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Chapter 4 - Forces and Motion: Newton’s Framework
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CHAPTER 4 Forces and Motion: Newton’s Framework Newton’s laws of motion When forces add up to zero: the first law What force really is: the second law Units Inertial mass, gravitational mass, and the principle of equivalence Adding forces: vectors One dimension Two or more dimensions Force diagrams Vector components More on friction Object or system? Momentum and its conservation. Action, reaction, and Newton’s third law One more motion that is everywhere: rotation Uniform circular motion Angular momentum and torque The angular momentum of particles What does it take to get something to move?You have to push a book to make it start to slide along the table. You have to throw a ball to make it leave your hand to fly through the air.The push on the book and that of your hand on the ball as you throw it are the forces that determine the motion.The book’s motion depends not only on how hard you push, but also on the table and how smooth it is.The ball’s motion also depends on forces other than that of your hand. Once the ball leaves your hand, the hand no longer exerts a force on it.The other forces continue to act: the earth pulls it down with the force of gravity. And on its way the air pushes against it and affects the path that it follows. 58 / Forces and Motion: Newton’s Framework It’s easy to think of more complicated examples. When you are on a bicycle, the downward push of your feet is linked to forces that make the bicycle move forward. And just think of all the forces that act in a moving car. It took a long time for the relation between force and motion to be clarified. It was Isaac Newton, in the seventeenth century, who developed the framework that we still use today. 4.1 Newton’s laws of motion When the forces add up to zero: the first law One of Newton’s breakthrough contributions was to see that it takes no force at all just to keep an object moving in a straight line with constant speed. A nonzero net force is there only when the motion changes in speed or direction, in other words, when there is an acceleration. Let’s look at what happens when we slide a book along a table. At first it just sits there. We push it and it speeds up. We let go and it slides along by itself for a short distance. It slows down and comes to rest. On a smoother table it goes farther. On ice the same push makes it go quite far. In each case there is some friction, but the less friction there is, the farther the book moves. We can now imagine, as Newton did, that if there were no friction at all, the book would continue to move without losing speed. Today we can get quite close to that situation by letting an object move on a cushion of air, on an air track or air table. (You may also be familiar with a game called air hockey, in which a puck moves on a cushion of air, almost without friction.) To make an object slide on a smoother and smoother surface is something we can do. It’s an experiment. To make it move without any friction is something we cannot do. It’s an ideal situation that we can only approach. Newton imagined what would happen in this ideal case, and concluded that if there were no friction, and no other horizontal force, the book would continue to move in a straight line with constant speed. Are there any forces on the book when it just sits still on the table? Is the earth still pulling down on it? If the table were not there, the earth would pull the book down and it would fall to the floor. The table keeps it from falling, and while the earth pulls down, the table pushes the book up. The two forces, the force down by the earth and the force up by the table, are of equal size but in opposite directions. Their effects cancel each other out and the net force is equal to zero. Since there is no net force there is no change in the motion of the book. Ftb Feb Each force is an interaction. It takes two! Whether it’s...