Problem about circular motion

Question

a 9kg ball is suspended from a hook in the ceiling by a string 1.0m long. it is set into motion in a horizontal circle with speed such that a string maintains an angle of 30deg. calculate the speed of the ball and the tension in the string.

Answer 1

19.8lb from a string in a ceiling?

Text book questions could be more fun if they were real.

Since the speed of the ball is zero because it fell on the floor.

What gave way first?

The string, the hook, or the ceiling?

Did you want to try this or just have us do your homework?

Answer 2

There are two forces on the ball:  Gravity and the centripetal force.  The centripetal force is directed horizontally.

Fg= mg

Fc = mw^2r

w= angular velocity = v/r

Now draw your right triangle.  Fg down, Fc radial

Tan 30 = Fc/Fg

1/sqrt(3) = Fc/Fg

Fc = Fg/sqrt(3)

Tension = sqrt (Fc^2 + Fg^2)

Speed of ball

Fc = mw^2r = Fg = mg

w = sqrt (g/r)

Since v= wr,

v = sqrt (g*r)

r = l * sin 30

Chug n' plug