TP 9.27

Given: m₁ = 0.004 kg, v_1,i = 650 m/s

            m₂ = 0.095 kg, v_2,i = 0

               v_2,f = 23.0m/s

Find: (a) v_1,f

p_{tot, i} = m₁ v_1,i + m₂ v_2,i = m₁ v_1,i 

p_tot,f = m₁ v_1,f + m₂ v_2,f

p_tot,i = p_tot,f 

m₁ v_1,i  = m₁ v_1,f + m₂ v_2,f

m₁ v_1,f =  m₁ v_1,i  -  m₂ v_2,f

v_1,f =  (m₁ v_1,i  -  m₂ v_2,f ) / m₁

v_1,f =  104 m/s

(b)  Part of the bullet's initial kinetic energy went into the deformation of the block, thus we expect the final energy to be less than initial.

(c) 

K_tot,i  = 1/2 m₁ v_1,i² = 845 J

 K_tot,f  = 1/2 m₁ v_1,f² + 1/2 m₂ v_2,f² = 21.6 J + 25.1 J = 46.7 J, just what we expected!