What is the kinetic energy of the piece of mass

AI Thread Summary
A body at rest explodes into two pieces with masses 2M and 3M, resulting in a total kinetic energy E. The conservation of momentum is applied to relate the velocities of the two pieces, leading to the equation 2u = 3v, where u and v are their respective velocities. The total kinetic energy is calculated using the formula 0.5mv², resulting in an expression of 15/4(m)(v²) = E. The kinetic energy of the mass 2M is derived to be 9v²m/4, which simplifies to (3/5)E. Thus, the kinetic energy of the piece of mass 2M is 3/5 of the total kinetic energy E.
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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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