Question

Blocks A and B are moving toward each other. A has a mass of 6.1 kg and a velocity of 1.5m/s, while B has a mass of 1.7kg and a velocity of −9.8m/s. They suffer a completely inelastic collision. During the collision, how much kinetic energy is lost?

Answer 1

The law of conservation of momentum says

$$m_Av_A+m_Bv_B=(m_A+m_B)u$$

The final velocity of system

$$u=\frac{m_Av_A+m_Bv_B}{m_A+m_B}\\=\frac{6.1*1.5+1.7*(-9.8)}{6.1+1.7}=-0.96\:\rm m/s$$

The loss in kinetic energy

$$\Delta E=\frac{m_Av_A^2}{2}+\frac{m_Bv_B^2}{2}-\frac{(m_A+m_B)u^2}{2}$$

$$\Delta E=\frac{6.1*1.5^2}{2}+\frac{1.7*9.8^2}{2}-\frac{(6.1+1.7)*0.96^2}{2}$$

$$\Delta E=85\:\rm J$$