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Mechanics in Review By now, you should have the distinct impression that Newton’s laws of motion are pretty much responsible for everything in mechanics. If you really understand them, as opposed to being able to repeat them, then you understand all the concepts in mechanics. In addition, you should see that the problem solving techniques for mechanics fit into four categories: FBD’s, kinematics, energy, or momentum. Sometimes there is more than one way to skin a problem, but all solutions fit into one of the four topics. So, the rest of this presentation is devoted to emphasizing where to apply the techniques in problem solving. Knowing When to Apply What A major advancement in your ability to do physics is realizing which problem solving technique works best for a particular situation. Being able to discern among these techniques and their applications, then, is of paramount importance for your eventual success. What follows is a discussion of how and what to recognize in the events in a problem so that you may attempt solving the problem quickly. Generally, I recommend a series of self-interrogative questions that will guide to approaching the problem in a fashion that will allow you to solve it correctly. Was there a collision? Generally, the first place to start is by asking yourself if some kind of collision occurred. In 99% of these situations recognizing a collision is easy. One object runs into another. However, I maintain that a collision can occur even when the two objects don't "hit," so to speak. It is just as much a collision when the field of the objects interact. In fact, objects never truly hit each other, so all collisions are really merely field interactions. Regardless, when you see a problem where one object moves toward another such that the two objects exert forces on each other a collision has taken place. Why is this important? Whenever a collision occurs, you know momentum must be conserved. Whether it is linear or angular, momentum is conserved. Guaranteed! So does this mean that you immediately jump into writing an expression where momentum before equals momentum after? Not necessarily. There are several possible approaches. Conservation of linear momentum (mv)--is most likely in a situation where you have two objects moving in straight lines before and after the collision. Frequently, you will also need to consider conservation of energy if the collision is elastic or where energy is conserved once the collsion has taken place. Remember momentum must be conserved in all dimensions (x, y, and z). Conservation of angular momentum (Iw or mvrsin q)--is likely in a situation where you have orbits or collisions with objects that will rotate as opposed to translate. Here, too, conservation of energy may be used if the collision is elastic or where energy is conserved once the collsion has taken place. Impulse (Dp = FDt--you can frequently see this when graphical information is present. Also, be alert when time is mentioned as a consideration. Was there a change in position and velocity? Your first thought should jump to energy considerations, although force and kinematics may allow an alternate approach (this only works for constant forces, at least as far as what we have studied). Therefore, using work and energy is generally safer when approaching problems like this. Work/Energy (DKE +DU = Wncf or Fxcos q). Where non conservative forces aren't present, then the sum of the changes in potential and kinetic energies is 0 (known as conservation of energy). Far and away, the most prominent non conservative force is friction. However, friction doesn't act as a non conservative force unless sliding is involved. When rolling occurs, friction acts to transfer potential energy to rotational kinetic energy instead of it all going to translational kinetic energy. |