A ball with a mass of $6 kg$ is rolling at $2 m/s$ and elastically collides with a resting ball with a mass of $8 kg$ . What are the post-collision velocities of the balls?

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Answer 1 · 2018-03-30T14:47:57

The post collision velocities of the balls are $=-2/7ms^-1$ and $=12/7ms^-1$

As the collision is elastic, there is conservation of momentum and conservation of kinetic energy

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$1/2m_1u_1^2+1/2m_2u_2^2=1/2m_1v_1^2+1/2m_2v_2^2$

The mass the first ball is $m_1=6kg$

The velocity of the first ball before the collision is $u_1=2ms^-1$

The mass of the second ball is $m_2=8kg$

The velocity of the second ball before the collision is $u_2=0ms^-1$

The velocity of the first ball after the collision is $=v_1$

The velocity of the second ball after the collision is $=v_2$

$6*2+8*0=6v_1+8v_2$

$3v_1+4v_2=6$

$v_1=(6-4v_2)/3$ ..................... $(1)$

$1/2*6*2^2+1/2*8*0=1/2*6*v_1^2+1/2*8*v_2^2$

$6v_1^2+8v_2^2=24$

$3v_1^2+4v_2^2=12$ ........................... $(2)$

From equations $(1)$ and $(2)$ , calculate $v1$ and $v_2$

$3*((6-4v_2)/3)^2+4v_2^2=12$

$36-48v_2+16v_2^2+12v_2^2=36$

$28v_2^2-48v_2=0$

$4v_2(7v_2-12)=0$

$v_2=0$ or $v_2=12/7$

$v_1=2$ or $v_1=-2/7$

A ball with a mass of 6 kg 6 kg is rolling at 2 m/s2 m/s and elastically collides with a resting ball with a mass of 8 kg 8 kg. What are the post-collision velocities of the balls?