Circular motion (conical pendulum)

[kingkong69]

A ball, B, of mass 2kg is attached to one end of a light, inextensible string. The string passes through a smooth, fixed ring, O, and a second Ball, A, of mass 4 kg, is attached to the other end. B is made to move as a conical pendulum while A hangs vertically below the ring. If the speed of B is 7ms^(-1), how long is the section BO of the ring.

I drew a little pixie.
[PLAIN]http://img263.imageshack.us/img263/7783/54071583.png

F=mrW(angular velocity)^2, v=rWThe answer is 4/3 metres.

ATTEMPT:
my attempt:
solve horizontally, so mrW^2=(r/d)*T
r is radius on both sides, d is the distance BO, T is tension in the moving string
r/d is cosB

7=rW
W^2=49/r^2

so
98/r=(r/d)*T

Vertically

4*g=sinB*T

Im stuck here.

 

[cupid.callin]

you must show your attempt in order to get help

 

[kingkong69]

my attempt:
solve horizontally, so mrW^2=(r/d)*T
r is radius on both sides, d is the distance BO, T is tension in the moving string
r/d is cosB

7=rW
W^2=49/r^2

so
98/r=(r/d)*T

Vertically

4*g=sinB*T

and that's what i have so far

 

[Doc Al]

Vertically

4*g=sinB*T

4*g is the weight of the hanging ball (A), not the moving ball (B).

You'll need vertical force equations for both balls.

 

[kingkong69]

please Doc Al be more specific

 

[Doc Al]

please Doc Al be more specific

What forces act on each ball? Write force equations for horizontal and vertical components for each ball. (You've already done some of that.) You'll end up with three equations, which you'll solve together.

 

[kingkong69]

I understand I should solve it alone for my own benefit but I spent hours and I really stuck, sorry for being so reliant but will you help me out on this question?

 

[tiny-tim]

welcome to pf!

hi kingkong69! welcome to pf!

(have an omega: ω and try using the X² icon just above the Reply box )

my attempt:
solve horizontally, so mrW^2=(r/d)*T
r is radius on both sides, d is the distance BO, T is tension in the moving string
r/d is cosB

7=rW
W^2=49/r^2

so
98/r=(r/d)*T

Vertically

4*g=sinB*T

and that's what i have so far

You'll need vertical force equations for both balls.

please Doc Al be more specific

you need the vertical equation for B

 

[Doc Al]

I understand I should solve it alone for my own benefit but I spent hours and I really stuck, sorry for being so reliant but will you help me out on this question?

As I mentioned in post #4, you need to correct this equation:

Vertically

4*g=sinB*T

I think you meant that to be for the moving mass (B), but you used the wrong mass.

You also need an equation for the vertical forces on the hanging mass (A). (That one's easy.)

 

[kingkong69]

Got it! Thanks a ton!