A ball with a mass of 3 kg is rolling at 8 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.
Jan 5, 2018

The post collision velocities are =-1.14ms^-1 and =6.86ms^-1

Explanation:

In an elastic collision, there is conservation of momentum and conservation of kinetic energies.

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

Here,

The masses are

m_1=3kg

and m_2=4kg

The initial velocities are

u_1=8ms^-1

and u_2=0ms^-1

3*8+4*0=3*v_1+4*v_2, <=>, 3v_1+4v_2=24........(1)

1/2*3*8^2+1/2*4*0^2=1/2*3*v_1^2+1/2*4*v_2^2

3v_1^2+4v_2^2=192.............................(2)

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

From (1), v_2=(24-3v_1)/4

Substituting is (2)

3v_1^2+4*((24-3v_1)/4)^2=192

12v_1^2+(24-3v_1)^2=768

12v_1^2+576-144v_1+9v_1^2=768

21v_1^2-144v-192=0

7v_1^2-48v-64=0

v_1=(48+-sqrt((-48)^2-4*7*(-64)))/(2*7)

=(48+-sqrt(4096))/(14)

=(48+-64)/(14)

So,

v_1=((48+64)/14)=8ms^-1, =>, v_2=0ms^-1

This is the initial conditions.

or

v_2=((48-64)/14)=-1.14ms^-1, =>, v_2=6.86ms^-1

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