Answer to Question #86603 in Mechanics | Relativity for Richard G. Cadizal

Question

Two equal mass object experience a totally inelastic elastic collision. Mass 1 has an initial velocity of 10 m/s in the negative y-direction. Mass 2 has an initial velocity of 10 m/s in the positive x-direction. The collision occurs at the origin. What is the magnitude and direction of the velocity of the combined mass? What is the kinetic energy conserved in the collision? If not what fraction of kinetic energy was lost?

Answer 1

According to the law of conservation of momentum:

$$u= (mv_1+mv_2)/(m+m)=(v_1+v_2)/2=10 m/s$$

Direction of the velocity of the combined mass:

$$α=135 ̊$$

The kinetic energy after the collision:

$$W_k=((m_1 +m_2)u^2)/2=100m$$

Fraction of kinetic energy was lost:

$$ΔT=W_k^{before collision}-W_k^{after collision}=(m_1 m_2)(v_1-v_2)^2/2(m_1+m_2)=0$$