What is the kinetic energy of the piece of mass

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Homework Help Overview

The problem involves a body that explodes into two pieces of different masses, specifically 2M and 3M, and seeks to determine the kinetic energy of the piece with mass 2M after the explosion, given a total kinetic energy E.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to set up the kinetic energy equations for both pieces but expresses uncertainty about how to calculate their velocities. They seek guidance on how to proceed with the problem.

Discussion Status

Some participants have introduced the concept of conservation of momentum as a potential approach to the problem. There is an ongoing exploration of how the kinetic energy relates to the masses and their velocities, but no consensus has been reached on the final answer.

Contextual Notes

The discussion includes hints about conservation principles, but specific values or methods for calculating the kinetic energy have not been fully resolved. The original poster's question reflects a common challenge in understanding the relationship between mass, velocity, and kinetic energy in explosive scenarios.

a150daysflood
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Homework Statement


A body, initially at rest, explodes into two pieces of mass 2M and 3M respectively, having a total kinetic energy E.
What is the kinetic energy of the piece of mass 2M after the explosion?


Homework Equations


0.5mv²=K.E


The Attempt at a Solution


The velocity of the 2 pieces of objects is different,how do i calculate?
Can anyone guide me on how to start?
0.5(2m)(v_1)² + 0.5(3m)(v_2)²=E
How do i proceed?
Thanks for reading,thinking,replying.
 
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Hint: During an explosion, what physical quantity (if any) of all the pieces is conserved?
 
Solution

using conservation of momentum,
0=2mu + 3m(-v)
2mu=3mv
2u=3v
u=3v/2

Total K.E
=1/2(2m)(3v/2)² + 1/2(3m)(v)²
=15/4(m)(v²)
=E

K.E for mass of 2m:
1/2(2m)(3v/2)²
=9v²m/4

Hence,K.E for 2m is 3m/5.
Okies thanks.
 
a150daysflood said:
Hence,K.E for 2m is 3m/5.
You mean KE = (3/5)E.
 

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