* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 6: Newton`s Laws of Motion
Survey
Document related concepts
Coriolis force wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Fictitious force wikipedia , lookup
Classical mechanics wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Seismometer wikipedia , lookup
Centrifugal force wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Mass versus weight wikipedia , lookup
Hunting oscillation wikipedia , lookup
Equations of motion wikipedia , lookup
Work (physics) wikipedia , lookup
Classical central-force problem wikipedia , lookup
Transcript
6 Science TEKS 8.7 A Newton’s Laws of Motion T he noise is deafening as drivers gun their engines, waiting for the signal to start the race. The signal comes, and the cars speed forward. One car pulls ahead but has to slow down to make the turn. What makes the cars move so fast? How do they change direction? What causes them to slow down? In this chapter you will learn how to describe motion. You’ll also learn about the laws of motion that made this race possible, and how they determine the motion of objects around you. What do you think? Science Journal Look at the picture below with a classmate. Discuss what this might be or what is happening. Here’s a clue: You would have to be high above Earth to see a sunrise that looks like this. Write your answer or best guess in your Science Journal. 152 EXPLORE C ACTIVITY onsider the countless possibilities for motion in the universe. Billions of stars orbit around the center of the galaxy. The wind bounces air molecules from leaf to leaf in a grove of trees creating a cool breeze. A roller coaster plummets down a steep hill before twisting and looping along its tracks. A fly darts about a room faster than the eye can follow. Just three laws of motion explain why objects move the way they do and how different types of forces cause these movements. Observe these laws in this activity. Observe motion along varying slopes 1. Lean one end of a ruler on top of three books to form a ramp. Use a plastic ruler with a groove down the middle. 2. Tap a marble so it rolls up the ramp. Measure how far it rolls up the ramp before stopping and rolling back down. 3. Repeat step 2 using two books, one book, and no books. The same person should tap the marble each time, trying to keep the force constant. Observe What would happen if you tapped the marble on a smooth, flat path? Write your observations and predictions in your Science Journal. FOLDABLES Reading &Study & Study Skills Making a Question Study Fold Asking yourself questions helps you to stay focused and better understand Newton’s Laws of Motion when you are reading the chapter. 1. Place a sheet of paper in front of you so the long side is at the top. Fold the paper in half from the left side to the right side and then unfold. 2. Fold each side in to the centerfold line to divide the paper into fourths. Fold the paper in half from top to bottom and unfold. 3. Through the top thickness of paper, cut along both of the middle fold lines to form four tabs as shown. Label each tab Motion,First Law, Second Law,and Third Law as shown. 4. As you read the chapter, write under the tabs some questions you have concerning the main ideas in each section. Motion cond Sea L w First Law Third Law 153 SECTION Motion What is motion? Contrast distance and displacement. ■ Define speed, velocity, and acceleration. ■ Calculate speed, velocity, and acceleration. ■ Vocabulary displacement speed velocity acceleration Motion occurs constantly all around you. Figure 1 A hiker might be interested in the total distance traveled along a hike, or in the displacement. Can total distance be greater than total displacement? Explain. N Cars drive past on streets and freeways. The wind swirls and causes leaves and paper to fly about. Inside you, your heart pumps and sends blood throughout your body. When walking, skating, jumping, or dancing, you are in motion. In fact, motion is all around you. Even massive pieces of Earth’s surface move— if only a few centimeters per year. A traveler wants to know the distance between home and another place. Is it close enough to walk? Will a flight take half the day? The coach at your school wants to analyze various styles of running. Who is the fastest sprinter? Who can change direction easily in a sprint? To answer these questions, you must be able to describe motion. Distance and Displacement One way you can describe the motion of an object is by how it changes position. There are two ways to describe how something changes position. One way is to describe the entire path the object travels. The other way is to give only the starting and stopping points. Picture yourself on a hiking trip through the mountains. The path you follow is shown in Figure 1. By following the trail, you will walk 22 km but end up only 12 km from where you started. The total distance you will travel is 22 km. However, you will end up only 12 km north of where you started. Displacement is the distance and direction between starting and ending positions. Your displacement is 12 km north. Finish Start 0 154 1 2 km CHAPTER 6 Newton’s Laws of Motion Figure 2 For position to change, one object must move relative to another object. Which object did the person