# General Conservation of Momentum Question

• putongren
In summary, the conversation discusses the use of conservation of momentum in solving planet versus satellite problems. The participants question why this principle is chosen and why other methods such as dynamics or conservation of energy may be more complex. It is explained that using conservation laws allows for a simpler solution and avoids the need to solve differential equations. However, solving the problem using other principles may require finding the trajectory and differentiating it, making it more complicated.
putongren
Hey All,

I was looking at several conservation of momentum question, and one question caused me to thinking about something. In those planet versus satellite questions, a satellite passes through a moving planet and the gravitational pull of the planet alters the final satellite's velocity and vice versa. I was wondering why do we use the conservation of momentum principle to solve for the final velocity of the satellite and the planet.

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Because that's the most simple way to solve the problem. One could try and solve the problem using dynamics or conservation of energy, but it's more complicated.

Hey Andy,

Thanks for the reply, but I think what I'm really trying to ask is why does the conservation of momentum principle work in solving this type of problem. It's not enough for me to just memorize the fact that you use conservation of momentum to solve the planet versus satellite problem, I have to know why you choose it to work. Also, you mentioned other ways to solve this type of problem by using dynamics or conservation of energy. Can you give me an example of how one would go about using those principles?

how would you try and solve the problem?

Allthough I havn't gone through the calculations then I think that solving problems like that with anything other then conservation laws you would have to find the path of the trajectory (which involves solving some differential equations) and then get the final velocity from the trajectory path by differentiation.

This of course is a lot more complicated then with simple algebra using conservation laws.

Hope this explains it a bit (again, I havn't gone through the calculations so take this with a grain of salt).

## 1. What is the law of conservation of momentum?

The law of conservation of momentum states that the total momentum of a closed system remains constant over time, regardless of any external forces acting on the system. This means that the total amount of momentum before an event or interaction is equal to the total amount of momentum after the event or interaction.

## 2. How is momentum defined?

Momentum is defined as the product of an object's mass and velocity. It is a vector quantity, meaning it has both magnitude and direction. The unit of momentum is kilogram-meter per second (kg*m/s).

## 3. What is an example of the conservation of momentum in action?

A common example of the conservation of momentum is when two billiard balls collide. Before the collision, each ball has a certain amount of momentum. After the collision, the total momentum of both balls remains the same, even though they may have changed directions or speeds.

## 4. Does the conservation of momentum apply to all types of systems?

Yes, the conservation of momentum applies to all types of systems, including macroscopic objects, subatomic particles, and even the entire universe. However, in some cases, the conservation of momentum may appear to be violated due to external forces that are not taken into account.

## 5. How is the conservation of momentum related to Newton's laws of motion?

The 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 other words, the momentum lost by one object in an interaction is equal to the momentum gained by the other object, resulting in the total momentum remaining constant.

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