Solving Energy & Momentum Homework Problem on Mass 8.13 kg

[physics.geeks]

Homework Statement

A block of mass 8.13 kg in outerspace is moving at 2.19 m/s with no external forces acting on it. After an explosion, the block is split into two parts both having mass equal to half the mass of the original block. The explosion supplies the two masses with an additional 19.5 J of kinetic energy. Neither mass leaves the line of original motion. Calculate the magnitude of the velocity of the mass that is moving at a greater velocity.

Homework Equations

Efinal=Einitial+19.5
Pf=Pi

The Attempt at a Solution

i worked out the answer, this question has been asked on the forums before but i initially did Efinal+19.5=Einitial but you're supposed to add the 19.5 to Einitial and this is what i don't understand, why is 19.5 added to the initial total energy and not the final?

 

[algebrat]

Because the final energy consists of both the initial energy and the energy contribution from the explosion. It may be hard to get definitions to tell you whether an energy contribution is positive or negative or whether its initial of final, so try relying on a little intuition to decide on signs and where it goes. Maybe a defintion would suggest work of explosion is positive change, so Efinal-Einitial is positive.