Law of conservation of momentum problem

[Ahalp]

Homework Statement

A falling rock gains momentum as its speed increases. Does this observation contradict the law of conservation of momentum. Explain.

Answer in the textbook:

This observation does not contradict the law of conservation of momentum. The momentum of the Earth increases toward the falling object. The amount of change in the earth’s velocity is so small it is imperceptible, so it appears the law of conservation is being contradicted, but it is not.

The Attempt at a Solution

My initial answer was that it doesn't contradict the law of conservation of momentum because it doesn't satisfy the conditions for the law. For momentum to be conserved, the net force on the system has to be zero. I wrote that the net force on the system is not zero as the apple is accelerating due to gravity. So, the law of conservation of momentum does not apply to it.

The textbook includes Earth in the system, but I didn't. However, if we don't include Earth in the system, would my answer make sense?

Thanks

 

[Matterwave]

Yes. If you define your system as the apple only, then your answer is correct. If you define your system as the apple and the Earth, then the book is correct. You can think of it in either way, which ever way is more convenient.

 

[Ahalp]

Yes. If you define your system as the apple only, then your answer is correct. If you define your system as the apple and the Earth, then the book is correct. You can think of it in either way, which ever way is more convenient.

Alright, thanks!

I just have one quick question relating to the original problem. If the system is set accordingly to include all the objects (like Earth and the apple in the original question), is momentum always conserved?