Equilibrium
∑Fy = 0 ∑Fx = 0
Hanging Box - Center of Rope
Find Rope Tension
∑Fy = 0
W - [TcosӨ - TcosӨ] = 0 W - 2TcosӨ = 0
T = W/2cosӨ
Hanging Box - Off center
Ex) A 10. kg box, two ropes at an angle of 45 and 30 degrees. Which rope has more tension?
Rope on the left, more vertical
Find T1 and T2
Not drawn to scale
Not drawn to scale
Box at rest
∑Fy = 0 [T1y + T2y] = mg
T1sin45 + T2sin30 = 100 N [T1sin45 + T2sin30] = 100N
∑Fx = 0
T1x = T2x
T1cos45 = T2cos30 T1 = 1.22T2
T1sin45 + T2sin30 – 100N = 0
[1.22T2]sin45 + T2sin30 – 100. N = 0 .86T2 + .50T2 = 100 N .86T2 + .50T2 = 100 N 1.36 T2 = 100 N T2 = 74 N
T1 = 1.22T2 T1 = 1.22(74 N) T1 = 90 N
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