Merry Go Round (Centripetal Force)

[Chandasouk]

Homework Statement

Two identical twins, Jena and Jackie, are playing one December on a large merry-go-round (a disk mounted parallel to the ground on a vertical axle through its center) in their school playground in northern Minnesota. Each twin has a mass of 29.0 kg. The icy coating on the merry-go-round surface makes it frictionless. The merry-go-round revolves at a constant rate as the twins ride on it. Jena, sitting a distance 1.80 m from the center of the merry-go-round, must hold on to one of the metal posts attached to the merry-go-round with a horizontal force of 58.0 N to keep from sliding off. Jackie is sitting at the edge, a distance 3.67 m from the center.

With what horizontal force must Jackie hold on to keep from falling off?

If Jackie falls off, what will be her horizontal velocity when she becomes airborne?


I attempted this problem but got the wrong answer. What I did first was

58N = 29kg*V^2
=========
1.80

V = 1.89 m/s

Fnet = m*v^2
---------
R

Fnet = (29kg)(1.89m/s)^2
--------------------
3.67

Fnet = 28.4N


What did I do wrong?

 

[rl.bhat]

1.89 m/s is not the velocity of Jack. Their angular velocities is the same.
And angular velocity ω = v/R.
So v1/R1 = v2/R2. So find v2.

 

[Chandasouk]

So

1.89m/s
-------- = V2/3.67m
1.80 m

V2 = 3.8585 m/s ?

Then

Fnet = (29kg)(3.8585m/s)^2/3.67m = 117.6N ?

 

[rl.bhat]

Yes. That is right.