Inelastic collision and circular motion

[seanpk92]

Homework Statement

A 20.00kg lead sphere is hanging from a hook by a thin wire 3.50m long, and is free to swing in a complete circle. Suddenly it is struck horizontally by a 5.00kg 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

w = omega
a = alpha
[STRIKE]o[/STRIKE] = theta
a = (rw)^2
w = w(i) + at
[STRIKE]o[/STRIKE] = [STRIKE]o[/STRIKE](i) + w(i)t + .5at^2
m(a1)v(a1) + m(b1)v(b1) = (m[a] + m)*v(2)
acc(rad) = v^2/R

The Attempt at a Solution

m(a1) = 20kg m(b1) = 5kg
v(a1) = 0m/s v(b1) = ?m/s r = 3.5m

20*0 + 5*? = 25*v(2)


I have no idea what to do with this. Like so I find velocity first?

 

[gneill]

In order to make a circular loop, what minimum speed must the sphere+dart have at the top of the loop?

 

[seanpk92]

Should I use the uniform circular motion equation for the Vmin at the top of the loop

 

[seanpk92]

Should I use the uniform circular motion equation for the Vmin at the top of the loop

I figured it out, I think. I used:
mg = m(v^2/R)
v = sqrt(gR)
K(1) + U(g1) = K(2) + U(g2)

U(g1) = 0
y(2) = 2R
drop the masses since they cancel out
.5v(c)^2 = .5v(2)^2 + 2gR
then plug v(c) back into COM and solve.
I got 65.5m/s

 

[gneill]

You're getting there. What value did you get for the velocity of the sphere plus dart at the top of the loop? How about at the bottom?

Your value for the velocity of the dart looks a tad high to me. Perhaps you could show your calculation.