A ball with a mass of 2 kg2kg is rolling at 25 m/s25ms and elastically collides with a resting ball with a mass of 2 kg2kg. What are the post-collision velocities of the balls?

1 Answer
Nov 11, 2017

The velocities of the balls are =0ms^-1=0ms1 and =25ms^-1=25ms1

Explanation:

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

Let the velocity before collision be u_1ms^-1u1ms1 and u_2ms^-1u2ms1

Let the velocity after collision be v_1ms^-1v1ms1 and v_2ms^-1v2ms1

m_1u_1+m_2u_2=m_1v_1+m_2v_2m1u1+m2u2=m1v1+m2v2

1/2m_1u_1^2+1/2m_2u_2^2=1/2m_1v_1^2+1/2m_2v_2^212m1u21+12m2u22=12m1v21+12m2v22

Here, we have

m_1=m_2=2kgm1=m2=2kg

u_1=25ms^-1u1=25ms1

u_2=0ms^-1u2=0ms1

Therefore,

v_1+v_2=25v1+v2=25

v_1^2+v_2^2=25^2=625v21+v22=252=625

v_1=25-v_2v1=25v2

(25-v_2)^2+v_2^2=625(25v2)2+v22=625

625-50v_2+v^2+v^2=62562550v2+v2+v2=625

2v_2^2-50v_2=02v2250v2=0

2v_2(v_2-25)=02v2(v225)=0

v_2=25v2=25 and v_1=0v1=0