Object Suspended by Two Strings (Tension Problem)

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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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Answers and Replies

  • #2
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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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