How Can Momentum and Radial Force Help Solve a Collision Problem?

[fiestyman001]

Homework Statement

A 17.00 kg lead sphere is hanging from a hook by a thin wire 3.00 m long, and is free to swing in a complete circle. Suddenly it is struck horizontally by a 5.00 kg steel dart that embeds itself in the lead sphere.

What must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision?

Homework Equations

momentum: P1=P2
Force radial=mv^2/R

The Attempt at a Solution

Here is the start to my thought process, but it doesn't go anywhere from here.
You calculate the circumference of the circle that the combined sphere and dart go. We need to find the V in the Radial force equation which is equal to the sqrt(Frad*radius/mass). We have all of the knowns except for Frad and V (V is the final speed of both objects together for it to go around one loop):

radius= 3.0m
mass dart = 5kg
mass sphere = 17kg

I know momentum has a part to play..
You could say P1=P2
5kg(Vd) = 22kg(Vds) (the 22 is the mass of the dart + sphere) and Vds is the final V

and now I'm stuck, do I use the radial force equation and substitute 5Vd/22 in for V? I'm still left with an Fradial value which i don't know what to do with.

 

[Doc Al]

First figure out what the speed of the "sphere + dart" must be at the top of the motion to make it over without collapsing the thin wire. (Newton's 2nd law will help.) Then figure out what the speed must have been just after the dart embedded itself in the sphere (at the bottom of the circle). Then figure out what the speed of the dart must have been to produce such a speed in the "sphere + dart" after the collision.

 

[treverd]

bump i,m still not understand how to use Newtons second law.