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Q9CQ

Expert-verifiedFound in: Page 287

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**Under what circumstances is momentum conserved?**

Momentum is conserved only in the absence of net external force (F_{net}) acting on the system.

The Law of conservation of momentum states that the total momentum of a system always remains constant before and after collisions or we can say that the initial momentum before the collision of a system is equal to the final momentum of the system after the collision

We have the equation for the momentum of an object of mass m moving with a velocity, *v* is given by $p=mv$

According to the law of conservation of momentum, $p=acons\mathrm{tan}t$

Or $mv=acons\mathrm{tan}t$

We know that *m *is a constant, so v must be a constant so that the above equation is valid.

That is $v=acons\mathrm{tan}t$

The velocity of an object is constant only when there is no force acting.

That is when *F* = 0, $v=acons\mathrm{tan}t$

We have Newton’s second law of motion in terms of momentum given by the equation,

${F}_{net}=\frac{\Delta p}{\Delta t}$ ,

where *F*_{net }is the net external force acting on the system.

Substitute the value of${F}_{net}=\text{}0\text{}N$ in the above equation we get,

$\frac{\Delta p}{\Delta t}=0$

Or we can say that,$\u2206p=0$ , or there is no change in momentum or momentum is a constant or momentum is conserved.

Hence, momentum will conserve only when there is no net external force acting on the system.

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