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.
'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).
To explain why the motion of the snowball sticking to the tree does not defy the Law of Conservation of Momentum, we can analyze the situation using the principle of momentum conservation.
According to the Law of Conservation of Momentum, the momentum of a system remains constant if there is no external force acting on it. In this case, the system consists of the child, the snowball, and the tree.
Before the collision (when the snowball hits the tree), the snowball and the child have some initial momentum. After the collision, the snowball sticks to the tree and both the snowball and the child come to rest.
Since there is no external force acting on the system (ignoring factors like air resistance), the total momentum of the system should remain unchanged before and after the collision. This means that the sum of the momentum of the child and the snowball before the collision is equal to the sum of their momentum after the collision, even if they come to a stop.
So, even though both the snowball and the child come to rest, the momentum is still conserved. However, after the collision, the momentum of the child and the snowball is transferred to the tree. The tree being a significantly larger and more massive object does not show any visible motion due to the transfer of momentum. This transfer of momentum allows the total momentum of the system to remain constant, in accordance with the Law of Conservation of Momentum.
In summary, the motion of the snowball sticking to the tree does not defy the Law of Conservation of Momentum because even though both objects come to rest, the momentum is transferred to the tree, ensuring that the total momentum of the system remains conserved.
To explain why the motion of the snowball sticking to the tree does not defy the Law of Conservation of Momentum, we need to consider the principles of momentum and the concept of an isolated system.
The Law of Conservation of Momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In this case, we can consider the snowball and the tree as the system.
Now, let's break down the situation step by step:
1. Initially, the snowball is moving towards the tree with a certain velocity. It has momentum (p1) given by the product of its mass (m) and velocity (v). The tree, being stationary, has zero momentum.
2. Once the snowball sticks to the tree, both the snowball and the tree come to a rest. This means that their final velocities are zero.
3. According to the Law of Conservation of Momentum, the total momentum of the system should remain constant. Therefore, the initial momentum of the system (p1) must be equal to the final momentum of the system (p2).
Now, let's consider where the momentum goes in this situation:
Since both the snowball and the tree come to a rest, their final velocities are zero (v = 0). Therefore, the final momentum of both the snowball and the tree (p2) is zero.
Now, the change in momentum (Δp) is given by the difference between the initial momentum (p1) and the final momentum (p2). In this case, Δp = p2 - p1 = 0 - p1 = -p1.
This negative change in momentum implies that the momentum of the system has decreased. But where does this momentum go?
In this case, as the snowball sticks to the tree, the momentum is transferred from the snowball to the tree. The tree, being a much larger and more massive object, absorbs the momentum of the snowball. This transfer of momentum causes both objects to come to a rest.
Therefore, while the individual momenta of the snowball and the tree change, the total momentum of the system (snowball + tree) remains conserved, in accordance with the Law of Conservation of Momentum.
To summarize, the motion of the snowball sticking to the tree does not defy the Law of Conservation of Momentum because, even though both objects come to a rest, the momentum is transferred from the snowball to the tree, resulting in a conservation of momentum for the system as a whole.