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
The topic is Momentum
1 Answer
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"ml⋅vli+ms⋅vsi=ml⋅vlf+ms⋅vsf .....(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
m_l*v_"li" = (m_l+m_s)*v_"f"ml⋅vli=(ml+ms)⋅vf
=> v_"f"=(m_l*v_"li")/(m_l+m_s)⇒vf=ml⋅vliml+ms
Inserting given values we get
v_"f"=(16.0*1.10)/(16.0+4.40)vf=16.0⋅1.1016.0+4.40
=> v_"f"= 0.863\ ms^-1
B) Initial KE
Final KE