A 1 ~kg ball moving with a speed of 6 ~ms ⁻¹ collides headon with a 0.5 ~kg ball moving in the opposite direction with a speed of 9 ~ms ⁻¹ . If the coefficient of restitution is 1 3 , then the energy lost in the collision is

Step-by-step solution

Using KE = m₁ m₂ 2 (m₁+m₂ ) (1-e^2 ) (u₁+u₂ )^2 Given: m₁=1 ~kg aligned & m₂= 1 2 ~kg ; & u₁=6 ~ms ⁻¹ ; u₂=9 ~ms ⁻¹ and e= 1 3 & KE = 1 1 2 2 (1+ 1 2 ) [1- ( 1 3 )^2 ](6+9)^2 & = 1 2 2 6 8 9 (15)^2 & = 1 6 8 9 225 & =33.33 ~J aligned