Conservation of Momentum and Energy

mrbling

We are doing Cons. of Momentum in my intro to physics class.. and I am stuck on this problem:

An explosion breaks an object into two pieces, one of which has 1.58 times the mass of the other. If 7370 J were released in the explosion, how much kinetic energy did the heavier piece acquire?

I'm not quite sure where to begin, it seems like the question is misisng some info.. like if the peices are travelling at the same velocity or at different velocities.. I'm guessing this is relating conservation of momentum to conservation of kinetic energy where we can get a variable to cancel out.. but i can't seem to get started.. any hints?

KLscilevothma

Let the two pieces be A and B respectively. You need to use conservation of momentum to find out the ratio of velocity of A and that of B first. Since momentum before explosion is zero, so you can use m₁v₁ = - m₂v₂.

Let mass of A = 1.58x, mass of B = x.
If velocity ratio of A to B is 1:y, then let velocity of A = k and velocity of B = yk where k and x are constants.

Edit: Now you know their velocities and masses, try to relate them to the energy released in the explosion. The answer to this question can be easily found from here.

Remember conservation of momentum doesn't always imply conservation of energy.

mrbling

i've been thinking along the lines of ratios.. but the momentum to energy conversion was screwing me up.. (the equations I was coming up with were rediculous!)

in the end, I just looked at the contribution of mass vs. velocity between momentum and energy to solve it..

so between momentum and energy, mass doesnt make any difference since there is a 1 to 1 ratio.. but for velocity, there is power difference (v vs. v^2)..

thanks for the help!