Circular Motion and String Tension

[eriadoc]

Working with circular motion ...

Homework Statement

Jill of the Jungle swings on a vine 6.9m long. What is the tension in the vine if Jill (63-kg) is moving at 2.4 m/s when the vine is vertical?

Homework Equations

T=mgsinθ
Fc=m(v^2/r)

The Attempt at a Solution

T = (63)(9.81) = 618N
Calculated (63)(2.4^2) / (6.9) = 52.6N
Acp = 0.835 m/s^2

This is incorrect. The correct answer is 670N. If the vine was simply hanging static with Jill at the end, the tension would be 618N (mg). Since it's in motion, and at the bottom of its arc, I assume that the difference between 618N and the correct answer of 670N is apparent weight? But I don't really know how to go about finding that, if I'm even correct in that assumption. Just for kicks, I divided 670 by 618 and got 1.084, a number that seems to have little relevance to anything I know, but I hoped maybe it would prompt some thought process in my head. No dice.

Help? TIA.

 

[JaredJames]

You're basically right with what you're saying.

To find the tension in the vine when vertical, you take the force of Jill acting outwards = Fc =(m*v^2)/r and add it to the force Jill exerts vertically. At the bottom of the vine it's Fc + Jills weight, at the top it's Fc - Jills weight.

The force of Jill acting downwards is 618N. You add to that the force of her from swinging = 52.6N. This gives you the tension when the vine is vertical (maximum tension in it). Which is 670N.

Jared

 

[eriadoc]

Gah! So close! Thank you very much.