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

1 Answer
May 25, 2018

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"mlvli+msvsi=mlvlf+msvsf .....(1)

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

v_"lf" =v_"sf"=v_"f"vlf=vsf=vf

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

m_l*v_"li" = (m_l+m_s)*v_"f"mlvli=(ml+ms)vf
=> v_"f"=(m_l*v_"li")/(m_l+m_s)vf=mlvliml+ms

Inserting given values we get

v_"f"=(16.0*1.10)/(16.0+4.40)vf=16.01.1016.0+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

DeltaKE= Final KE - Initial KE = 7.59- 9.68 = -2.09\ J