on the bench move relative to? Relative Motion Something that is in motion changes its position. The position of an object is described relative to another object, which is the reference point. Suppose you look out the window in the morning and see a truck parked next to a tree. When you look out the window later, the truck is parked further down the street. How can you tell that the truck has been in motion? The truck has changed position relative to the tree. The same is true for the person in Figure 2. How can you tell whether an object has changed position? Speed When running, you are interested not only in the distance you travel, but also in how fast you are moving. To describe how quickly or slowly you are moving, you give your speed. Speed is the distance traveled divided by the time needed to travel the distance. In equation form, distance speed time If you run 3 km in 0.5 h, your speed is Grade 7 TEKS Review For a review of the Grade 7 TEKS There is a Relationship Between Force and Motion, see page 740. (3 km) speed 6 km/h (0.5 h) If you run farther in the same amount of time, your speed is greater. The greater your speed is, the faster you move. SECTION 1 Motion 155 Math Skills Activity Calculating Speed MATH TEKS 8.2 A, B; 8.5 A Example Problem A hockey puck slides along the ice for 3 s before crossing the goal line 6 m away. What is the average speed of the puck before it crossed the goal line? Solution This is what you know: distance = 6 m time = 3 s This is what you need to know: speed This is the equation you need to use: speed = distance/time Substitute the known values: speed = 6 m/3 s = 2 m/s Check your answer by multiplying it by the time. Do you calculate the same distance that was given? Practice Problem A swimmer takes 40 s to swim 100 m. What is his or her average speed? For more help, refer to the Math Skill Handbook. Constant Speed If you are riding in a car with the cruise Figure 3 When you read a speedometer, you are finding your instantaneous speed. When would your instantaneous speed be the same as your average speed? control on, the speed doesn’t change. In other words, the car moves at a constant speed. If you are running at a constant speed of 5 m/s, you run 5 m each second. Whether you give your speed for the first 5 m you run or the last 5 m, you cover each 5-m interval in 1 s. When you are traveling at a constant speed, the speed at any instant of time is the same. Changing Speed For some motion, speed is not constant. If you are riding your bike, you must slow down for intersections and turns and then pedal faster to resume your speed. Your average speed for your trip would be the total distance traveled divided by the time you were riding. If you wanted to know how fast you were going at just one instant, you would be interested in your instantaneous speed. A car speedometer like the one in Figure 3 shows instantaneous speed—how fast the car is moving at any moment. When speed is constant, average speed and instantaneous speed are the same. 156 CHAPTER 6 Newton’s Laws of Motion Velocity Sometimes you might be interested not only in how fast you are going, but also in the direction. When direction is important, you want to know your velocity. Velocity is the displacement divided by time. For example, if you were to travel 1 km east in 0.5 h, you would calculate your velocity as follows. displacement velocity time (1 km east) v (0.5 h) v 2 km/h east Figure 4 Airplane pilots are interested in their velocity. Who else would be concerned about their velocity? Like displacement, velocity includes a direction. Velocity is important to pilots flying airplanes. They rely on control panels like the one in Figure 4 because they need to know not only how fast they are flying, but also in what direction. Acceleration Displacement and velocity describe how far, how fast, and where something is going. You also might want to know how motion is changing. Is the car going faster and faster, or is it slowing down? Is a skater changing direction? Acceleration is the change in velocity divided by the amount of time required for the change to occur. Recall that velocity includes speed and direction. If an object changes its speed, its direction, or both, it is accelerating. Speeding Up and Slowing Down When you think of an object accelerating, you might think of it moving faster and faster. If someone says a car accelerates, you think of it moving forward and increasing its velocity. However, when an object slows down, it also is accelerating. Why? Recall that an object is accelerating when its velocity changes. Velocity can change if the speed of an object changes, whether the speed increases or decreases, or if it changes direction. If an object slows down, its speed changes. Therefore, if an object is speeding up or slowing down, it is accelerating. Measuring Motion Procedure 1. Measure a fixed distance such as the length of your driveway. 