Perfectly Inelastic Collisions

A block with a mass of 2.0kg has an initial velocity of 5.0 m/s. This block hits another block that has a mass of 1.0 kg that is initially at rest. What is the velocity of the two blocks after the collision? What percentage of initial kinetic energy do the blocks have after the collision? What is the total momentum after the collision?

Assume a perfectly inelastic collision and that there is no friction.

Momentum is conserved

Momentum – mass x velocity

P_f=P_i     \frac{(m_1+m_2) \cdot V_f}{m_1+m_2}=\frac{m_1 \cdot V_i}{m_1+m_2}

V_f=\frac{m_1 \cdot V_i}{m_1+m_2}  V_f=\frac{(2.0kg)(5.0m/s)}{2.0kg+1.0kg)}


\frac{KE_f}{KE_i} \cdot 100\% - \frac{\frac{1}{2}(m_1+m_2)(V_f)^2}{\frac{1}{2}m_1 \cdot (V_i)^2}\cdot 100 \%

=\frac{(2.0kg + 1.0kg)(3.3m/s)^2}{(2.0kg)(5.0m/s)^2} \cdot 100 \%


P_f = (m_1+m_2)V_f P_f=(2.0kg+1.0kg)(3.3m/s)

P_f=10.0 \frac{kg \cdot m}{s}