What Calculations Reveal Tarzan's Vine Tension at Point 3?

In summary, Tarzan (mass of 80kg) uses a 18m vine to swing across a gorge to visit Jane's hut. One day, Jane interfered by attaching a branch to the vine below the pivot point. To calculate the tension in the vine at point 3, we use the equations Ug = mgh, ΣE = 0, Ek = 0.5mv^2, and ΣF = ma. By setting Ug = Ek and solving for v, we get a velocity of 18.795 m/s at point 2. Using Fnet = ma and solving for T, we get a tension of 784.8 N, which is 15.34 times greater than Tar
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Homework Statement



Tarzan (mass of 80kg) has an 18m vine stretched horizontally from his hut to a pivot point P, as shown. He uses it to swing across the gorge to visit Jane's hut, starting from rest to conserve energy. One day Jane spoiled his plans by fastening a strong, thin, smooth, horizontal branch to intercept the vine at B, 15m directly below P. Tarzan hung on and followed the dotted path 1 to 2 to 3. Calculate the tension in the vine as he passed through point 3. How many times greater than his weight is his tension?

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The answer is 15.34 (I'm unsure which question this answers)

Homework Equations


Ug =mgh
ΣE = 0
Ek = 0.5mv2
ΣF = ma

The Attempt at a Solution


1: [/B]Ug = 80(9.81)(18)= 14,126.4 J
Ek = 0.5mv2 = 0

2: Ug = 0
Ek = 0.5mv2
14 126.4= 0.5mv2
v = 18.795 m/s

Ft = mg = 784.8 N
 
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  • #2
it answers the tension in the vine as he passed through point 3. because if it would be the weight then the units would have been mentioned.
 
  • #3
In your step 2 you calculate a velocity. At what point is that his velocity? At which point do you need to determine his velocity?
As I'm sure you know, Fnet=ma. If the tension at point 3 is T, what is Fnet? What is his acceleration at that point?
 

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The formula for calculating work is:
W = F * d
Where W is work, F is the force applied, and d is the distance over which the force is applied.

2. How do I calculate the kinetic energy of an object?

The formula for calculating kinetic energy is:
KE = 1/2 * m * v^2
Where KE is kinetic energy, m is the mass of the object, and v is the velocity of the object.

3. How do I calculate potential energy?

The formula for calculating potential energy is:
PE = m * g * h
Where PE is potential energy, m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the object.

4. What is the relationship between work and energy?

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5. How do I approach a complex work and energy problem?

When approaching a complex work and energy problem, it is important to break it down into smaller, more manageable parts. Identify all the given information and the unknowns, and then use the appropriate formulas to solve for the unknowns. It may also be helpful to draw a diagram or use a visual representation to better understand the problem.

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