2. Use a watch to measure the time it takes you to stroll, rapidly walk, and run this distance. Analysis 1. Calculate your average velocity in each case. 2. Use your results to predict how long it would take you to go 100 m by each method. SECTION 1 Motion 157 Calculating Acceleration If an object speeds up or slows down, only the speed of the object is changing. You can then use the change in speed to calculate the acceleration using the following equation. (final speed initial speed) acceleration time For example, suppose the ball in Figure 5 goes from being at rest to moving at 29.4 m/s in 3 s. What is its acceleration? The ball’s final speed is 29.4 m/s, and its initial speed is zero because it started from rest. The time it took for the changes in speed to occur is 3 s. According to the formula above, the ball’s acceleration is Figure 5 When this ball is dropped, it accelerates downward, speeding up from 0 m/s to 29.4 m/s in 3 s. (29.4 m/s 0 m/s) acceleration 3s 2 9.8 m/s Math Skills Activity Calculating Acceleration MATH TEKS 8.1 A, B; 8.2 A, B Example Problem Riding your skateboard, it takes you 12 s to accelerate from 2 m/s to 8 m/s. Find your acceleration. Solution initial speed 2 m/s final speed 8 m/s time 12 s This is what you need to know: acceleration: a This is the equation you need to use: a (final speed initial speed)/time Substitute the known values: a (8 m/s 2 m/s)/12 s a (6 m/s)/12 s 0.5 m/s2 Check your answer by multipling your answer by the time. Add the initial speed. Do you calculate the same final speed that was given? This is what you know: Practice Problem A horse canters at 11 m/s. It takes 3 s to reach a gallop of 17 m/s. Find the acceleration. For more help, refer to the Math Skill Handbook. 158 CHAPTER 6 Newton’s Laws of Motion Turning When an object turns or changes direction, its veloc- Figure 6 ity changes. This means that any object that changes direction is accelerating. To help understand acceleration, picture running a race, as shown in Figure 6. As soon as the race begins, you start from rest and run faster. You speed up, therefore, you accelerate. When you follow the turn in the track, you are changing your direction. Because you turn, your velocity changes and you accelerate. After you pass the finish line, you slow down to a steady walk. Because your speed changes, you accelerate again. When the race starts, the runner accelerates by speeding up. When rounding the corners of the track, the runner accelerates by turning. After crossing the finish line, the runner accelerates by slowing down. What are three ways to accelerate? Section Assessment 1. Compare and contrast displacement, velocity, and acceleration. 2. You walked 100 m forward, then 35 m backward. What distance did you walk? 3. In question 2, what is your displacement? 4. Why is turning a form of acceleration? 5. Think Critically When you ride in a train that passes a train moving in the opposite direction, the other train appears to rush past you at a speed greater than if you were watching from a parked car at a crossing. How does the speed of your train affect your impression of the passing train’s speed? 6. Comparing and Contrasting You and a friend swim out a distance 40 m and swim back 40 m. Your friend lands on his starting spot, but you land 6 m north of your starting point. If you both swam for 60 s, compare and contrast total distance, displacement, and average speed. For more help, refer to the Science Skill Handbook. 7. Solving One-Step Equations A car is moving forward at 12 m/s. It takes 4 s to come to a stop. Calculate the car’s average acceleration. Include the direction of the acceleration. For more help, refer to the Math Skill Handbook. SECTION 1 Motion 159 SECTION Newton’s First Law Laws of Motion Define force. Describe Newton’s first law of motion. ■ Contrast balanced and unbalanced forces. ■ ■ Vocabulary force first law of motion balanced forces unbalanced forces A picture might tell a thousand words, but sometimes it takes a thousand pictures to show a motion. Look at the strobe photo in Figure 7. The smoothness of the overall motion is the result of many individual motions—hands move and legs flex. Some trainers who work with athletes use such films to help them understand and improve performance. What causes such complex motions to occur? Each individual motion can be explained and predicted by a set of rules that were first stated by Isaac Newton. These rules are called Newton’s laws of motion. Force An object’s motion changes in response to a force. A Forces cause motion to change. Figure 7 A gymnast’s motion can be explained by Newton’s laws of motion. 160 force is a push or a pull. A force has a size and a direction—both are important in determining an object’s motion. For example, pushing this book on one side will slide it across the desk in the same direction. Pushing it harder will make it move faster in the direction of your push. However, if you push the book straight down, it will not move. The force you exert on the book when you push is called a contact force. A contact force is a force that is exerted when two objects are touching each other. Long-Range Forces However, a force can be exerted if two objects are not in contact. If you bring a magnet close to a paper clip, the paper clip moves toward the magnet, so a force must be acting on the paper clip. The same is true if you drop a ball—the ball will fall downward, even though nothing appears to be touching it. The forces acting on the paper clip and the ball are long-range forces. These forces can cause an object’s motion to change without direct contact. Long-range