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 [itex]M=8.2[/itex] kg be the mass of the object before the explosion.
Let the mass of the two pieces after explosion be [itex]m_1,\quad m_2[/itex]
Let their velocities be [itex]v_1,\quad v_2[/itex]
Let their accelerations be [itex]a_1,\quad a_2[/itex]
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) [itex]m_1+ m_2 = M[/itex]
(2) [itex]\frac {a_1}{a_2}=- \frac{m_1}{m_2}[/itex]
(3) [itex]0=m_1v_1+m_2v_2[/itex]
(4) [itex]\Delta K=\frac12m_1v_1^2+\frac12m_2v_2^2[/itex]
(5) [itex]v_1=a_1t[/itex]
(6) [itex]v_2=a_2t[/itex]

 

[mfb]

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

 

[bkraabel]

Duh! thanks...