Object Suspended by Two Strings (Tension Problem)

In summary, given an object with a mass of 18 kg suspended from two cables, with tensions T1 and T2, the tension in both ropes can be calculated using the equations T1 = mg/sinθ and T2 = T1cosθ. If string 2 is cut, the free-body diagram for the object will change and its acceleration will be 8.31 m/s2 in the x direction. In part (e), T1 will be different from its value in part (b), with the new value being mg⋅sinθ, or 149.6 N. This is in contrast to the friend's suggestion of mg⋅cosθ, which would result in a tension of 93
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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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1. What is the tension in the strings holding the object?

The tension in each string is equal and is determined by the weight of the object and the angle at which the strings are attached.

2. Can the tension in the strings be negative?

No, the tension in the strings can only be positive as it represents the force acting to hold the object in place.

3. How do changes in the angle affect the tension in the strings?

As the angle between the strings and the object changes, the tension in the strings also changes. A smaller angle will result in a greater tension in the strings, while a larger angle will result in a lower tension.

4. What happens to the tension in one string if the other string is cut?

If one string is cut, the tension in the remaining string will increase to support the weight of the object.

5. How does the weight of the object affect the tension in the strings?

The weight of the object directly affects the tension in the strings. A heavier object will require a greater tension in the strings to hold it in place.

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