An explosion breaks an object into two pieces

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In summary, the conversation discusses an explosion that breaks an object into two pieces with different masses and calculates the kinetic energy acquired by each piece using conservation of momentum and kinetic energy equations. It also acknowledges a mistake made in the calculation.
  • #1
pupatel
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Can someone help me with this...what is the answer to this and how do i get it? :eek:

An explosion breaks an object into two pieces, one of which has 1.5 times the mass of the other. If 7800 J were released in the explosion, how much kinetic energy did each piece acquire?
 
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  • #2
Note that since there are only two pieces, you can get by without explicit use of vectors for the momenta.

From the point of view of the center of mass, conservation of momentum implies

m1 v1 = m2 v2

or, substituting what you know about masses and taking m1 to be the lesser,

m1 v1 = 1.5 m1 v2

where I am letting each speed be a positive number, since I am not using vector language. You can divide that last equation through by m1 to get that v2 = (2/3) v1.

Kinetic energy, again from the center of mass point of view, is

(1/2) m1 v1^2 + (1/2) m2 v2^2 = 7800.

Subtituting again,

(1/2) m1 v1^2 + (1/2)(3/2) m1 [(2/3) v1]^2 = 7800,

which means

KE1 + (1/3) KE1 = 7800.

So KE1 = (3/4) 7800, and that means KE2 = (1/4) 7800. Take it from here with your calculator.
 
Last edited:
  • #3
I agree with Janitor in almost everything; but I get: KE1+(2/3)KE1=Total energy => KE1=(3/5) of total energy.
 
  • #4
Wisky40, I looked back through what I wrote and I can't find an error--but that doesn't mean I am correct! I would advise pupatel to go through each step on his/her own and not take anything for granted.
 
  • #5
I think EK1(1+(3/2)(2/3)^2)=EK1(1+(2/3))=EK1(5/3).
 
  • #6
Janitor said:
(1/2) m1 v1^2 + (1/2)(3/2) m1 [(2/3) v1]^2 = 7800,

which means

KE1 + (1/3) KE1 = 7800
No, it means KE1 + (2/3) KE1 = 7800. I suspect you multiplied 3/2 by (2/3)2 but then divided it by 2, which you shouldn't do because 1/2 is part of the KE expression.
 
  • #7
Yep, that's what I did. You guys are completely correct. My mistake!
 

1. What causes an explosion to break an object into two pieces?

An explosion can be caused by a sudden release of energy, which can result from chemical reactions, nuclear reactions, or rapid expansion of gases.

2. How does an explosion break an object into two pieces?

An explosion creates a shockwave that travels through the object, causing it to fracture and break into two or more pieces.

3. Can any object be broken into two pieces by an explosion?

Yes, any object can be broken into two pieces by an explosion if enough force is applied. However, the size and strength of the object may affect the outcome of the explosion and the number of pieces it breaks into.

4. Is there a difference between an explosion breaking an object into two pieces and an object breaking into two pieces on its own?

Yes, there is a difference. An explosion breaks an object into two pieces by applying external force, while an object breaking on its own is usually due to internal stress or weakness within the object itself.

5. Can an explosion break an object into more than two pieces?

Yes, an explosion can break an object into multiple pieces, depending on the force and impact of the explosion. The number of pieces will also depend on the material and strength of the object.

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