Centripetal Acceleration with Tarzan

[PeachBanana]

Homework Statement

Tarzan plans to cross a gorge by swinging in an arc from a hanging vine, as shown in the figure.
If his arms are capable of exerting a force of 1200 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 100 kg, and the vine is 4.5 m long.

Homework Equations

Tension force - mg = ma
(a * r)^1/2 = v

The Attempt at a Solution

1400 N = (100 kg)(a)+(100 kg)(9.8m/s^2)
420 N = 100kg * a
a = 4.20 m/s^2

(4.20 m/s^2)(2.25m)^1/2 = v

Why is it incorrect to use 2.25 m as the radius? They gave the entire length of the vine.

 

[BruceW]

If you look at the picture, what point is tarzan 'orbiting around' ?

 

[genericusrnme]

If you look at the picture, what point is tarzan 'orbiting around' ?

I lol'd

The picture reminds me of a picture on one of the exams I did a while back in high school, there's some bizarre half black half white basketball playing hybrid

Also, what BruceW said

 

[PeachBanana]

If you look at the picture, what point is tarzan 'orbiting around' ?

Oh I see. That's more clear. He's orbiting around the very top of the tree, not the middle of the vine.

 

[asteriatic]

I would like to point out that there are a few assumptions being made in this problem that may affect the accuracy of the solution. Firstly, the figure does not specify the angle at which Tarzan will swing, which could affect the length of the arc and therefore the radius. Secondly, the figure also does not account for any external forces such as air resistance or friction, which could also affect the maximum speed Tarzan can tolerate.

That being said, using the entire length of the vine as the radius may not be the most accurate approach. This is because when Tarzan is swinging, the vine is not fully extended and therefore the radius is not equal to the length of the vine. A more accurate approach would be to use the length of the arc that Tarzan swings through as the radius. This can be calculated using the angle at which Tarzan swings and the length of the vine.

In conclusion, while the approach taken in the attempt at a solution may give an approximate answer, it may not be the most accurate. To improve the accuracy, we would need more information such as the angle at which Tarzan swings and the presence of any external forces.