How Do You Calculate the Weight of a Pumpkin Suspended by Two Scales?

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To calculate the weight of a pumpkin suspended by two scales reading 33 N and 49 N at an angle of 131 degrees, the law of cosines can be applied to find the resultant force. The discussion emphasizes that instead of calculating individual angles, one can directly use vector addition to determine the resultant force from the two tension forces. There is confusion regarding the method used, as some participants suggest that finding angles may not be necessary for this problem. The relationship between the vector sum of the tensions and the weight of the pumpkin is crucial for solving the problem correctly. Clarifying the approach and showing work may help in resolving the issue with the calculations.
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Find the weight of a pumpkin hanging from two scales, if scale one reads 33 N, scale two reads 49 N, and the angle θ between the strings coming from the two scales is 131 degrees.
[URL]http://a1.educog.com/res/msu/plough/physlibrary/graphics/pumpkin.gif[/URL]

I attempted to do this. I used law of cosines to find the other two angles and then i found both Y-components of scale 1 and scale 2. Then i added them. And I'm pretty sure that's the method to do it. And yet, when I enter it into the computer, it says "wrong answer".

Any help?
 
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jeetp26 said:
Find the weight of a pumpkin hanging from two scales, if scale one reads 33 N, scale two reads 49 N, and the angle θ between the strings coming from the two scales is 131 degrees.
[URL]http://a1.educog.com/res/msu/plough/physlibrary/graphics/pumpkin.gif[/URL]

I attempted to do this. I used law of cosines to find the other two angles and then i found both Y-components of scale 1 and scale 2. Then i added them. And I'm pretty sure that's the method to do it. And yet, when I enter it into the computer, it says "wrong answer".

Any help?

Finding the individual angles is possible but quite tedious. I don't quite see what you mean when you claim that you found them from the cosine law.
If by "cosine law" you mean the vector addition formula, then you don't need to find the angles and you don't need to add components. Maybe you can show some work. This looks like homework.
 
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nasu said:
Finding the individual angles is possible but quite tedious. I don't quite see what you mean when you claim that you found them from the cosine law.
If by "cosine law" you mean the vector addition formula, then you don't need to find the angles and you don't need to add components. Maybe you can show some work. This looks like homework.

Yes it is a homework problem. Don't get the idea that I'm trying to get people to do my homework for me. Haha.

Below are the law of cosines:

[PLAIN]http://www.ies.co.jp/math/java/trig/yogen1/yogen-moji.gif
 
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Then why don't you post it in the homework section?

Regarding the cosine law, I still don't see how you calculate the "other two angles" but it does not matter.
Do you know how to use it to find the resultant (sum) of two vectors when you know their magnitudes and the angles between them? The two forces here are the tensions in the wires.
What is the relationship between the vector sum of the two tensions and the weight?
 
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