Statics problem. Determine Magnitudes. Vector sum = 0?

Question

http://i322.photobucket.com/albums/nn403/staticsproblems/251.jpg

I need help solving this problem. i need the magnitudes of Fa and Fg.

Thanks

Answer 1

Break each vector down to X and Y component, set sum of each to zero.

Fax +  Fbx + Fcx + Fdx + Fex + Fgx = 0

-Fa*cos70 -Fc*cos40 +Fd*cos40 +Fg*cos50 = 0

-Fa*0.633 -16*0.667 +9*0.667 +Fg*0.965 = 0

Fay +  Fby + Fcy + Fdy + Fey  + Fgy = 0

Fa*sin70 -Fb +Fc*sin40 + Fd*sin40 -Fe+Fg*sin50 = 0

Fa*0.774 -20 +16*0.745 + 9*0.745 -20 +Fg*0.262 = 0

now you just have 2 eq with 2 unknowns.

-Fa*0.633 -16*0.667 +9*0.667 +Fg*0.965 = 0

-Fa*0.633 -10.672 +6.003 +Fg*0.965 = 0

-Fa*0.633 +Fg*0.965 -4.669 = 0

Fa*0.774 -20 +16*0.745 + 9*0.745 -20 +Fg*0.262 = 0

Fa*0.774 -40 +11.920 + 6.705  +Fg*0.262 = 0

Fa*0.774  +Fg*0.262 -21.375 = 0

Fa*0.774  = 21.375 - Fg*0.262

Fa = (21.375 - Fg*0.262) / 0.774

Fa = (27.616 - Fg*0.339)

substitute

- (27.616 - Fg*0.339)*0.633 +Fg*0.965 -4.669 = 0

- 0.224*Fg - 17.48 + Fg*0.965 - 4.669 = 0

Fg*0.741 = 22.15

Fg = 29.89

Fa = 27.616 - Fg*0.339

Fa = 27.616 - 29.89*0.339

Fa = 17.48

but check my arith...

Answer 2

Hey man, no problem

first we sum the forces in the x-axis direction.  THis is how:

FaCos70 + 16Cos40 - 9Cos40 - FgCos50 = 0  

This leads to:

FaCos70 - FgCos50 = -5.36

Then we sum forces in the y-axis direction.  THis is how:

FaSin70 + 16Sin40 + 9Sin40 + FgSin50 - 40 = 0

This leads to:

FaSin70 + FgSin50 = 23.93

We now have two equations and two unknowns.  We can solve the problem.  First we convert the cosines and sines into numbers and put the two equations together.

We get:

.342Fa - .643Fg = -5.36

.939Fa + .766Fg = 23.93

now we need to eliminate one of the unknowns.  Let us eliminate Fg first.  .643 multiplied by 1.19 is .766.  So if we multiply the top equation by 1.19 then the coefficient of Fg is the same on both equations as shown here:

.407Fa - .766Fg = -6.38

.939Fa + .766Fg = 23.93

if we add the two equations then we get one equation with one unknown.

1.346Fa = 17.55

Thus, Fa = 13kn

Now we substitute 13 into one of our equation in the place of

Fa.  using this we find Fg.  

Fg = 15.3kn

good luck in your statics class!