Solving Momentum & Energy for Particles: Masses m & 3m

[Maybe_Memorie]

Homework Statement

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.

Homework Equations

Conservation of momentum, conservation of energy.

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.

 

[tiny-tim]

Hi Maybe_Memorie!

(try using the X² tag just above the Reply box )

… The system rests on a smooth horizontal table
…
Conservation of energy, 1/2(3m)u^2 = 3mgh +1/2(3m)v^2
u^2 = 2gh + v^2

erm … leave out the mgh !

 

[Maybe_Memorie]

erm … leave out the mgh !

Why? The 3m mass gains vertical height.

 

[tiny-tim]

Why? The 3m mass gains vertical height.

No …

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.

… everything's horizontal.

 

[Maybe_Memorie]

No …

… everything's horizontal.

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

 

[tiny-tim]

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

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??

 

[Maybe_Memorie]

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??

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.

 

[Maybe_Memorie]

Any suggestions?