# Circular Motion and String Tension

In summary, the conversation discusses finding the tension in a vine while Jill of the Jungle swings on it at a speed of 2.4 m/s, with the vine being 6.9m long. The correct answer is 670N, which is found by adding the force of Jill's weight (618N) to the force she exerts from swinging (52.6N). This gives the maximum tension in the vine when it is vertical.
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?

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.

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

Gah! So close! Thank you very much.

## 1. What is circular motion?

Circular motion is a type of motion where an object moves along a circular path at a constant speed. This means that the object is continuously changing direction but maintaining the same speed.

## 2. How is circular motion related to string tension?

In circular motion, an object is typically attached to a string or rope that is being pulled towards the center of the circular path. This creates tension in the string, which is necessary to keep the object moving in a circular path.

## 3. What factors affect the amount of string tension in circular motion?

The amount of string tension in circular motion is affected by the mass of the object, the speed at which it is moving, and the radius of the circular path. A larger mass or speed will require more tension, while a larger radius will result in less tension.

## 4. How is string tension calculated in circular motion?

The formula for calculating string tension in circular motion is T = (mv^2)/r, where T is the tension, m is the mass of the object, v is the speed, and r is the radius of the circular path.

## 5. What happens to string tension if the radius of the circular path is decreased?

If the radius of the circular path is decreased, the string tension will increase. This is because the object is now moving in a smaller circle, which requires more tension to maintain the same speed.

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