# Homework Help: Momentum, Energy

1. May 16, 2010

### Maybe_Memorie

1. The problem statement, all variables and given/known data
Two particles of masses m and 3m are connected by a light rigid rod. The system rests on a smooth horizontal table, the heavier mass due east of the lighter mass. The heavier mass is projected with initial velocity uj. Find the velocities of the particles when the rod runs north-south.

2. Relevant equations
Conservation of momentum, conservation of energy.

3. The attempt at a solution
Applying conservation of momentum in the j direction, 3m(u) + m(0) = 3mv + mw.
3u = 3v + w.

Conservation of energy, 1/2(3m)u2 = 3mgh +1/2(3m)v2
u2 = 2gh + v2

I've no idea where to go from here.
This isn't homework, just a question I came across while revising for exams.

Last edited: May 17, 2010
2. May 16, 2010

### tiny-tim

Hi Maybe_Memorie!

(try using the X2 tag just above the Reply box )
erm … leave out the mgh !

3. May 17, 2010

### Maybe_Memorie

Why? The 3m mass gains vertical height.

4. May 17, 2010

### tiny-tim

No …
… everything's horizontal.

5. May 17, 2010

### Maybe_Memorie

The 3m mass is projected with a velocity uj, i.e. a velocity of u in the j-> direction, upwards.

6. May 17, 2010

### tiny-tim

Where I live, that's the k direction.

Anyway, if the rod starts east-west, and ends up north-south (as in the question), how can it ever move upwards??

7. May 18, 2010

### Maybe_Memorie

It's like the large mass moves in a circle around the small mass. So the 3m mass gains height in rotating.

It may be possible to treat it as a compound pendulum.

8. May 18, 2010

### Maybe_Memorie

Any suggestions?