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”
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: