Hanging Mass - Answer says that I am wrong

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The discussion revolves around calculating the tension in a rope supporting a 2.0 kg mass in equilibrium. The initial calculation yielded a tension of 38 Newtons for each rope, but the textbook claims it should be 76 Newtons. The discrepancy arises from the interpretation of the angle in the tension formula, where halving the angle leads to incorrect results. The calculations suggest that the textbook may have errors in its presentation, particularly in how the angle was applied in the tension formula. Ultimately, the correct approach should involve using the full angle to accurately determine the tension in the system.
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Homework Statement


The relevant forces are tension in the rope, which acts in two directions on the object, and the force of gravity, the object's weight which acts down.
http://img291.imageshack.us/img291/9788/2kgut8.th.gif

Calculate the tension in the rope.

mass= 2.0 kg
tension force = unknown

Homework Equations



Force (tension) - Force (weight of mass) = 0 (because the system is in equilibrium).

The Attempt at a Solution



I put it up on image-shack:

http://img413.imageshack.us/my.php?image=pict0037hv3.jpg

I got 38 Newtons of tension on each rope. But the text tells me that I am wrong and that EACH string should equal 76 Newtons.
 
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Given your angle of 15, 38N should be correct...but the only way to get their answer is if the angle is approximately halved.
 
Looks like a typo possibly born out of someone carelessly adding where they shouldn't. Using half the angle only yields 75N for me whereas the problem in the illustration yields something quite close to 38N (37.9N for me). For the text calculation to be based on just half the angle then the claim 76N would be too much in error. To claim exactly twice then suggests carelessness in preparing the text description of the answer.
 
Last edited:
your right,.. all they did was take 19.6/sin(15). should have been 19.6/(2sin(15))
 
2Tsin15(tension)-2*9.8kg=0

am i right?
 
Last edited:
19.6/2sin15 is coming something 15.07!
 
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