Uniform Circular Motion-Centripetal Force

[PianoMan]

Bah I say. ;) I'm so confused...

A "swing" ride at a carnival consists of chairs that are swung in a circle by 15.0-m cables attached to a vertical rotating pole at an angle of 60.0 degrees to the pole. Suppose the total mass of a chair and its occupant are 179kg. (a) Determine the tension in the cable attached to the chair. (b) Find the speed of the chair.


Ok, so I'm looking at part a. I have a nice drawing going, a right triangle with the lower right dot representing the chair, and a 60 degree theta up top. I drew a force diagram, which you can see at http://pics.bbzzdd.com/users/johnjohn/no19.JPG (you have to copy and paste the link, it's not going to work otherwise).

And now I have no idea what to do next. :( I know how to find the Fg and FN obviously, but then how do I use that to find FT?

Thanks guys. I have a test tomorrow, hopefully I won't be posting here too much.

 

[PianoMan]

Nevermind, got it. :)

 

[M98Ranger]

Hey there! Uniform circular motion can definitely be confusing, but I'm sure you'll get the hang of it with some practice. In this scenario, the key concept to understand is that the centripetal force is what keeps the chair and its occupant moving in a circular path. This force is provided by the tension in the cable attached to the chair.

To find the tension in the cable, you can use the equation Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the object, v is the speed, and r is the radius of the circular path. In this case, the radius is 15.0m, and the mass is 179kg. So, you can plug in those values and solve for Fc, which will give you the tension in the cable.

Once you have the tension, you can use the equation Fc = FT, where FT is the tension in the cable, to find the speed of the chair. Again, you can plug in the values you know (Fc and FT) and solve for v.

I hope this helps! Just remember to always think about the forces acting on an object in uniform circular motion, and use the appropriate equations to solve for the unknown values. Good luck on your test tomorrow!