How to Calculate Kinetic Energy from an Internal Explosion?

[Bones]

Homework Statement

An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.6 times the mass of the other. If 25000 J is released in the explosion, how much kinetic energy does each piece acquire?

Homework Equations

The Attempt at a Solution

I am not sure where to begin.

 

[LowlyPion]

Homework Statement

An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.6 times the mass of the other. If 25000 J is released in the explosion, how much kinetic energy does each piece acquire?

Homework Equations

The Attempt at a Solution

I am not sure where to begin.

Here is a similar problem:
https://www.physicsforums.com/showthread.php?t=267683

 

[Bones]

Ok so m1=1.6m2
How do I figure out v1?

 

[Bones]

Would v1 be 1/1.6v2?

 

[LowlyPion]

Would v1 be 1/1.6v2?

It depends on which piece is the heavier.

What must be true in this problem?

 

[Bones]

The heavier piece will have less velocity than the lighter piece.

 

[Bones]

25000 J = 2.6/1.6 * 1/2 * m2v22
So 25000J*.81=20250J for the lighter piece and 25000J-20250J=4750J for the heavier piece.
Is that correct??

 

[LowlyPion]

25000 J = 2.6/1.6 * 1/2 * m2v22
So 25000J*.81=20250J for the lighter piece and 25000J-20250J=4750J for the heavier piece.
Is that correct??

Not quite.

They want the KE of the pieces. And the KE is mv²/2 not mv²

Check your math.

 

[Bones]

I am not sure what I am doing...that was just kinda of a guess.

 

[LowlyPion]

I am not sure what I am doing...that was just kinda of a guess.

25000 J = 2.6/1.6 * 1/2 * m2v22

So what does mv²/2 equal in your equation?

Isn't that the KE of m2?

Isn't that 1 part of what they asked?

 

[Bones]

So 25000 J=2.6/1.6*1/2mv2v2^2 which is the same thing as 25000 J=2.6/1.6*mv2v2^2/2

25000J=0.8125m2v2

Am I on the right track?

 

[LowlyPion]

So 25000 J=2.6/1.6*1/2mv2v2^2 which is the same thing as 25000 J=2.6/1.6*mv2v2^2/2

Yes but 25000 J = 2.6/1.6 * 1/2*m*v² = 2.6/1.6 * KE2

Isn't the question "Find KE1 and KE2" ?

 

[Bones]

Yes.
So 1.625*KE2=25000
KE2=15385J the lighter piece
KE1=9615J the heavier piece
?

 

[LowlyPion]

Yes.
So 1.625*KE2=25000
KE2=15385J the lighter piece
KE1=9615J the heavier piece
?

That's what it looks like.

 

[Bones]

Great! Thanks ;)