forces include gravity, magnetism, and electricity. When scientists need to measure force, they use the newton, which is abbreviated N and named for Isaac Newton. One newton is about the amount of force needed to lift half a cup of water. Figure 8 If you were to stop the cart suddenly, the boxes would keep moving. Newton’s First Law of Motion When you are riding in a car and it comes to a sudden stop, you feel yourself continuing to move forward. Your seat belt slows you down and pulls you back into your seat. This can be explained by the first law of motion—An object will remain at rest or move in a straight line with constant speed unless it is acted upon by a force. For a long time it was thought that all objects come to rest naturally. It seemed that a force had to be applied continually to keep an object moving. Newton and others theorized that if an object already is moving, then it will continue to move in a straight line with constant speed. For the object to slow down, a force has to act on it. Think about what keeps you in your seat when a car comes to a sudden stop. You can feel yourself moving forward, but the seat belt applies a force to pull you back and stop your motion. If you were to push a cart with boxes on it as in Figure 8 and you suddenly stopped the cart, the boxes would continue moving and slide off the cart. In a car crash, a car comes to a sudden stop. According to Newton’s first law, passengers inside the car will continue to move unless they are held in place. Research the various safety features that have been designed to protect passengers during car crashes. Write a paragraph on what you’ve learned in your Science Journal. SECTION 2 Newton’s First Law 161 Figure 9 Inertia and Mass The first law of motion is sometimes The more massive the body is, the more inertia it has. It is easy to speed up or slow down a small child in a wagon. Changing the motion of a wagon carrying a larger child is harder. How does inertia affect collisions between cars? called the law of inertia. Inertia measures an object’s tendency to remain at rest or keep moving with constant velocity. Inertia depends on the mass of the object. The more mass an object has, the more inertia it has and the harder it is to change the motion of the object. Look at Figure 9. It is easy to get a wagon to start moving if only one small child is sitting in it. You must exert more force to start the wagon moving if it holds more mass. The same is true if you try to stop the wagon after it is moving. You need to exert a larger force to stop the wagon that has more mass. What is inertia? Adding Forces Research Visit the Glencoe Science Web site at tx.science.glencoe.com for information about how airplanes land on aircraft carriers. These airplanes have a lot of inertia due to their large mass and require a lot of force to bring them to a stop on the short runway. Communicate to your class what you learn. 162 According to Newton’s first law, the motion of an object changes only if a force is acting on the object. Sometimes more than one force acts on an object, as when several people push a stalled car to the side of the road. Motion depends upon the size and direction of all the forces. If two people push in opposite directions on a box with an equal amount of force, the box will not move. Because the forces are equal but in opposite directions, they will cancel each other out and are called balanced forces. When forces on an object are balanced, no change will occur in the object’s motion because the total force on the object is zero. If one force pushing on the box is greater than the other, the forces do not cancel. Instead, the box will move in the direction of the larger force. Forces acting on an object that do not cancel are unbalanced forces. The motion of an object changes only if the forces acting on it are unbalanced. The change in motion is in the direction of the unbalanced force. CHAPTER 6 Newton’s Laws of Motion Changes in Motion and Forces How do unbalanced forces affect the motion of an object? Look at the dancer in Figure 10. When she jumps, she pushes off with a force greater than the force of gravity pulling her down. This creates an unbalanced force upward, and the dancer moves upward. After she has left the ground and her feet are no longer in contact with the floor, gravity becomes the only force acting on her. The forces on her are unbalanced and her motion changes—she slows down as she rises into the air and speeds up as she returns to the ground. The motion of an object changes when unbalanced forces act on the object. Recall that if the motion of an object changes, the object is accelerating. The object can speed up such as when the dancer in Figure 10 comes back down to the stage. It might slow down—think of a parachutist after the chute has opened. The object might turn, as when a bicyclist is hit by a sudden crosswind. In all cases, an object acted on by an unbalanced force changes velocity. Section Force due to gravity Figure 10 Because the motion of this dancer is changing, forces are unbalanced. Assessment 1. What does the first law of motion say about the motion of an ice-skater sliding across the ice at constant velocity? 2. The force of gravity is pulling you toward the ground. Is this a balanced or an unbalanced force? Explain. 