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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

 

 

 

 

Pulleys

 

 

 

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