Object Suspended by Two Strings (Tension Problem)

AI Thread Summary
The discussion revolves around calculating the tensions in two cables supporting an 18 kg object and how these tensions change if one cable is cut. Initially, T1 is calculated as 208 N and T2 as 110 N, with the object's acceleration determined to be 8.31 m/s² when string 2 is cut. A key point of confusion arises regarding the value of T1 after string 2 is cut, with one calculation suggesting it should be 149.6 N, while a friend's input suggests it should be 93.5 N. The conversation emphasizes understanding the implications of different angles on tension values, particularly in extreme cases of 90° and near 0°. Clarifying these concepts is essential for grasping how tension behaves under varying conditions.
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Homework Statement


An object with a mass of 18 kg is suspended from 2 cables as shown in the below diagram. The tensions in the cables are T1 and T2.
a) Draw a free-body diagram for the object. (already solved)
b) Find the tension in both ropes, T1 and T2. (already solved)
c) If string 2 were cut, how would its FBD change at that instant? Sketch a new one. (already solved)
d) What would be the magnitude and direction of the object's acceleration at that instant? (already solved)
e) Would T1 be different in part (b) than in part (d)? If so, what is its new value?

2. Homework Equations

ΣF = max = w sinθ (w is weight)

The Attempt at a Solution


b) T1 = mg/sinθ = (18*9.8)/sin58 = 208 N
T1,x = T2 = T1cosθ = 208 (cos58) = 110 N

d) ax = g⋅sinθ = 9.8 (sin58) = 8.31 m/s2

Now the real question...
e) Yes, T1 = mg⋅sinθ = (18)(9.8)(sin58) = 149.6 N

Friend says that it will be mg⋅cosθ = 93.5 N

Please help out with this question! I know it may be simple but I'm having trouble understanding how T1 changes.
 

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Imagine the extreme case of 90° or an angle very close to 0°. What do the two different results give, and which one is realistic?
 
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