Explosive separation with conservation of momentum and energy

[bkraabel]

Homework Statement

An 8.20-kg object is sliding across the ice at 2.34 m/s. An internal explosion occurs, splitting the object into two equal chunks and adding 16 J of kinetic energy to the system. What is the average acceleration of the two chunks if the explosive separation takes place over a 0.16-s time interval?

Homework Equations

Let M=8.2 kg be the mass of the object before the explosion.
Let the mass of the two pieces after explosion be m_1,\quad m_2
Let their velocities be v_1,\quad v_2
Let their accelerations be a_1,\quad a_2
Work in cm frame, so initial kinetic energy is zero.
change in kinetic energy is still 16 J.

The Attempt at a Solution

I get six equations with six unknowns, but I can't solve them!

(1) m_1+ m_2 = M
(2) \frac {a_1}{a_2}=- \frac{m_1}{m_2}
(3) 0=m_1v_1+m_2v_2
(4) \Delta K=\frac12m_1v_1^2+\frac12m_2v_2^2
(5) v_1=a_1t
(6) v_2=a_2t

 

[mfb]

"two equal chunks" - they have the same mass, that simplifies the equations a lot.

 

[bkraabel]

Duh! thanks...