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Answer to Question #4269 in Mechanics | Relativity for valeria

Question #4269
Two ropes in a vertical plane exert equal magnitude forces on a hanging weight but pull with an angle of 86.0 between them.What pull does each one exert if their resultant pull is 372 directly upward?
Expert's answer
<img src="data:image/png;base64,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" alt="">
P-weight of an object
T-pull of rope
alfa=86.0 -angle between ropes
If we project all forces on vertical axis we obtain
2Tcos(alfa/2)=P=372
Hence T=372/2/cos(86.0/2)=372/2/0.73=254.8 - pull exerting by each rope

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