Two bodies of masses 1 kg and 0.5 kg move towards each other with velocities `10 cm *s^(-1) and 5 cm *s^(-1)` respectively . After collision, the bodies coalesce (join together). Find the common velocity after collision and the loss in kinetic energy.

Explanation

Let the velocity of the combined mass after collision be v. from the law of conservation of momentum ,
`m_1u_1+m_2u_2=(m_1+m_2)v`
` or, 1xx0.1+0.5xx(-0.05) =(1+0.5)v`
`or, 0.1 -0.025=1.5 v or, v=(0.075)/(1.5) =0.05 m*s^(-1)`.
This implies that the velocity of the combined mass is along the direction of the initial velocity of the 1 kg mass.
Initial kinetic energy of the bodies
`=(m_1u_1^2)/2+(m_2u_2^2)/(2) =1/2xx1xx(0.1)^2+1/2xx(0.5)xx(0.05)^2=5.625xx10^(-3)`J
Final kinetic energy of the combined mass after collision
`=(m_1+m_2)^((v_2)/(2))`
`=1/2 xx(1+0.5)xx(0.05)^2=1.875xx10^(-3)`J
`therefore` Loss in kinetic energy
`=(5.625-1.875)xx10^(-3)=3.75xx10^(-3)`J.