . . . . .\(\displaystyle \Rightarrow\)

. . . . .\(\displaystyle F_2\, =\, \dfrac{600}{\cos(60^{\circ})\, \tan(20^{\circ})\, +\, \sin(60^{\circ})}\, =\, 572,5\, N\)

Can someone please explain why this equation is not 2F2=600/(cos60tan20+sin60) ?

 

[Deleted member 4993]

Hey guys

. . . . .\(\displaystyle F_2\, \dfrac{\cos(60^{\circ})}{\cos(20^{\circ})}\, \sin(20^{\circ})\, +\, F_2\, \sin(60^{\circ})\, -\, 600\, =\, 0\)

. . . . . .\(\displaystyle \Rightarrow\)

. . . . .\(\displaystyle F_2\, =\, \dfrac{600}{\cos(60^{\circ})\, \tan(20^{\circ})\, +\, \sin(60^{\circ})}\, =\, 572,5\, N\)

Can someone please explain why this equation is not 2F2=600/(cos60tan20+sin60) ?

I assume you meant:

2F₂ = 600/(cos60tan20+sin60)

If that was true - then:

2F₂ = 600/(cos60tan20+sin60)

2F₂ * (cos60tan20+sin60) = 600 ...... Now distribute 2F₂

2F₂ * cos60tan20 + 2F_{2 *} sin60 = 600

Now you have that extra "2" multiplied - it was not in your original equation!

 

[slow_engineer]

. . . . .\(\displaystyle F_2\, \dfrac{\cos(60^{\circ})}{\cos(20^{\circ})}\, \sin(20^{\circ})\, +\, F_2\, \sin(60^{\circ})\, -\, 600\, =\, 0\)

. . . . . .\(\displaystyle \Rightarrow\)

. . . . .\(\displaystyle F_2\, =\, \dfrac{600}{\cos(60^{\circ})\, \tan(20^{\circ})\, +\, \sin(60^{\circ})}\, =\, 572,5\, N\)

I assume you meant:

2F₂ = 600/(cos60tan20+sin60)

If that was true - then:

2F₂ = 600/(cos60tan20+sin60)

2F₂ * (cos60tan20+sin60) = 600 ...... Now distribute 2F₂

2F₂ * cos60tan20 + 2F_{2 *} sin60 = 600

Now you have that extra "2" multiplied - it was not in your original equation!

Thank you for your reply, but I don't follow. Maybe I explained my question poorly. If you take a look at the attachment, the answer has F not 2F, and I don't understand how they got rid of that one F.

 

[mmm4444bot]

Can someone please explain why this equation is not 2F₂=600/(cos60tan20+sin60) ?

How did you get 2*F₂? Given:

F₂ * cos(60°)*sin(20°)/cos(20°) + F₂ * sin(60°) - 600 = 0

After adding 600 to each side, factor out F₂ on the left-hand side:

F₂ * [cos(60°)*tan(20°) + sin(60°)] = 600

Divide, to finish. :cool: