# Find tension in cables supporting giant swing

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1. Mar 4, 2016

### heartshapedbox

1. The problem statement, all variables and given/known data
Picture a seat that is supported by two cables. One is horizontal, and the other makes an angle of 40 degrees to the vertical. The swing swings in a horizontal circle at a rate of 32 rev/min. The horizontal cable is 7.5 m long. The person sitting on the seat at the end of the cables weighs 825N and the seat weighs 255N. What is the tension in each cable?

2. Relevant equations
see below

3. The attempt at a solution
I have worked out that;
mv^2/r=F(horizontal)+F(slanted)sin40 i hat
F(slanted)cos(40)=255+825 k hat

My problem is that I feel as though i am not correctly determining the velocity, as I am not arriving at the correct answer. Here is my attempt:

Radius to the centre of the circle: 7.5m
this gives me distance traveled in m.
The swing moves 32 revolutions per min.
therefore, 32x circumference is the total distance traveled per min
multiply by 60 to get m/second.

This number ends up getting way to huge! :(

2. Mar 5, 2016

### drvrm

make out a free body diagram of the swing with the man sitting on it moving on circular path ; i think there will be two force equations; one in vertcal dir. another in horizontal direction!

3. Mar 5, 2016

### haruspex

You might want to think some more about that.

Also, what value are you using for m in the horizontal force equation?

4. Mar 5, 2016

### heartshapedbox

I multiplied by 60 to get from from metres/min to metres/second. Can u explain whats wrong? thank :)

5. Mar 5, 2016

### heartshapedbox

I have done that :) K hat and I hat!

6. Mar 5, 2016

### haruspex

I can easily walk at 60 metres per minute. I have no chance of walking at 3600 metres a second.

Edit: one way to get these conversions right is to treat the units as though they are variables.
(60 m/min) / (60 sec/min) = ?

Last edited: Mar 6, 2016
7. Mar 5, 2016

### drvrm

well i did your calculation i get speed around 25 m/second thats not huge!

8. Mar 5, 2016

### haruspex

Including "multiply by 60"?

9. Mar 6, 2016

### drvrm

No, my 60 was in the denominator- Actually it has 32 rev. per minute so if i write rev per sec then it would be (32/60) rev per sec......

10. Mar 6, 2016

### haruspex

As I would hope.