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# The Momentum Principle Vs Newton’s 2nd Law

Practical problem solving: When we do use conservation of momentum to solve a problem? When do we use Newton’s laws of motions?

Sometimes we need to use only one or the other; other times both are equally useful. And on other occasions some problems may require the use of both approaches. Rhett Allain on Wired.com  discusses this in “Physics Face Off: The Momentum Principle Vs Newton’s 2nd Law”

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CONSIDER THE FOLLOWING physics problem.

An object with a mass of 1 kg and a velocity of 1 m/s in the x-direction has a net force of 1 Newton pushing on it (also in the x-direction). What will the velocity of the object be after 1 second? (Yes, I am using simple numbers—because the numbers aren’t the point.)

Let’s solve this simple problem two different ways. For the first method, I will use Newton’s Second Law. In one dimension, I can write this as:

F (net – x) = m x ax

Using this equation, I can get the acceleration of the object (in the x-direction). I’ll skip the details, but it should be fairly easy to see that it would have an acceleration of 1 m/s2. Next, I need the definition of acceleration (in the x-direction). Oh, and just to be clear—I’m trying to be careful about these equations since they are inherently vector equations.

a = delta Vx / time

The article continues here:

Physics Face Off: The Momentum Principle Vs Newton’s 2nd Law