Forces and laws of motion -- Big gorilla hanging from two vines

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The discussion revolves around calculating the tension in vines supporting a 310 kg gorilla hanging at a 30° angle from the vertical. Participants express confusion over the correct formula and the use of cosine in the calculations, particularly why it appears twice in the denominator. The textbook answer for the tension is 1.76 × 10^3 N, but one user arrives at a different value due to misinterpretation of the formula. The importance of drawing a free-body diagram to visualize the forces involved is emphasized as a crucial step in solving the problem accurately. Understanding the forces and angles is essential for correctly determining the tension in the vines.
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About 50 years ago, the San Diego Zoo, in California, had the largest gorilla on Earth: its mass was about 3.10 × 102 kg. Suppose a gorilla with this mass hangs from two vines, each of which makes an angle of 30.0° with the vertical. Draw a free-body diagram showing the various forces, and find the magnitude of the force of tension in each vine. What would happen to the tensions if the upper ends of the vines were farther apart?
I've been trying 310kg * 9.8m/s2/(2)(cos30)*(cos-30). This gives me 3038/1.5 = 2.03*10^3N. The textbook answer is 1.76*10^3. What detail may I possibly be missing?
 
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Why did you divide by cosine twice?
Also, that's one absolute unit of a gorilla :)
 
I was trying to follow the solution my teacher edition gave. I have no idea where the 2 in the denominator came from either. I finally got the solution by adding (Cos30) + (Cos-30) in the denominator.
 
HiReinhardt said:
I was trying to follow the solution my teacher edition gave. I have no idea where the 2 in the denominator came from either. I finally got the solution by adding (Cos30) + (Cos-30) in the denominator.
Working backwards from the given answer is no way to do these problems. Why not try doing as suggested:
problem statement said:
Draw a free-body diagram showing the various forces,
 
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