How Do You Calculate the Tension in a Rope Holding a Suspended Box at an Angle?

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To calculate the tension in a rope holding a 2kg box at a 37-degree angle from the vertical, the weight of the box (w = mg) is 19.6 N. The vertical component of the tension must balance this weight, leading to the equation Tsin(37) = 19.6 N. The correct tension is found to be 14.7 N after resolving the components correctly. The initial calculation of 32.5 N was incorrect due to misunderstanding the angle's impact on the vertical force balance. Accurate vector resolution is crucial for determining the correct tension in such scenarios.
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Homework Statement


A 2kg box is suspended to the ceiling using only one rope. A horizontal force keeps the rope at 37 degrees from the vertical. Find the tension of the rope


Homework Equations


w = mg
F = ma


The Attempt at a Solution


my understanding:
http://img507.imageshack.us/img507/8840/diagdd2.jpg
sum of y = Tsin37 - 2*9.8 = 0
T = 32.5 N
the correct answer is 14.7
please help:confused:
 
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37 degrees from the vertical...you show horizontal...
 
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