Math Help - Mechanics Question

1. Mechanics Question

A comet has broken into three pieces of masses m1, m2, m3 with velocities
v1, v2 and v3 respectively. Find the velocity v0 of the comet before it has
broken.

2. Originally Posted by Unoticed
A comet has broken into three pieces of masses m1, m2, m3 with velocities
v1, v2 and v3 respectively. Find the velocity v0 of the comet before it has
broken.
Use conservation of linear momentum.

RonL

3. Is this just M*v0 = m1*v1 + m2*v2 + m3*v3 where M is the mass of the comet before it breaks up?

4. Originally Posted by Unoticed
Is this just M*v0 = m1*v1 + m2*v2 + m3*v3 where M is the mass of the comet before it breaks up?
Yes, but remember that this is a vector equation, so the momenta add vectorally. (ie. if this is a problem in 2D then you actually have two equations:
$M*v_{0x} = m_1*v_{1x} + m_2*v_{2x} + m_3*v_{3x}$
and
$M*v_{0y} = m_1*v_{1y} + m_2*v_{2y} + m_3*v_{3y}$)

-Dan

5. Originally Posted by Unoticed
Is this just M*v0 = m1*v1 + m2*v2 + m3*v3 where M is the mass of the comet before it breaks up?
But the mass before braekup is equal to the sum of the masses after break up so you have:

$(m_1+m_2+m_3)\bold{v_0} = m_1 \bold{v_1} + m_2 \bold{v_2} + m_3 \bold{v_3}$

RonL