Question

An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.3 times the mass of the other. If 8800 J is released in the explosion, all of which goes into the kinetic energy of the two pieces, how much kinetic energy does each piece acquire?

Answer 1

k_2 =3826.08 J

K_1 = 4973.91 J

Step-by-step explanation:

from conservation of momentum principle

`0 = m_1v_1+m_2v_2`

we know that kinetic energy is given as

`k_1 = (1)/(2) m_1v_1^2`

`k_2 = (1)/(2) m_2v_2^2`

we have
`v_1 =-1.3v_2`,
`m_2 = 1.3m_1`

therefore
`k_1 =(1)/(2) ((m_2)/(1.3))(-1.3v_2)^2 = 1.3k_2`

now

`k_1+k_2 = 8800`

`1.3k_2 +k_2 =8800`

k_2 =3826.08 J

K_1 = 4973.91 J