# Kinetic energy quesion need help

#### walker

Having some problems with this question, was wondering if anyone could lend some hints/explanation.

Q.
A body of mass 8.0kg is travelling at 2.0m/s under the influence of no external agency. At a certain instant an internal explosion occurs, splitting the body into two chunks of 4.0kg mass each; 16 joules of translational kinetic energy are imparted to the two-chunk system by the explosion. Neither chunk leaves the line of the original motion. Determined the speed and direction of motion of each of the chunks after the explosion.

Are they saying the system imparts an additional 16 joules of energy from the explosion. Because the initial kinetic energy is equal to 16 joules, they could have just said kinetic energy is conserved.

I've tried using just conservation of kinetic energy and momentum and the results show that the two pieces continue on in the same direction with the same speed of 2.0 m/s, it doesn't seem like much of an explosion.

Any help with this would be great.

Thanks.

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#### jamesrc

Gold Member
I think they are trying to say that 16 J is added to the system by the explosion (converted from potential energy (maybe chemical? not important, though)). So the kinetic energies are related by:

.5*m1*v1^2 + .5*m2*v2^2 = Ko + 16J = 32 J

and the conservation of momentum still holds:

m1*v1 + m2*v2 = M*vo = 16 Ns

That should be solvable, right?

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#### jamesrc

Gold Member
oops, I forgot my 1/2's in the energy equation. If that's right, I get 4 m/s for one piece and the other piece stays at the explosion site.

__________

OK; fixed above too.

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#### walker

That's what I came up with as well, but do you think that momentum is still conserved if the explosion imparts additional kinetic energy into the system?

#### jamesrc

Gold Member
Yes. I think it's pretty common for momentum to be conserved while kinetic energy isn't (any collsions that are not completely elastic (read any real collision) comes to mind). Conservation of momentum should apply as long as there are no non-negligible external forces to deal with, which seems to be the case here.

(Oh, and I edited my last post, so you may want to reload the page).

#### lavalamp

If you consider the centre of mass of the two particles, it is still moving at 2m/s and therefore overall momentum is conserved.
Think of it like this; the momentum of a particle will only be conserved when no external force acts on it, the explosion is an internal force, therefore overall, momentum is conserved.

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