Question

A 16.0 kg fish swimming @ 1.10m/s suddenly gobbles up a 4.40 kg fish. That is initially at rest. A) Find the speed of the large fish just after it eats the small one B) How much mechanical energy is lost?

The topic is Momentum

Answer 1

A) Using Law of Conservation of momentum that initial momentum is equal to final momentum we have

`m_l*v_"li" + m_s*v_"si" = m_l*v_"lf" + m_s*v_"sf"` .....(1)

After the smaller fish is eaten, both move with the same speed, hence

`v_"lf" =v_"sf"=v_"f"`

Also it is given that `v_"si"=0` With these two substitutions (1) becomes

`m_l*v_"li" = (m_l+m_s)*v_"f"`
`=> v_"f"=(m_l*v_"li")/(m_l+m_s)`

Inserting given values we get

`v_"f"=(16.0*1.10)/(16.0+4.40)`
`=> v_"f"= 0.863\ ms^-1`

B) Initial KE `= 1/2m_lv_"li"^2 =1/2xx16.0xx(1.10)^2= 9.68\ J`
Final KE `= 1/2(m_l+m_s)v_"f"^2 =1/2(16.0+4.40)(0.863)^2= 7.59\ J`

`Delta`KE`=` Final KE `-` Initial KE `= 7.59- 9.68 = -2.09\ J`