2 3 5 6 Motion in a Motion in Two and Using Newton’s Energy, Work, Straight Line Three Dimensions 4 Laws and Power Force and Motion What You Know What You’re Learning How You’ll Use It ■ You can express motion quantities ■ Here you’ll learn to adopt the Newtonian ■ Chapter 4 is largely restricted to as vectors in one, two, or three paradigm that the laws governing one-dimensional motion. But the dimensions. motion are about change in motion. principles you learn here work ■ You can describe motion quantitatively ■ You’ll explore Newton’s three laws of in Chapter 5, where you’ll apply when acceleration is constant. motion and see how together they Newton’s laws in multiple dimensions. ■ You’re especially familiar with provide a consistent picture of motion ■ In Chapters 6 and 7 you’ll see how projectile motion under the influence from microscopic to cosmic scales. Newton’s second law leads to the of gravity near Earth’s surface. ■ You’ll learn the concept of force and its fundamental concepts of energy and energy conservation. ■ You understand that circular motion is relation to acceleration. a case of accelerated motion, and you ■ You’ll be introduced to the fundamental ■ You’ll apply Newtonian ideas to can find the acceleration given speed forces of nature. gravity in Chapter 8. and radius of the circle. ■ You’ll see how the force of gravity acts ■ In Chapter 9 you’ll see how the on objects near Earth’s surface. interplay of Newton’s second and third laws underlies the behavior of ■ You’ll learn to distinguish weight from complex systems. apparent weight. ■ Newton’s laws will continue to govern ■ You’ll see how springs provide a the more complex motions you’ll study convenient means of measuring force. in Part 2 of the book and beyond. n interplanetary spacecraft moves effortlessly, yet its engines shut down years ago. Why Adoes it keep moving? A baseball heads toward the batter. The batter swings, and sud- denly the ball is heading toward left field. Why did its motion change? Questions about the “why” of motion are the subject of dynamics. Here we develop the ­basic laws that answer those questions. Isaac Newton first stated these laws more than 300 years ago, yet they remain a vital part of physics and engineering today, helping us guide spacecraft to distant planets, develop better cars, and manipulate the components of ­individual cells. 4.1 The Wrong Question We began this chapter with two questions: one about why a spacecraft moved and the other about why a baseball’s motion changed. For nearly 2000 years following the work of Aristotle (384–322 bce), the first question—Why do things move?—was What forces did engineers have to consider when the crucial one. And the answer seemed obvious: It took a force—a push or a pull—to they developed the Mars Curiosity rover’s “sky keep something moving. This idea makes sense: Stop exerting yourself when ­jogging, crane” landing system? and you stop moving; take your foot off the gas pedal, and your car soon stops. ­Everyday experience seems to suggest that Aristotle was right, and most of us carry in our heads the ­Aristotelian idea that motion requires a cause—something that pushes or pulls on a moving object to keep it going. 51 M04_WOLF3724_03_SE_C04.indd 51 21/10/14 5:12 PM 52 Chapter 4 Force and Motion Actually, “What keeps things moving?” is the wrong question. In the early 1600s, Galileo Galilei did experiments that convinced him that a moving object has an intrinsic “quantity of motion” and needs no push to keep it moving (Fig. 4.1). Instead of answering cit always “What keeps things moving?,” Galileo declared that the question needs no answer. In so rises to its starting height c doing, he set the stage for centuries of progress in physics, beginning with the achieve- If a ball is ments of Issac Newton and culminating in the work of Albert Einstein. released here c The Right Question Our first question—about why the spacecraft keeps moving—is the wrong question. So what’s the right question? It’s the second one, about why the baseball’s motion changed. Dynamics isn’t about what causes motion itself; it’s about what causes changes in motion. Changes include starting and stopping, speeding up and slowing down, and changing cso if the direction. Any change in motion begs an explanation, but motion itself does not. Get used surface is made to this important idea and you’ll have a much easier time with physics. But if you remain a horizontal, the ball should roll forever. “closet Aristotelian,” secretly looking for causes of motion itself, you’ll find it difficult to understand and apply the simple laws that actually govern motion. Galileo identified the right question about motion. But it was Isaac Newton who formu- lated the quantitative laws describing how motion changes. We use those laws today for everything from designing antilock braking systems, to building skyscrapers, to guiding FIGURE 4.1 Galileo considered balls rolling spacecraft. on inclines and concluded that a ball on a horizontal surface should roll forever. 