Interesting Links (example problems):
Recoil velocity of a skater
Serway's presentation of momentum and impulse is more logical than mine. I have chosen to present only the methods of doing the problems rather than an integrated theory-problem solving document. For this reason, I discuss momentum in this document and leave impulse to the next, although they are interrelated. You should study Serway's presentation carefully, perhaps after going through these mini-lectures to find out how to do the problems.
Momentum:
Momentum is defined as mass times velocity, mv. Because velocity is a vector, momentum is also a vector with the same direction as velocity. When errors are made in doing momentum problems, they usually arise because the vector nature of momentum has been ignored.
Remember that the change in any quantity is the final value minus the initial value. The change in the momentum is the difference between vectors; if they are not one-dimensional, vector subtraction must be used!
Light has momentum, although it has no mass! So the definition is inadequate for electromagnetic waves (visible light is one example of an em wave). But that's not a topic for this course!
Conservation of Momentum:
Serway shows that, if an entire system of colliding bodies is included, the momentum of that system never changes. That's what "conservation" means and the law of conservation of momentum is one of great conservation principles of physics. You've already been introduced to the law of conservation of energy (which, as Einstein showed, needed to be broadened to "mass and energy"). The term "collision" may be a little more inclusive than you thought; explosions are collisions in reverse and the law applies to them as well. For example, a 300 kg artillery shell moving at 200 m/s in the x-direction has a momentum of 6 x 104i kg m/s. When it explodes, and supposing it breaks into only two particles (unlikely) , the (vector) sum of their momenta must be the same as the original momentum of the shell. Suppose one of the exploding pieces has a momentum of 12 x 104 i kg m/s. Then the other piece must have a momentum of -6 x 104 i kg m/s.
Kinds of Collisions:
When objects collide, some energy is usually lost to sound, deformation, and heat. Perhaps you've dropped a golf ball onto a hard surface to test its rebound. A good ball will rebound almost to the height from which you dropped it. If it returned to its original height exactly, it would have collided elastically with the surface. An elastic collision conserves kinetic energy; there is the same kinetic energy after the collision as before. Example 4 will illustrate the use of this conservation of "vis viva", as Christian Huygens called it several hundred years ago. Molecular collisions are good examples of elastic collisions.
Inelastic collisions are characterized by large changes in kinetic energy. The colliding bodies couple. Please see Example 2. Explosions are inelastic collisions (in reverse).
Partially elastic collisions are those that fall between the elastic and inelastic categories.
The conservation of momentum principle is the only conservation principle that can be used with partially elasic and inelastic collisions.
Example 1: A ball is thrown against a wall
Example 2: The collision of two railroad cars
Example 3: The decay of a radioactive isotope (explosion)
Example 4: The dance of the molecules