Calculating Tension on a Swinging Rope: A Scientific Approach

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Homework Help Overview

The discussion revolves around calculating the tension in a rope while swinging an airplane, focusing on the parameters of the rope length, mass of the airplane, and the time taken for a complete revolution. Participants are exploring concepts related to circular motion and forces.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the choice of radius used in calculations and whether the distance should be the full length of the rope or a different measurement. There are discussions about the correct interpretation of the problem, including the nature of the motion (horizontal vs. vertical) and the implications for the radius and forces involved.

Discussion Status

There is an ongoing exploration of the problem with participants providing insights and raising questions about the assumptions made regarding radius and motion. Some guidance has been offered regarding the relationship between the time for a revolution and the average linear velocity, but no consensus has been reached on the correct approach or calculations.

Contextual Notes

Participants note the ambiguity in the problem statement regarding the orientation of the rope and the motion of the airplane, which could significantly affect the calculations. There is also a mention of the need for clarity on whether the velocity is constant or if the airplane is accelerating.

JWest
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I need to figure this question out. I have to find the tension on the rope (1.14m) after swinging an airplane (.115kg) in the air for 1.49s. Any help?

I did it like this. I found the velocity (v=d/t) using .82m as the distance (radius) (or should I have used 1.14m instead?). The velocity was .77m/s^2. Then, I found the centripetal force (Fc=mv^2/r) (once again using .82m as "r"). The centripetal force was .08N so I said the tension was .08N.

Can anyone tell me what I did wrong, and how to do it right? Thanks.
 
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How is the radius .82m? Units on velocity are m/s.
You are correct ins aying the tension is the force, but the rest doesn't really make sense.
 
whozum said:
How is the radius .82m? Units on velocity are m/s.
You are correct ins aying the tension is the force, but the rest doesn't really make sense.

I meant .57m for radius. Would that be right, or would I use 1.14 for the distance/radius in the equations?

How would I find the force then if it doesn't make sense?
 
Well, the airplane traces a circle around your hand, correct? Whats the radiuso f that circle? The rope, or half hte rope?

If it makes a revolution in 1.49 seconds, then the circumference of the circle divided by the time gives you the average linear velocity.
 
JWest said:
I need to figure this question out. I have to find the tension on the rope (1.14m) after swinging an airplane (.115kg) in the air for 1.49s. Any help?

I did it like this. I found the velocity (v=d/t) using .82m as the distance (radius) (or should I have used 1.14m instead?). The velocity was .77m/s^2. Then, I found the centripetal force (Fc=mv^2/r) (once again using .82m as "r"). The centripetal force was .08N so I said the tension was .08N.

Can anyone tell me what I did wrong, and how to do it right? Thanks.

You have not stated the problem well enough for anyone to know for sure if you are doing the right thing, or what you are doing wrong. If 1.49 sec is the time for the plane to go around the circle one time, then you need to say so. If the velocity is constant, it is one sort of problem. If you are doing something to speed the plane up, it is a totally different problem.
 
Also, did the question specify whether the airplane was moving in a horizontal plane or whether the rope was parallel to the horizontal, because this will affect the value of the radius.
 
Not the radius, but the force diagram definitely.
 

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