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Explosive separation with conservation of momentum and energy

  1. Jun 6, 2013 #1
    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 [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.


    3. 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]
     
  2. jcsd
  3. Jun 6, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    "two equal chunks" - they have the same mass, that simplifies the equations a lot.
     
  4. Jun 6, 2013 #3
    Duh! thanks...
     
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