Angel Vector
Posted in equipment on 09/10/2010 11:50 pm by adminVectors help, please? I've tried so hard and I can't figure it out. I'll love you forever!?
Niki, Jeanette and Allen are playing a three-way tug-of-war. Three ropes of equal length are tied together. Niki pulls with a force of 210 N, Jeanette pulls with a force of 190 N, and Allen pulls with a force of 200 N. The angels between the ropes are equal.
a) Draw a scale diagram showing the forces on the knot. (I did this part)
b) Determine the magnitude and direction of the resultant force on the knot.
The answer at the back of the book is 17.3 N at a bearing of 30 degrees.
I have no idea how to do it 
. Please please help! I'd appreciate it to no end.
Tysm<3
a)
I'm not sure how your diagram looks exactly. For reference I'll put Niki's rope along the +x-axis.
b)
Get components for all 3 forces.
Niki:
Nx = 210 N
Ny = 0 N
Jeanette:
Jx = 190*cos120˚ = -95 N
Jy = 190*sin120˚ = 164.5 N
Allen:
Ax = 200*cos240˚ = -100 N
Ay = 200*sin240˚ = -173.2 N
Add components together:
Fx = Nx + Jx + Ax
Fx = 210 - 95 - 100 = 15 N
Fy = Ny + Jy + Ay
Fy = 0 + 164.5 - 173.2 = -8.7 N
Find magnitude of force:
F = sqrt[(Fx)^2 + (Fy)^2]
F = sqrt[15^2 + (-8.7)^2]
F = 17.3 N
Find direction of force:
tanθ = Fy/Fx
tanθ = -8.7/15
θ = -30˚ --> This means 30˚ clockwise from Niki's rope.
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