Name: Necessity of Friction
Uploaded: 2019-07-19
Duration: 4 min 40 s
Description: This video enables students to learn about friction, friction used in routine activities, loss of energy in the form of heat due to friction.

Question

State principle of conservation of linear momentum. Illustrate by an example.

Accepted Answer

The principle of conservation of linear momentum states that,

If no external forces act on the system of colliding objects, then the vector sum of the linear momentum of each body remains constant and is not affected by their mutual interaction.

To prove this principle, we consider a collision between two spheres A and B having masses of $m_{1}$ and $m_{2}$ respectively.

Let $u_{1}$ and $u_{2}$ be the velocities of the spheres before collision such that $u_{1}$ > $u_{2}$ and moving on the same straight line as shown in the figure. After collision, let their velocities be $v_{1}$ and $v_{2}$ on the same line. If they collide with each other for a short time interval t, each sphere exerts a force on the other sphere and so, the force experienced by A is given as

$F_{A B} = \frac{C h a n g e i n m o m e n t u m}{t i m e} = \frac{m_{1} (v_{1} - u_{1})}{t}$

Similarly, force experienced by B is

$F_{B A} = \frac{C h a n g e i n m o m e n t u m}{t i m e} = \frac{m_{2} (v_{2} - u_{2})}{t}$

According to Newton's third law of motion, the force experienced by A and B are equal and opposite,

$F_{A B} = - F_{B A}$

$\frac{m_{1} (v_{1} - u_{1})}{t} = \frac{- m_{2} (v_{2} - u_{2})}{t} m_{1} (v_{1} - u_{1}) = - m_{2} (v_{2} - u_{2}) m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$

Total momentum before collision is equal to the total momentum after collision, if no external forces act on them which proves the principle of conservation of linear momentum.

State principle of conservation of linear momentum. Illustrate by an example.

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