Centripetal force with circular motion

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Homework Help Overview

The problem involves Tarzan swinging across a river on a vine, with a focus on centripetal force and the maximum mass he can have without breaking the vine. The vine's length, Tarzan's speed, and the breaking strength are key elements of the scenario.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between centripetal force and the forces acting on Tarzan, including tension and gravitational force. There are attempts to set up equations based on the forces involved, and questions arise regarding the correct interpretation of the breaking strength of the vine.

Discussion Status

Some participants have provided insights into the forces at play, suggesting that the breaking strength is not the centripetal force but rather the maximum tension the vine can withstand. There is ongoing exploration of the equations and calculations, with some participants expressing confusion about their results.

Contextual Notes

Participants note the importance of considering both the tension in the vine and the gravitational force acting on Tarzan. There is mention of drawing diagrams to aid understanding, and some calculations yield results that differ from expected values, indicating potential misunderstandings in the setup.

catch-22
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This problem seems simple, but I can't get the answer:

Homework Statement



Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 10.0 m long. His speed at the bottom of the swing is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1000 N. What is the largest mass that Tarzan can have and still make it safely across the river.

Homework Equations



Fc=(m*v2)/(r)

The Attempt at a Solution



1000 N=(m*(8 m/s)2)/(10 m)
The answer is apparently 62 kg, and what I'm getting is over double that, so I'm obviously doing something wrong. I'm really not sure what I'm missing.
 
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catch-22 said:
This problem seems simple, but I can't get the answer:

Homework Statement



Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 10.0 m long. His speed at the bottom of the swing is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1000 N. What is the largest mass that Tarzan can have and still make it safely across the river.

Homework Equations



Fc=(m*v2)/(r)

The Attempt at a Solution



1000 N=(m*(8 m/s)2)/(10 m)



The answer is apparently 62 kg, and what I'm getting is over double that, so I'm obviously doing something wrong. I'm really not sure what I'm missing.

The 1000 N is not Fc. It is the breaking strength (so the maximum tension the vine can withstand). There are two forces to consider. You have neglected to take into account Tarzan's mass on the vine. Draw a diagram to see it.
 
Ft is not the only force in this example.


mv2/r = Fc
Fc= Ft-Fg
 
Epsillon said:
Ft is not the only force in this example.


mv2/r = Fc
Fc= Ft-Fg

I'm still not getting the right answer.

Using this, I've come up with

m=[10m*(1000 N-9.81m/s2*kg)]/(8.0m2/s2), which keeps working out to around 154 kg, still way off. What am I missing here?
 
Nevermind, I got it. Thanks guys.
 
maximum tension is the tension at the lowest point
and
tension at the lowest point = mv2/r + mg
works to around 61.72 by taking g = 9.8m/s
 

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