Question

Determine the momentum of a system of the two objects. One object, m1, has a mass of 3.5 kg and a velocity of 20 m/s towards the north and the second object, m2, has a mass of 15 kg and a velocity of 40 m/s towards the south. What direction is the momentum of the system?

Answer 1

Given:

The mass of the 1st object, m₁=3.5 kg

The velocity of the 1st object, v₁=20 m/s to north

The mass of the second object, m₂=15 kg

The velocity of the second object, v₂=-40 m/s to south

To find:

The momentum of the system.

Explanation:

Let us consider north as the positive y-axis and south as the negative y-axis. Thus the velocity of the second object is negative.

The momentum of an object is the product of the mass of the object and the velocity of the object.

The total momentum of a system is equal to the sum of the momentum of the individual entities of the system

Thus the total momentum of the system is given by,

$p=m_1v_1+m_2v_2$

On substituting the known values,

$\begin{gathered} p=3.5\times20+15\times-40 \\ =-530\text{ kg}\cdot\text{m/s} \end{gathered}$

The negative sign of the momentum indicates that the direction of the total momentum of the system is directed towards the south.

Final answer:

The total momentum of the system is 530 kgm/s towards the south.