Swing Torque: Tension in Chains for Boys & Girls

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Homework Help Overview

The discussion revolves around a torque problem involving a swing supported by chains, with a boy and a girl sitting at specified distances. The participants are exploring how to calculate the tension in the chains based on the weights of the individuals and the swing itself.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of torque equations and the conditions for equilibrium. There are attempts to calculate the tension in the chains, with some questioning the positioning of the individuals and the assumptions made about the forces acting on the swing.

Discussion Status

The discussion is active, with participants providing feedback on each other's reasoning and calculations. Some guidance has been offered regarding the relationship between the tensions and the total forces acting on the swing, although there is no explicit consensus on the final values of the tensions.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There are indications of confusion regarding the setup and the forces involved, particularly in relation to the equilibrium condition.

Schaus
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Homework Statement


A 355.0N boy and a 300.0.0N girl sit on a 50.5N porch swing that is 1.5m long. The swing is supported by a chain on each end. What is the tension in each chain when the boy sits .35m from one end and the girl sits .45m from the other? ( ans: boys side = 390 N, girls side = 320 N)

Homework Equations


τcw=τccw

The Attempt at a Solution


I don't have much practice with torque questions especially not ones that are hanging.
Στ= 0 = (T2)(1.5m) - (355N)(0.35m) - (50.5N)(0.75m) - (300N)(1.05m)
Στ = 0 = (T2)(1.5m) - 124.25Nm - 37.875Nm - 135Nm
(T2)(1.5m) = 477.125Nm → divide both sides by 1.5m
318N = T2
I'm trying to figure out how to get the tension on T1 now.
 
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It looks like you have positioned the girl sitting somewhat on the boy.
 
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Do you see the mistake?
 
Awesome! Didn't notice that, thanks! I can't figure out the tension on the boys side though.
 
Well, if you figured out one tension, then you know all of the forces except one - the other tension. And since the swing is in equilibrium (not accelerating), you know that the sum of the forces have to equal 0, true?
 
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Yes. The T1=T2. 320N = 320N? If I added his extra 55N it would only equal 375N
 
I haven't worked this problem yet so I don't know the answer. But, you can't just say that T1 = T2. Neither can you add his weight to one tension to get the other tension. The sum of ALL of the forces have to equal 0. Or, how I prefer to think about it: The upward forces have to equal the downward forces. But you have to make sure that you include all of them.
 
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Ah I see! Thanks a lot! I've gotten my answer again!
 
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Schaus said:
Yes. The T1=T2. 320N = 320N?

Huh? They can't be equal.

Have you drawn a force diagram? What are the 5 (4 known and 1 unknown) vertical forces acting on the swing? What must they add up to?

EDIT: Sorry cross posted
 
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Yes I drew a force diagram and I realize that statement is wrong. I added up all my weights going down and minused the tension I found in T2 to get my last tension.
 

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