A ball with a mass of 5 kg is rolling at 1 m/s and elastically collides with a resting ball with a mass of 4 kg. What are the post-collision velocities of the balls?

1 Answer
Jun 28, 2018

The post collisions velocities are =011ms^-1 and =1.411ms^-1

Explanation:

Since the collision is elastic, we have conservation of momentum

m_1u_1+m_2u_2=m_1v_1+m_2v_2

And conservation of kinetic energy

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=5kg

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

The mass of the second ball is m_2=4kg

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_1ms^-1

The velocity of the second ball after the collision is =v_2ms^-1

Therefore,

5*1+4*0=5*v_1+4*v_2

4v_2+5v_1=5....................................(1)

1/2*5*1^2+1/2*4*0=1/2*5*v_1^2+1/2*4*v_2^2

4v_2^2+5v_1^2=5..............................(2)

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

From equation (1), v_2=(5(1-v_1))/4

Substituting in equation (2)

5v_1^2+4*((5(1-v_1))/4)^2=5

4v_1^2+5+5v_1^2-10v_1=4

9v_1^2-10v_1+1=0

v_1=(10+-sqrt(((-10)^2)-4(9)(1)))/(18)=(10+-8)/18

Therefore,

v_1=1ms^-1 or v_1=1/9=0.11ms^-1

v_2=0ms^-1 or v_2=10/9=1.11ms^-1

The first solutions are the initial conditions.

The post collisions velocities are =011ms^-1 and =1.411ms^-1