'No' is the answer to your first paragraph question. The tree moves slightly after being hit, thus conserving momentum. The tree soon stops swaying and reverses direction due to forces applied to the roots by the soil.
Your second paragraph does not correctly state the Law of Conservation of Energy. You are talking about momentum conservation. In the case of the tree hit by the snowball, there IS a net force applied to the system (at the tree's roots).
Please Help !
A child throws a snowball at a tree and it sticks to the tree. Does this motion defy the Law of Conservation of Momentum? Explain.
The Law of Conservation of Energy states: "If there is no net force acting on a system of objects, the total momentum in that system before a collision is equal to the total momentum in the system after the collision."
How can I use this to explain how the aforementioned situation does not defy the law. Maybe help by explaining where the momentum would go given that p=mv and neither object is changing mass, but they are both coming to a rest.
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