What is the maximum force on the vine during Tarzan's swing?

  • Thread starter Zlex
  • Start date
In summary, the author asks a question about a swing and how much force is needed to break the vine. The student tries to solve the problem but gets stuck. They realize they need to assume the vine has elastic properties and work from there. They eventually solve the problem and get the answer correct.
  • #1
Zlex
40
1
I'm pretty sure that this question isn't as hard as I'm making it, but I'm having a brain block here.

Tarzan, who weighs 700 N, swings from a cliff at the end of a convenient vine that is 17 m long. From the top of the cliff to the bottom of the swing, he descends by 5.3 m. The vine will break if the force on it exceeds 1580 N. What would the greatest force on the vine be during the swing?

I'll show you guys how far I've gotton and then maybe you can help me from there, or show me where I am mistaken

Emech(initial) = Ep + Ek
Emech(initial) = mgh
Emech(initial) = 700*5.3
Emech(initial) = 3710

Emech(final) = Ep + Ek
Emech(final) = Es + Ek
Emech(final) = (kx^2)/2 + (mv^2)/2

*We can assume Emech is conserved

3710 = (kx^2)/2 + (mv^2)/2

kx^2 + mv^2 - 7420 = 0

Also I know that

F= m*a
F=mv^2 / R

And,
kx^2 + mv^2 - 7420 = 0
v^2 = (7420 -kx^2) / m

F = 7420-kx^2 / R
F = 7420-kx^2 / 17

Also,

Fmax = kx
1580 = kx
1580/x = k

Sub into F = 7420-kx^2 / 17

F = (7420 - 1580x) / 12

And thusly I am stuck.

Too many unknowns, not enough equations.

:confused:
 
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  • #2
(kx^2)/2 ?

Is this vine a spring?
 
  • #3
gnome said:
(kx^2)/2 ?

Is this vine a spring?

Its's not a spring, but it does unfortunatly have elastic properties. I really wish it didn't, the problem would be much easier.

Took me about 20 minutes of getting the answer wrong and wondering why they told me Fmax before I figured that out though.

When I realized it I thought I had solved the problem, only to realize I had gained two variables and only one equation.

=\

Now I am even more frustrated.
 
  • #4
Just a question...how do you know that you are meant to assume that the vine has elastic properties? If the author intended for students to consider them, you would think he/she would give the elastic spring constant k, in the problem, as well as a statement that the elastic restoring force of the vine can be described by Hooke's law. It doesn't say so anywhere...?
 
  • #5
yea, I would also think that the book would specify that to you...
 
  • #6
cepheid said:
Just a question...how do you know that you are meant to assume that the vine has elastic properties? If the author intended for students to consider them, you would think he/she would give the elastic spring constant k, in the problem, as well as a statement that the elastic restoring force of the vine can be described by Hooke's law. It doesn't say so anywhere...?

Alright; perhaps you are right. I've done the problem for the case where the rope is not elastic however I get an incorrect answer.

Maybe you can show me where I went wrong.

[tex]Et_i = E_p +E_k[/tex]

[tex]Et_i = E_p +0[/tex]

[tex]Et_i = mgh[/tex]

[tex]Et_i = 700(h)[/tex]

[tex]Et_i = 3,710[/tex]

*Assume no energy lost

[tex]Et_f = E_p +E_k[/tex]

[tex]Et_f = 0 +\frac{mv^2}{2}[/tex]

[tex]3,710 = \frac{mv^2}{2}[/tex]

[tex]\frac{7420}{m} = v^2[/tex]

[tex]F=ma[/tex]

[tex]F=\frac{mv^2}{R}[/tex]

[tex]F = \frac {m \frac{7420}{m}}{R}[/tex]

[tex]F = \frac {7420}{17}[/tex]

[tex]F = 436.47N[/tex]
 
  • #7
It is sum of forces = ma

I assume u have the free body diagram drawn for when tarzan is at the bottom

then sum of the forces is not F, but :

T - W

where T is the tension and W is tarzans weight.
 
  • #8
Oh man. Thank you so much, alright so then the last step would be:

[tex]\sum{F} = F_t - W[/tex]
[tex]\sum{F} = F_t - 700[/tex]
...
[tex]436.47 + 700 = F_t[/tex]
[tex]F_t = 1136.47[/tex]

Which...is so damn right.

Thank you so much. I can't believe it was such a stupid mistake. :rofl:
 
Last edited:

1. Who is Tarzan King of the Jungle?

Tarzan King of the Jungle is a fictional character created by author Edgar Rice Burroughs. He is a man who was raised by apes in the African jungle and possesses incredible strength and agility.

2. What is the origin story of Tarzan King of the Jungle?

Tarzan's origin story varies slightly depending on the version, but the general premise is that his parents, British aristocrats, were stranded in the jungle and died, leaving him to be raised by apes. He was given the name Tarzan, which means "white skin" in the apes' language.

3. What are Tarzan's abilities and skills?

Tarzan is known for his incredible physical abilities, including superhuman strength, agility, and speed. He is also a skilled hunter and tracker, able to communicate with animals and live off the land in the jungle.

4. Who are the main characters in the Tarzan King of the Jungle story?

The main characters in the Tarzan King of the Jungle story include Tarzan himself, his love interest Jane Porter, his ape "brother" Terk, and his arch-nemesis Clayton. Other important characters include Tarzan's adoptive ape family and various animals in the jungle.

5. What is the significance of Tarzan King of the Jungle in popular culture?

Tarzan has been a popular character in literature, film, and other media for over a century. He is seen as a symbol of strength and independence, and his story has been adapted and retold in many different forms, making him a beloved and well-known figure in popular culture.

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