# Homework Help: Explosive separation with conservation of momentum and energy

1. Jun 6, 2013

### bkraabel

1. The problem statement, all variables and given/known data
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?

2. Relevant 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.

3. 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) $v_2=a_2t$

2. Jun 6, 2013

### Staff: Mentor

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

3. Jun 6, 2013

### bkraabel

Duh! thanks...