Conservation of Linear Momentum and kinetic energy of explosion

[peaceandlove]

Homework Statement

An object, with mass 71 kg and speed 23 m/s relative to an observer, explodes into two pieces, one 5 times as massive as the other; the explosion takes place in deep space. The less massive piece stops relative to the observer. How much kinetic energy is added to the system during the explosion, as measured in the observer's reference frame?

Homework Equations

Equation 1: m1=5m2
Equation 2: (1/2)mv^2
Equation 3: mv1 (intiial) + mv2 (initial) = mv1 (final) + mv2 (final)

The Attempt at a Solution

I used equation 1 go determine the masses of the two exploded pieces and determined the initial kinetic energy by plugging in 71 kg and 23 m/s into equation 2. I then plugged in all the data into equation 3, where mv2 (final) is equal to 0, and solved for mv1 (final). I then plugged the final velocity for object 1, as well as the mass, into equation 2. When I subtracted the initial kinetic energy from the final kinetic energy, I came up with 93897.5 J.

 

[Delphi51]

Have to do conservation of momentum to find the speed of that heavier piece.
Only then can you calculate the KE after the explosion.

Oh, sorry, I guess that is just what you did! Did you get v = 27.6 for the bigger piece?

 

[peaceandlove]

Oh! I think I know what I did wrong. For some reason I read that the LARGER piece stopped relative to the observer, but it's the SMALL piece that stops. In that case, wouldn't the answer be 3755.9 N? I got that by doing (1/2) times the mass of the larger piece times the final velocity of the larger piece. From that I subtracted (1/2) times the mass of the entire object before it exploded times the velocity of the entire object before it exploded.

 

[Delphi51]

Yes, I got 3755!