A ball with a mass of 5 kg is rolling at 12 m/s and elastically collides with a resting ball with a mass of 2 kg. What are the post-collision velocities of the balls?

1 Answer
May 22, 2018

The velocities are =5.14ms^-1 and =17.14ms^-1

Explanation:

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_2^21/2m_1v_1^2+1/2m_2v_2^2

Threfore,

5*12+2*0=5v_1+2v_2

5v_1+2v_2=60............................(1)

1/2*5*12^2+1/2*2*0^2=1/2*5v_1^2+1/2*2v_2^2

5v_1^2+2v_2^2=720.........................(2)

Solving for v_1 and v_2 in equations (1) and (2)

{(5v_1+2v_2=60),(5v_1^2+2v_2^2=720):}

<=>, {(v_2=1/2(60-5v_1)),(5v_1^2+2v_2^2=720):}

5v_1^2+2*(1/2(60-5v_1))^2=720

10v_1^2+3600-600v_1+25v_1^2=1440

35v_1^2-600v_1+2160=0

v_1=(600+-sqrt((-600)^2-4*35*2160))/(2*35)

=(600+-240)/70

Therefore,

v_1=12ms^-1 or v_1=5.14ms^-1

v_2=0ms^-1 or v_2=17.14ms^-1