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

In summary, the San Diego Zoo had a gorilla with a mass of 3.10 × 102 kg hanging from two vines at a 30.0° angle with the vertical. Based on a free-body diagram, the magnitude of the force of tension in each vine can be calculated as 1.76*10^3N. However, there may be a detail missing in the given solution and dividing by cosine twice may not be necessary.
  • #1
HiReinhardt
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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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  • #2
Why did you divide by cosine twice?
Also, that's one absolute unit of a gorilla :)
 
  • #3
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.
 
  • #4
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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What is a force?

A force is a push or pull that can cause an object to accelerate or change its motion. It is measured in Newtons (N).

What are the three laws of motion?

The three laws of motion, also known as Newton's laws, are:
1. An object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an unbalanced force.
2. The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
3. For every action, there is an equal and opposite reaction.

How do forces affect the motion of a big gorilla hanging from two vines?

The forces acting on the gorilla are its weight (due to gravity) pulling it downwards and the tension in the vines pulling it upwards. These two forces are equal in magnitude and opposite in direction, resulting in a state of equilibrium where the gorilla remains hanging.

What is the difference between weight and mass?

Weight is a force that is dependent on the mass of an object and the acceleration due to gravity. It is measured in Newtons (N). Mass, on the other hand, is the amount of matter an object contains and is measured in kilograms (kg).

How do the laws of motion apply to the gorilla hanging from two vines?

The first law of motion states that the gorilla will remain hanging at a constant velocity unless acted upon by an unbalanced force. The second law explains that the acceleration of the gorilla is directly proportional to the net force acting on it, which in this case is zero. The third law states that for every action (the gorilla's weight pulling downwards), there is an equal and opposite reaction (the tension in the vines pulling upwards).

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