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

AI Thread Summary
Tarzan, with a mass of 80 kg, swings on an 18m vine, encountering a branch that alters his path. The calculations reveal that the gravitational potential energy at the start is 14,126.4 J, leading to a velocity of 18.795 m/s as he passes point 3. The tension in the vine at this point is calculated to be 15.34 times his weight, equating to 784.8 N. The discussion emphasizes the importance of understanding the net force and acceleration at point 3 to fully grasp the dynamics involved. The calculations and concepts presented highlight the interplay between gravitational and kinetic energy in Tarzan's swing.
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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?

FullSizeRender.jpg


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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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.
 
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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