Swing Torque: Tension in Chains for Boys & Girls

In summary, the conversation was about finding the tension in each chain of a porch swing when a 355.0N boy and a 300.0N girl sit on it, with the boy sitting 0.35m from one end and the girl sitting 0.45m from the other. The solution involved using torque equations and realizing that the sum of all the forces (including the boy's weight) must equal 0 in order for the swing to be in equilibrium. The final answer was 390N for the tension on the boy's side and 320N for the tension on the girl's side.
  • #1
Schaus
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5

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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  • #2
It looks like you have positioned the girl sitting somewhat on the boy.
 
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  • #3
Do you see the mistake?
 
  • #4
Awesome! Didn't notice that, thanks! I can't figure out the tension on the boys side though.
 
  • #5
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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  • #6
Yes. The T1=T2. 320N = 320N? If I added his extra 55N it would only equal 375N
 
  • #7
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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  • #8
Ah I see! Thanks a lot! I've gotten my answer again!
 
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  • #9
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
 
  • #10
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.
 

1. What is swing torque?

Swing torque refers to the tension or force applied to the chains of a swing set when it is in motion. This tension is created by the weight of the person on the swing and the force of their movement.

2. Why is swing torque important for boys and girls?

Swing torque is important for both boys and girls because it affects the stability and safety of the swing set. Too much tension in the chains can cause the swing to break or become unstable, putting the child at risk of injury.

3. How is swing torque measured?

Swing torque is typically measured using a tension gauge, which measures the amount of force applied to the chains. The tension gauge should be used regularly to ensure that the swing set is at a safe and appropriate tension level.

4. Can swing torque be adjusted?

Yes, swing torque can be adjusted by adjusting the length of the chains on the swing set. Shortening the chains will increase the tension and lengthening them will decrease the tension. It is important to follow the manufacturer's instructions for adjusting swing torque to ensure safety.

5. What are the potential risks of incorrect swing torque?

Incorrect swing torque can lead to accidents and injuries, such as the swing breaking or tipping over. It can also cause discomfort or pain for the child using the swing. It is important to regularly check and adjust swing torque to prevent these risks.

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