Object Suspended by Two Strings (Tension Problem)

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SUMMARY

The discussion focuses on the tension problem involving an 18 kg mass suspended by two cables, with tensions labeled T1 and T2. The calculated tension in cable T1 is 208 N when both cables are intact, while the tension changes to 149.6 N when one cable is cut. The acceleration of the object at that instant is determined to be 8.31 m/s². The conversation emphasizes the importance of understanding how tension varies with the angle of suspension and the implications of cutting one of the cables.

PREREQUISITES
  • Understanding of free-body diagrams (FBD)
  • Knowledge of Newton's second law (ΣF = ma)
  • Familiarity with trigonometric functions in physics (sine and cosine)
  • Basic principles of tension in cables
NEXT STEPS
  • Study the effects of changing angles on tension in cables
  • Learn about dynamic systems and how forces interact when one component is removed
  • Explore advanced topics in mechanics, such as equilibrium and non-equilibrium states
  • Investigate real-world applications of tension problems in engineering and physics
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for practical examples of tension problems in real-world scenarios.

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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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