# Solving Giant Swing Horizontal Cable Tension

• jasonchiang97
In summary, the seat swings in a horizontal circle at a rate of 33.0 rev/min. If a 295-N person is sitting in it, the tension in the horizontal cable is 869 N.
jasonchiang97
1. Homework Statement
In one of the versions of the "Giant Swing", the seat is connected to two cables, one of which is horizontal (Figure 1) . The seat swings in a horizontal circle at a rate of 33.0 rev/min .

If the seat weighs 295 N and a 869-N person is sitting in it, find the tension in the horizontal cable.

## Homework Equations

Fc=mv2/r
Period=circumference/velocity so 2πR/v

## The Attempt at a Solution

I drew two FBD(free body diagrams). One for the person and one for the chair
For the person : TsinΘ-W-Fn=0
T=(W+Fn)/sinΘ
Fn = Weight of the chair

For the chair: Th+TcosΘ=mv2/r
Th = mv2/r - TcosΘ
mv2/r - [(Wc + Wp)/sinΘ]*cosΘ

To get the velocity, we use period = circumference /velocity
33 rev/min * 1min/60 sec = 0.55 rev/sec
0.55 = 2π(7.5)/v
v=85.68m/s
m= (Wp + Wc)/9.8
So (Wp+Wc/9.8)(81.68)2/7.5 - (295+869)/tan40

Basically I end up getting a huge number and I'm fairly certain that it's wrong but can't see why

jasonchiang97 said:

I drew two FBD(free body diagrams). One for the person and one for the chair
I haven't checked your work in detail (sorry) but you should be able to treat the person and chair as a single object. The vertical component of the tension in the slanted cable must balance the weight of the person+chair, and the horizontal components of the two tensions must provide the centripetal acceleration.

Nathanael said:
I haven't checked your work in detail (sorry) but you should be able to treat the person and chair as a single object. The vertical component of the tension in the slanted cable must balance the weight of the person+chair, and the horizontal components of the two tensions must provide the centripetal acceleration.

yea that's basically what I did. I guess my main problem is I don't know how to convert rev/min to m/s so I just took the rev/min and divided it by 60 to get rev/sec which gives 0.55rev/sec

I then took 2π(7.5)/0.55 to get velocity. Wondering if that step is correct

Check the units in the above equation. If it is not meters/second then try to fix it so it is.

## 1. What is the purpose of solving giant swing horizontal cable tension?

The purpose of solving giant swing horizontal cable tension is to determine the optimum tension required to support the weight of the swing and the individuals using it, while also ensuring the cable does not break or become too slack.

## 2. What are the main factors that affect the tension of the horizontal cable?

The main factors that affect the tension of the horizontal cable include the weight of the swing and the individuals using it, the length and angle of the cable, and environmental conditions such as wind speed.

## 3. How is the tension of the horizontal cable calculated?

The tension of the horizontal cable is calculated using the equations of static equilibrium, which take into account the weight of the swing and the individuals using it, the angle and length of the cable, and any external forces acting on the swing.

## 4. What are some potential challenges in solving giant swing horizontal cable tension?

Some potential challenges in solving giant swing horizontal cable tension include accurately measuring the weight of the swing and individuals, accounting for variations in cable materials and conditions, and ensuring the calculations are precise enough to support the weight without overloading the cable.

## 5. How can the tension of the horizontal cable be adjusted if necessary?

If the tension of the horizontal cable is not within the desired range, it can be adjusted by changing the length or angle of the cable, or by adding or removing weight from the swing. However, it is important to carefully recalculate the tension after making any adjustments to ensure the safety and stability of the swing.

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