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### College Physics (Urone)

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 (Fnet) acting on the system.

See the step by step solution

## Step1: The statement of the law of conservation of momentum.

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

## Step 2: Proving that the momentum will conserve only in the absence of net external force.

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 Fnet 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,$∆p=0$ , 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.