# Proving the Law of Conservation of Momentum: An Example

• lonelywizard
In summary, the law of conservation of momentum can be proven through the equation F = dp/dt = 0, which follows from Newton's first law. While it may not be possible to explain why momentum is conserved, it has not been disproven and is accepted through proof by contradiction.
lonelywizard
Can someone help me to prove the law of conservation of momentum using an example?

Hmm... right now I can't really think of any that actually PROVES it. But I can prove that it always works no matter what situation it is applied to. Just show a situation, e.g. car accidents, rockets, springs even.

lonelywizard said:
Can someone help me to prove the law of conservation of momentum using an example?
The proof is one line:

$$F = dp/dt = 0$$

That is the definition of force. If the force acting is 0, dp/dt = 0 so p is constant.

AM

I don't actually thinks that actually proves it. That just defines force. Other than practical experiments, or actually showing it works in every situations, I can't really think WHY it must be so.

Perhaps it is derived from elastic collisions, and kinetic energy is conserved. Perhaps not.

QuantumCrash said:
I don't actually thinks that actually proves it. That just defines force. Other than practical experiments, or actually showing it works in every situations, I can't really think WHY it must be so.
Conservation of momentum follows from Newton's first law. Since:

$$F = dp/dt$$

IF:

$$F = 0$$

then: P = constant.

Why is Newton's first law true? It may not be. But to prove something, youi have to start with a premise. The premise is that F = dp/dt, Newton's first law. So far, no one has been able to show that it is not true.

AM

Last edited:
Ohhh... the problem of asking to "prove" versus "verify/demonstrate".

Andrew Mason said:
Why is Newton's first law true? It may not be. But to prove something, youi have to start with a premise. The premise is that F = dp/dt, Newton's first law. So far, no one has been able to show that it is not true.
AM

Thats proof by contradiction that is. Since you can't disprove it that means its right. I suppose you might accept it that way. But what I am going about is more that you can't proof by induction and you can't really explain WHY momentum is conserved.

## 1. What is the Law of Conservation of Momentum?

The Law of Conservation of Momentum states that in a closed system, the total momentum before and after a collision remains constant. This means that the total combined mass and velocity of the objects involved in the collision will remain the same.

## 2. How can the Law of Conservation of Momentum be proven?

The Law of Conservation of Momentum can be proven through experimental evidence. By measuring the mass and velocity of objects before and after a collision, we can calculate the total momentum and see if it remains constant. If the total momentum is the same before and after the collision, the Law of Conservation of Momentum is proven to be true.

## 3. Can you provide an example of proving the Law of Conservation of Momentum?

Yes, an example would be two billiard balls colliding on a frictionless surface. Before the collision, the total momentum of the two balls would be equal to the mass of ball 1 multiplied by its velocity, plus the mass of ball 2 multiplied by its velocity. After the collision, the total momentum should remain the same, even if the direction and speed of each ball may have changed.

## 4. What factors can affect the conservation of momentum in a collision?

In a collision, external forces such as friction or air resistance can affect the conservation of momentum. However, in a closed system where there are no external forces present, the conservation of momentum will still hold true.

## 5. How does the Law of Conservation of Momentum relate to Newton's Third Law of Motion?

The Law of Conservation of Momentum is closely related to Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. In a collision, the objects involved exert equal and opposite forces on each other, resulting in a transfer of momentum that follows the Law of Conservation of Momentum.

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