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 4 kg. What are the post-collision velocities of the balls?

1 Answer
Narad T.
Nov 23, 2017

The velocities are 4/3ms^-1 and 40/3ms^-1

Explanation:

Here it's an elastic collision with no loss of kinetic energy.

We have the conservation of momentum.

m_1u_1+m_2u_2=m_1v_1+m_2v_2

m_1=5 kg

u_1=12 ms^(-1)

m_2=4 kg

u_2=0

v_1=?

v_2=?

5*12+4*0=5*v_1+4*v_2

5v_1+4v_2=60............(1)

There is also conservation of kinetic energies

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

5*12^2+4*0=5*v_1^2+4*v_2^2

5v_1^2+4v_2^2=720.........(2)

From (1), we get

v_1=(60-4v_2)/5

Plugging this value in (2)

5*((60-4v_2)/5)^2+4v_2^2=720

((60-4v_2))^2/5+4v_2^2=720

16(15-v_2)^2+20v_2^2=720*5=3600

4(15-v_2)^2+5v_2^2=900

4(225-30v_2+v^2)+5v_2^2=900

900-120v_2+4v_2^2+5v_2^2=900

9v_2^2-120v_2=0

v_2(9v_2-120)=0

v_2=0 or v_2=120/9=40/3=13.3ms^-1

v_1=(60-4*40/3)/5=4/3ms^-1

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