# Conservation of momentum of airplane in runway

On exercise 4.6 from Klepper's Book "Intro do mechanics" there is a plane on a landing lane. It has its engine off but is braking with force $$F_b$$. Also, it is attachted to a sandbag that does friction $$f_s$$. It asks how far the plane goes.

I found a solution for this exercise that says that momentum is conserved. But I do not understand how is the momentum conserved when there are external forces acting on the plane (the friction force of the sandbag). why is it conserved?

And if there were only the brakes, would the momentum be conserved?

Momentum is always conserved, but it is not always constant for any specified limited object or system. Forces transfer momentum from one object/system to another. In the case of the airplane, the friction removes momentum (and energy, but that's another question) from the plane, transferring it to the earth.

$$\vec{p}_f=\vec{p}_i + \int \vec{F} \mathrm{d}t$$

Remember: conservation does not necessarily mean constant for specified systems.

• “Momentum is always conserved, but it is not always constant for any specified limited object or system”. Well said! +1 – Dale Nov 22 at 14:43

Taking the earth and plane as the system momentum will be conserved as it will be an external force .As far as I know this is the only way it can be .

Even if there were only breaks friction on the tires is the external force on the plane system so it's not conserved

But then again if it was the earth mass system it will allways be conserved .