Question

State the principle of conservation of linear momentum. Explain, how you will prove this law. Explain one example, where we make use of this law.

Answer 1

Step 1: The principle of conservation of linear momentum

1. The principle of conservation of momentum states that if there is no external force is applied to the system of particles, then the linear momentum of the system of particles is conserved.

Step 2: Prove this law

1. Consider two objects of mass $m_1$ and $m_2$ are moving in the same direction with velocities $u_1$ and $u_2$ respectively. The two objects collide without any external force. After the collision, the two objects are moving with velocities $v_1$ and $v_2$.
2. The momentum of the system before the collision, $p_i=m_1{u}_1+m_2{u}_2$
   The momentum of the system after the collision, $p_f=m_1{v}_1+m_2{v}_2$
3. From Newton's second law, we have
   $F_{\text{ext}}=\frac{\text{change in momnentum}}{\text{time}}$
   $F_{\text{ext}}=\frac{p_f-p_i}{t}$
   Since, $F_{\text{ext}}=0,p_f=p_i$
   or $m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
   Hence, the momentum of the system is conserved.

Step 3: Example

1. We use this law in the case of collision of the gas molecules with the walls of the container in which they are kept.
2. The gas molecules have some speed with which they are moving inside the container.
3. They collide with the walls of the container and rebounded at the same speed.
4. Since there is no loss in the velocity due to any factor, the momentum of the system remains conserved.