1. DYNAMICS Force Mass and Weight Newton’s Laws “If I have been able to see further, it was only because I stood on the shoulders of giants.”—Isaac Newton

2. In chapters 2 and 3 we described motion in terms of position, velocity, and acceleration. We didn’t consider the causes of motion. In chapter 4, we begin our investigation of the causes of motion. The grade school definition—a force is a push or a pull—works OK here too. Chapter 4 Force and Motion: Dynamics 4.1 Force

3. Forces have both magnitude and direction, so forces are vector quantities. In our diagrams, we will show that a force is exerted on an object by “connecting” it to that object: F Later, it will matter where the force acts on the body, but don’t worry about that yet. Don’t draw forces like this: F

4. F The top ten reasons why I insist you draw forces emanating from the object… 10. To be consistent with Physics 23. 9. I’m the dictator here! That’s enough reasons for me.

5. Why study Newton’s laws? We use them to solve an enormous number of real-world problems. Most of the first half of your text is applications of Newton’s laws. Matter has inertia. Why study Newton’s laws?Why study Newton’s laws? We use them to solve an enormous number of real-world problems. Matter has inertia. An object at rest “wants” to stay at rest.Matter has inertia. An object at rest “wants” to stay at rest. A moving object “wants” to keep moving. There are lots of different ways to state Newton’s first law. Here’s one: an object at rest remains at rest unless acted on by a nonzero net force There are lots of different ways to state Newton’s first law. Here’s one: an object at rest remains at rest unless acted on by a nonzero net force, and an object moving with a uniform speed in a straight line continues that motion unless acted on by a nonzero net force. *If Galileo discovered this, why is it Newton’s law? 4.2 Newton’s* First Law of Motion

6. Newton’s laws are valid only in inertial (non-accelerated) reference frames. The earth is (approximately) such a reference frame. We already defined mass (chapter 1). In the context of this chapter, mass is the measure of the inertia of a body (a measure of its resistance to a change in its state of motion). Mass and weight are different, but you already know that… You may not realize there are two different kinds of mass.* *Which are, to the best of our ability to measure, the same. 4.3 Mass

7. It is an experimental observation that a net force applied to an object causes the object to accelerate, with the acceleration directly proportional to the force. Mathematically: This equation cannot be derived; it is a postulate that our experience suggests always works in macroscopic inertial reference frames. The SI unit of force is the newton: 4.4 Newton’s Second Law of Motion

8. A note on nomenclature and abbreviations— a unit named after a person is written in lowercase newton joule ohm watt but abbreviated in uppercase N J  (uppercase Greek letter) W. The English unit of force is the pound. To help your intuition get going, a force of 1 pound is equal to a force of 4.45 newtons.

9. Remember that a component version of an OSE is also an OSE, so the following are equally valid The summation sign on the left hand side is necessary because the net force—the sum of all forces acting—produces the acceleration. The net force produces a single acceleration, not a collection of accelerations which sum to a net acceleration.

10. What’s in your toolbox now? Kinematics, plus Newton’s second law. Newton’s second law requires an acceleration, so… D=55 m V i =100 km/hV f =0 a=? x x i =0 mx f =55 m …you know the kinematics problem-solving drill… Example 4-2. What net force is required to bring a 1500 kg car to rest from a speed of 100 km/h within a distance of 55 m.

11. D=55 m V i =100 km/hV f =0 a=? x x i =0 mx f =55 m this is the magnitude; the figure shows the direction

12. Time now for something different… …a force problem.

13. a F net m x this is the magnitude; the figure shows the direction

14. 4.5 Newton’s Third Law of Motion There is a new litany for force problems. Not surprisingly, it is called the “Litany for Force Problems.”Litany for Force Problems It may appear to be something new, but many of the steps correspond to steps in the Litany for Kinematics. “For every action, there is an equal and opposite reaction...”“For every action, there is an equal and opposite reaction...” That’s probably the way you’ve heard it before. “Action” and “reaction” refer to forces. A “better” way to phrase this law: if object A exerts a force on object B, then object B exerts and equal and opposite force on object A.

15. “Wait a minute… …if for every force, there is another equal and opposite force, shouldn’t the sum of all forces be zero and therefore motion impossible?” The forces in Newton’s second law are all the forces exerted by other objects on the object in question. The “equal and opposite” forces in Newton’s third law are forces on different objects. Only the forces on the object in question go into Newton’s second law. Let me do a couple of demonstrations of Newton’s third law… try to identify the action-reaction pairs.

16. If object A exerts a force on object B, then object B exerts and equal and opposite force on object A. More examples: (http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html identify all the action- reaction pairs

17. Example: (http://hyperphysics.phy-astr.gsu.edu/hbase/incpl.html#c1)http://hyperphysics.phy-astr.gsu.edu/hbase/incpl.html#c1 Let’s just look at the “rope” connecting the two masses. We will learn how to solve this problem soon. This example introduces the concept of “tension.” Read about on page 86 of your text.

18. Newton’s third law gives us one new OSE: How to remember the order of the subscripts: we will be particularly interested on the forces ON an object. Forces on come first. Therefore, you may write (if you wish)

19. 4.6 Weight The Force of Gravity and the Normal Force On earth, the weight of an object is the gravitational force exerted on the object by the earth. If the object has mass m, the magnitude of weight is always mg: In the inclined plane picture we saw a couple of slides back, the weight of the object on the plane is m 1 g, and the weight of the hanging object is m 2 g. Both are directed “down.” Caution: this picture violates at least one of the rules in our litany for force problems.

20. We also saw this picture a few slides back. The combined 250 N mass exerts a downward force on the scale. The scale exerts an equal and opposite force upward. The contact force resulting from an object pushing on a surface is always parallel to, or “normal” to, the surface; hence the term “normal force.” Don’t confuse the abbreviation N for newtons with N for normal force!

21. Normal force example: the table exerts an upward force on the lamp. Normal force example: the ramp exerts a force on the block. Normal force example: the table exerts an upward force on the lamp. The force is normal to the surface of the table. Normal force example: the ramp exerts a force on the block. The force is normal to the surface of the ramp. N N Remember, Learning Centers open 2-4:30, 6-8:30 TTh; individual tutor 7-9 M-Th room 208 Norwood.Learning Centers