Tension - Physics

[drspacheman]

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This refers to EK physics 1001 #281

A mass is hanging from a string, T3.
T3 is attached to 2 other strings, T1 and T2, which are attached to a ceiling, forming a triangle.
If the angle between the ceiling is 30 degrees for both T1 and T2, and the mass is 100kg, then what is the tension of T1?

The book says the answer is 1000N, but I don't understand this. I thought it would be 500N because it's sharing the weight with T2.

 

[Saint Fu]

Remember that tension always points along the string. That means that the y components of T1 and T2 add up to 1000N (500N each), but they also have an x-component as a result of the 30 deg angle. However, I'm not getting 1000N in T1 (more like 866N).

Edit: nevermind, I just punched numbers in wrong. guy below got it 🙂

 

[circulus vitios]

T3 is pulling straight down with (100 kg)(9.8 m/s^2) of force, or 980 N. T1 and T2 are at equal angles with respect to the ceiling, so they share the vertical component of the load. The vertical component of T2 is therefore 980 N / 2 = 490 N. Use sine to find the tension of T2: sin(30 degrees) = 490 N / T2. T2 is therefore 980 N.

 

[drspacheman]

Makes sense. Thanks to the both of you!