4.2 Newton’s First and Second Laws What caused the baseball’s motion to change? It was the bat’s push. The term force describes a push or a pull. And the essence of dynamics is simply this: Force causes change in motion. We’ll soon quantify this idea, writing equations and solving numerical problems. But the essential point is in the simple sentence above. If you want to change an object’s motion, you need to apply a force. If you see an object’s motion change, you know there’s a force acting. Contrary to Aristotle, and probably to your own intuitive sense, it does not take a force to keep something in unchanging motion; force is needed only to change an object’s motion. The Net Force You can push a ball left or right, up or down. Your car’s tires can push the car forward or backward, or make it round a curve. Force has direction and is a vector quantity. Further- Here there’s a nonzero more, more than one force can act on an object. We call the individual forces on an object net force acting on the interaction forces because they always involve other objects interacting with the object in car, so the car’s motion is changing. question. In Fig. 4.2a, for example, the interaction forces are exerted by the people push- ing the car. In Fig. 4.2b, the interaction forces include the force of air on the plane, the S engine force from the hot exhaust gases, and Earth’s gravitational force. F S 1 Fnet We now explore in more detail the relation between force and change in motion. Experiment shows that what matters is the net force, meaning the vector sum of all S individual interaction forces acting on an object. If the net force on an object isn’t zero, F 2 (a) then the object’s motion must be changing—in direction or speed or both (Fig. 4.2a). If The three forces sum to zero, the net force on an object is zero—no matter what individual interaction forces contribute so the plane moves in a straight to the net force—then the object’s motion is unchanging (Fig. 4.2b). line with constant speed. S S S Fnet = 0 Fair S Fengine Newton’s First Law S The basic idea that force causes change in motion is the essence of Newton’s first law: Fg (b) Newton’s first law of motion: A body in uniform motion remains in uniform FIGURE 4.2 The net force determines the motion, and a body at rest remains at rest, unless acted on by a nonzero net force. change in an object’s motion. M04_WOLF3724_03_SE_C04.indd 52 21/10/14 5:12 PM 4.2 Newton’s First and Second Laws 53 The word “uniform” here is essential; uniform motion means unchanging motion—that is, motion in a straight line at constant speed. The phrase “a body at rest” isn’t really necessary because rest is just the special case of uniform motion with zero speed, but we include it for consistency with Newton’s original statement. Video Tutor Demo | Cart with Fan and Sail The first law says that uniform motion is a perfectly natural state, requiring no explana- tion. Again, the word “uniform” is crucial. The first law does not say that an object moving in a circle will continue to do so without a nonzero net force; in fact, it says that an object moving in a circle—or in any other curved path—must be subject to a nonzero net force because its motion is changing. GOT it? 4.1 A curved barrier lies on a horizontal tabletop, as shown. A ball rolls along the barrier, and the barrier exerts a force that guides the ball in its curved path. After the ball leaves the barrier, Video Tutor Demo | Ball Leaves Circular Track which of the dashed paths shown does it follow? (a) (b) (c) Newton’s first law is simplicity itself, but it’s counter to our Aristotelian preconcep- tions; after all, your car soon stops when you take your foot off the gas. But because the motion changes, that just means—as the first law says—that there must be a nonzero net force acting. That force is often a “hidden” one, like friction, that isn’t as obvious as the push or pull of muscle.