An object with mass m , initially at rest, explodes into two fragments, one with

Question

An object with mass m, initially at rest, explodes into two fragments, one with mass mA and the other with mass mB, where mA+mB=m.

Part A

If energy Q is released in the explosion, how much kinetic energy does each fragment have immediately after the collision?

Express your answers in terms of the variables mA, mB, and Q. Enter your answers separated by a comma.

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Part B

What percentage of the total energy released does each fragment get when fragment A has four times the mass of the other?

Enter your answers numerically separated by a comma.

An object with mass m, initially at rest, explodes into two fragments, one with mass mA and the other with mass mB, where mA+mB=m.

Part A

If energy Q is released in the explosion, how much kinetic energy does each fragment have immediately after the collision?

Express your answers in terms of the variables mA, mB, and Q. Enter your answers separated by a comma.

SubmitMy AnswersGive Up

Part B

What percentage of the total energy released does each fragment get when fragment A has four times the mass of the other?

Enter your answers numerically separated by a comma.

Explanation / Answer

A)

First let's suppose that the all the energy during collision is converted to kinetic energy(in reality it does not- sound, light, heat, etc may be produced although at negligible amount).because if we don't there is no way to find any answer.
KE= 0.5mv^2
KE=(m^2)*(v^2)/(m*2)
KE=((mv)^2)/2m
KE= P^2/2m .... P is the momentum
P^2=KE*2m

Since momentum is conserved during collision,
PA-PB=0
PA=PB
PA^2=PB^2
KE of A *2m of A=KE of B *2m of B
(KE of A)/(KE of B)=(m of B / m of A)
KE of A = (m of B / m of A) *KE of B..... eqn 1
B)
From the supposition we made at the beginning,
KE of A + KE of B = Q
(m of B / m of A) *KE of B+KE of B =Q
KE of B ((m of B / m of A) +1)=Q
KE of B = Q/((m of B / m of A)).... eqn 2
use eqn 1 and eqn 2 to calculate calculate KE of A
The second question is just about putting the values.
A gets 20% and B gets 80%.

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