Question

4. A 30kg red ball is rolling to the right with a velocity of 4m/s and a green ball is rolling to the right with a velocity of 5m/s left. After the collision the red ball has a velocity of 2m/s left and the green ball is rolling to the left with a velocity of 4.5m/s left. What is the mass of the green ball?​

Answer 1

The question is confusing for the initial direction of the green ball. We assume to the left.

Answer:

The mass of the green ball is 360 Kg

Step-by-step explanation:

Law Of Conservation Of Linear Momentum

The total momentum of a system of bodies is conserved unless an external force is applied to it. The formula for the momentum of a body with mass m and velocity v is

P=mv.

If we have a system of bodies, then the total momentum is the sum of the individual momentums

`P=m_1v_1+m_2v_2+...+m_nv_n`

If some collision occurs, the velocities change to v' and the final momentum is:

`P'=m_1v'_1+m_2v'_2+...+m_nv'_n`

In a system of two masses, the law of conservation of linear momentum

is written as:

`m_1v_1+m_2v_2=m_1v'_1+m_2v'_2`

Let's call m1=30 Kg the mass of the red ball moving to the right at v1=4 m/s, m2 (unknown) the mass of the green ball moving at v2=-5 m/s to the left (assumed).

After the collision, the red ball rolls to the left at v1'=-2 m/s and the green ball is at v2'=-4.5 m/s. Thus:

`30*4+m_2*(-5)=30*(-2)+m_2(-4.5)`

Operating:

`120-5m_2=-60-4.5m_2`

`120+60=5m_2-4.5m_2`

`180=0.5m_2`

`m_2=180/0.5=360`

The mass of the green ball is 360 Kg