Question

How would you convince somebody that the momentum of an isolated system is constant?

Answer 1

The easiest and most effective way to convince him is by practical experiment.

For an isolated body, the total momentum should be conserved, this means that:
total momentum before collision = total momentum after collsion
M1V1 + M2V2 = M1V1' + M2V2'

So, get to masses and record their initial velocities. Then let these two masses collide and measure their final velocities.
Substitute with the masses and the recorded velocities in the above equations to verify the law.

Another way to convince him is by deriving the above equation from Newtons's second law.

Answer 2

The momentum of an isolated system is conserved.

Further Explanation:

The system is isolated in nature i.e., no external force is acting on the system.

Concept:

The Newton's second law states that the rate of change of momentum with respect to time is equal to the to the net force on the system.

The net force on the system is:

$F_{net}=\dfrac{\Delta p}{\Delta t}$                                           ....... (1)

Here, $F_{net|$ is the net force on a system, $\dfrac{\Delta p}{\Delta t}$ is the rate of change of momentum.

The equation (1) can be rewritten as:

$F_{net}=\dfrac{m(v-u)}{\Delta t}$                       ....... (2)

The net force on an isolated system is zero. Therefore, the above equation can be rewritten as:

$mv=mu$                                                            ...... (3)

Here, $m$ is the mass of the system, $u$ is the initial velocity of the system and $v$ is the final velocity of the system.

The momentum of a system is defined as the product of mass of the system and the velocity with which system is moving. Therefore, from equation (3) the initial momentum of the system is equal to the final momentum of the system.

$\fbox{\begin\\p_f=p_i\end{minispace}}$

Consider an isolated system of mass $m$, it contains $n$ number of particle. The particles present in the system are of different mass.

Initially the system is moving with velocity $u$. The net initial momentum of the system is equal to the initial momentum of each particle.

The net value of initial momentum of the system is:

$p_i={m_1}{u_1}+{m_2}{u_2}+{m_3}{u_3}+.........+{m_n}{u_n}$                                               ....... (4)

After certain time interval, the system starts to move with velocity

The net value of final momentum of the system is:

$p_f={m_1}{v_1}+{m_2}{v_2}+{m_3}{v_3}+.........+{m_n}{v_n}$                        ...... (5)

The net force on the entire system is equal to the amount of force acting on each particle.

The net force on the system is:

$F_{net}=F_1+F_2+F_3+...........+F_n$

The net force on an isolated system is zero and also from equation (2) the above expression can be written as:

$m_1({v_1}-{u_1})+m_2({v_2}-{u_2})+........+m_n({v_n}-{u_n})=0$

Simplify the above expression.

$({m_1}{v_1}+{m_2}{v_2}+............+{m_n}{v_n})-({m_1}{u_1}+{m_2}{u_2}+............+{m_n}{u_n})=0$

From equation (4) and equation (5) the above expression can be rewritten as.

$\fbox{\begin\\p_f=p_i\end{minispace}}$

Thus, the momentum of an isolated system is conserved.

Learn more:

1.  The motion of a body under friction brainly.com/question/4033012

2.  A ball falling under the acceleration due to gravity brainly.com/question/10934170

3. Conservation of energy brainly.com/question/3943029

Answer Details:

Grade: College

Subject: Physics

Chapter: Kinematics

Keywords:

Conservation, momentum, system of particles, initial momentum, final momentum, isolated system, net force, external force, second law of motion, rate of change of momentum with respect to time.