Force and Motion: An Illustrated Guide to Newton's Laws

17 Strategies for Applying Newton’s Laws

CHAPTER 17 Strategies for Applying Newton’s Laws In this chapter I’ll suggest some organized strategies that can help you in applying Newton’s Laws to understand physical situations and solve challenging physics problems. But before we get started, let’s talk about attitude. The Right Attitude There are some easy physics problems out there. “The net force acting on a cat is 5 N, and the cat is accelerating at 2 m/s2 . What is the mass of the cat?” (Answer: 2.5 kg.) If all you ever do are simple problems like this, you can easily get the impression that Fnet = ma is a two-out-of-three equation: Give me two out of the three quantities , and I’ll give you the third. But Fnet = ma is not a simple two-out-of-three equation. It’s not like “distance = rate × time” or “tip = bill × 15%.” The equation Fnet = ma is actually shorthand for an entire worldview: a grand vision of a mechanistic universe in which material particles are animated by their mutual interactions . Fnet = ma takes for granted the entire force concept, which took many pages to describe in Chapter 10. Fnet = ma demands that we know what acceleration means—a subtle concept that we spent three chapters on during the first half of this book. And finally , Fnet = ma relates two vectors that vary with time, with all the mathematical subtlety that that implies. 317 318 PART II EXPLAINING AND PREDICTING MOTION Please understand this: In physics problems of any significance , you are never “solving” Fnet = ma. Rather, you are using Fnet = ma as a framework to help you analyze a situation. I am talking about an important problem-solving attitude here. The grade-school attitude toward problem solving is “You give me the givens, and I’ll give you the unknown.” That won’t work in physics. In physics, I’ll give you a situation,and you’ll analyze it. What we’re looking for is a full understanding of the situation at hand. The specific quantities the problem does or doesn’t ask for are almost beside the point. A General Strategy for Solving Physics Problems A general strategy can help you get a handhold on a complicated problem that would otherwise leave you not knowing where to start. Even students who soak up physics like sponges have a hard time solving substantial problems until they learn good strategies. In fact, sometimes those students suffer even more in my classes, because their ability to do easier problems by ad hoc methods causes them to put off learning any disciplined strategies. Here, then, for your approval, is a general strategy for using Fnet = ma to solve physics problems. It’s the strategy I give to my students when I teach this subject. It takes most of a year for people to become fully comfortable with it. Some never even bother. But even in the early weeks of your study of physics, bits and pieces of the strategy can usually get you unstuck when you need a push. Without further ado, here’s the strategy. You’ll notice that there is no talk of “solving” anything until a tremendous amount of work has already been completed! After looking at the strategy, we’ll see how it plays out in an example. 1. For each target: a. Sketch the target’s acceleration vector at the instant of time under consideration. Do this by thinking about how the target is moving at this moment in time (speeding up/slowing/ turning). Make an assumption if you have to. b. Draw a force diagram showing all forces acting on the target. Give an algebra name to the magnitude of each force (we usually use letters like n, T, F1, F2, f , etc.). Chapter 17 Strategies for Applying Newton’s Laws 319 c. Based on the vectors in your force diagram, sketch the net force vector. Does the net force vector you sketched match the acceleration vector you sketched? If Fnet and a don’t point the same way, something’s wrong with your force diagram or your acceleration vector. d. Repeat this process for each of the targets in the problem. Don’tmoveonuntilyou’recomfortablewithyour force diagrams! Everything comes from the diagrams. Garbage in, garbage out. 2. Identify all of the Third Law pairs. This will help make sure you haven’t missed any forces...