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posted by  seto ghost on 9/18/2008 9:03:37 PM  |  status: Live  

Find magnitude and direction

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Determine the magnitude and direction of the resultant Fr = F1 +F2 +F3 of the three forces by first finding the resultant F' = F2 + F3 and then forming Fr = F' +F1.
 
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posted by EngAve on 9/19/2008 12:47:53 AM  |  status: Live
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Response Details:
F' = F2 + F3
x-component:
F'x = F2x + F3x = (-20N)(sin20°)+50N = 43.16 N
y-component:
F'y = F2y + F3y = (-20N)(cos20°) + 0N = -18.79 N
 
Fr = F' + F1
x-component:
Frx = F'x + F1x = 43.16N - (30N)(4)/(5) = 43.16N - 24N = 19.16 N
y-component:
Fry = F'y + F1y = -18.79N + (30N)(3)/(5) = -18.79N + 18N = -0.79N
 
Magnitude of Fr:
 
Direction of Fr:
arctan(Fry/Frx)=arctan(-0.79/19.16)=-2.36°
Resultant has a magitude: |Fr| = 19.17 N 
Directed at  2.36°  below the x-axis, (or 357.64° above the x-axis).
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