An explosion breaks an object into two pieces

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Discussion Overview

The discussion revolves around a physics problem involving an explosion that breaks an object into two pieces with differing masses. Participants explore the conservation of momentum and kinetic energy to determine how much kinetic energy each piece acquires after the explosion.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the problem and seeks help in calculating the kinetic energy of the two pieces after an explosion.
  • Another participant explains the conservation of momentum and derives a relationship between the velocities of the two pieces based on their mass ratio.
  • A different participant agrees with the previous explanation but arrives at a different conclusion regarding the proportion of kinetic energy each piece receives.
  • One participant acknowledges a potential error in their calculations and suggests that the original poster verify each step independently.
  • Another participant proposes a different expression for kinetic energy based on the derived velocities.
  • A participant challenges a calculation made by another, suggesting a misunderstanding in the application of kinetic energy formulas.
  • A participant admits to making a mistake in their calculations after being corrected by others.

Areas of Agreement / Disagreement

There is no consensus on the correct distribution of kinetic energy between the two pieces, as participants present differing calculations and interpretations of the problem.

Contextual Notes

Participants express uncertainty regarding specific steps in their calculations, and there are unresolved mathematical interpretations related to the kinetic energy expressions.

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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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:
I agree with Janitor in almost everything; but I get: KE1+(2/3)KE1=Total energy => KE1=(3/5) of total energy.
 
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.
 
I think EK1(1+(3/2)(2/3)^2)=EK1(1+(2/3))=EK1(5/3).
 
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.
 
Yep, that's what I did. You guys are completely correct. My mistake!
 

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