Conservation of Momentum and Energy in an explosion

In summary, an explosion breaks an object into two pieces. One piece has 1.58 times the mass of the other, and 7370 J of energy is released.
  • #1
mrbling
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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 traveling 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?
 
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  • #2
it seems like the question is misisng some info.. like if the peices are traveling at the same velocity or at different velocities..
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.
 
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  • #3
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 doesn't 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!
 

What is conservation of momentum?

Conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant over time, regardless of any internal or external forces acting on the system.

How does conservation of momentum apply to explosions?

In an explosion, the total momentum of the system before and after the explosion must remain the same. This means that the combined momentum of all the fragments and debris from the explosion must equal the momentum of the initial explosive material.

What is the relationship between momentum and energy in an explosion?

Momentum and energy are both conserved in an explosion, but they are not necessarily equal. The amount of energy released in an explosion can vary depending on the type and amount of explosive material, while the total momentum of the system remains constant.

How does the mass and velocity of an explosion affect conservation of momentum and energy?

The mass and velocity of an explosion are both important factors in determining the amount of momentum and energy involved. A larger mass or higher velocity will result in a greater amount of momentum and energy being transferred to the surrounding environment.

Can conservation of momentum and energy be violated in an explosion?

No, conservation of momentum and energy are fundamental laws of physics and cannot be violated. While the distribution of energy and momentum may change during an explosion, the total amount remains constant before and after the explosion.

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