Find tension in cables supporting giant swing

[heartshapedbox]

Homework Statement

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?

Homework Equations

see below

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
circumference=2(pi)(radius)
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! :(

 

[drvrm]

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:

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!

 

[haruspex]

multiply by 60 to get m/second.

You might want to think some more about that.

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

 

[heartshapedbox]

You might want to think some more about that.

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

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

 

[heartshapedbox]

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!

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

 

[haruspex]

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

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) = ?

 

[drvrm]

The swing moves 32 revolutions per min.
therefore, 32x circumference is the total distance traveled per min
multiply by 60 to get m/second.

well i did your calculation i get speed around 25 m/second that's not huge!

 

[haruspex]

well i did your calculation i get speed around 25 m/second that's not huge!

Including "multiply by 60"?

 

[drvrm]

Including "multiply by 60"?

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...

 

[haruspex]

No, my 60 was in the denominator- ..

As I would hope.