- #1

jasonchiang97

- 72

- 2

**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

F

_{c}=mv

^{2}/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: T

_{h}+TcosΘ=mv

^{2}/r

T

_{h}= mv

^{2}/r - TcosΘ

mv

^{2}/r - [(W

_{c}+ W

_{p})/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= (W

_{p}+ W

_{c})/9.8

So (W

_{p}+W

_{c}/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