3. What is a force? Give an example. 4. A dropped ball accelerates toward the ground. Does an unbalanced force act on the ball? Explain. 5. Think Critically Will a pick-up truck carrying a refrigerator be easier or harder to turn than the same truck with no load? Explain, using the principle of inertia. 6. Recognizing Cause and Effect An object in motion at constant velocity is an effect. What is the cause? For more help, refer to the Science Skill Handbook. 7. Communicating Natural philosophers studied motion for many years before discovering the first law of motion. Some thought that an object’s natural state was rest, which all objects in motion tried to attain. Explain why people might have thought this and what the first law of motion says about an object’s natural state. For more help, refer to the Science Skill Handbook. SECTION 2 Newton’s First Law 163 SECTION Newton’s Second Law The Second Law of Motion Predict changes in motion using Newton’s second law. ■ Contrast different types of friction. ■ Vocabulary second law of motion friction Newton’s second law explains and predicts how motion will change. Newton’s first law of motion can help predict when an object’s motion will change. Can you predict what the change in motion will be? You know that when you kick a ball, as in Figure 11, your foot exerts a force on the ball, causing it to move forward and upward. The force of gravity then pulls the ball downward. The motion of the ball can be explained by Newton’s second law of motion. According to the second law of motion, an object acted on by an unbalanced force will accelerate in the direction of the force, according to the formula force acceleration mass If a stands for the acceleration, F for the force, and m for the mass, this formula can also be written as follows. F a m If more than one force acts on the object, the force in this formula is the combination of all the forces, or the total force that acts on the object. What is the acceleration if the total force is zero? In what direction does an object accelerate when acted on by an unbalanced force? Figure 11 When you kick a ball, you apply a force to it. The ball moves in the direction of the applied force. Applied force 164 Using the Second Law How can Newton’s second law tell you about changes in motion? Recall that an object accelerates when a change in motion occurs. The second law allows you to calculate acceleration. For example, if a 10-N force acts on a 2-kg object, what acceleration does it give the object? force acceleration mass (10 N) a (2 kg) a 5 N/kg, or 5 m/s2 Research Visit the Glencoe Science Web site at tx.science.glencoe.com for information about how much acceleration the space shuttle and other space vehicles must have in order to safely escape Earth’s atmosphere. Communicate to your class what you learn. If you know the mass and acceleration of an object, you can use Newton’s second law to find the force. If both sides of the above equation are multiplied by mass, m, the equation becomes F = ma How do you find force if you are given mass and acceleration? Math Skills Activity Calculating Force Given Mass and Acceleration MATH TEKS 8.1 A, B; 8.2 A, B Example Problem A child has a mass of 71 kg. Her bike has a mass of 9 kg. The bike and rider are accelerated at a rate of 3.20 m/s2. Find the force used to accelerate the bike and the rider. Solution acceleration: a 3.20 m/s2 mass: m 71 kg 9 kg 80 kg This is what you need to find: Force: F This is the equation you need to use: F ma Substitute the known values: F (80 kg) (3.20 m/s2) 256 N Check your answer by solving the original equation (F ma) for m. Then substitute F and a. Do you calculate the same mass that was given? This is what you know: Practice Problem You are lowering a 12-kg bucket with an acceleration of 0.5 m/s2. Find the force being used. For more help, refer to the Math Skill Handbook. SECTION 3 Newton’s Second Law 165 The Force of Gravity What is the force of gravity on you? The weight of an object is the force of gravity on the object. Near Earth’s surface, the force of Earth’s gravity causes all objects to fall with the same acceleration: 9.8 m/s2. This is shown in Figure 12. When you are falling, the force of gravity on you is F m (9.8 m/s2) Even if you are standing on the ground, Earth still is pulling on you with this force. You are at rest because the ground exerts an upward force that balances the force of gravity. Because your weight is the force of gravity on you, your weight is given by the formula weight mass acceleration due to gravity Suppose your mass were 60 kg. On Earth, your weight would be weight (60 kg) (9.8 m/s2) weight 588 N As your mass increases, your weight on Earth also increases. Mass and Weight Weight and mass are sometimes spoken Figure 12 The strobe light flashes on and off at a steady rate. The ball’s speed is increasing steadily at 9.8 m/s2. The distance it falls in each flash also increases steadily. of as the same thing, but the two concepts are different. Weight is a force, just like a push of your hand is a force. Weight can change when the force of gravity changes, as it does when astronauts leave Earth’s surface. For example, your weight on the Moon is different than your weight on Earth. The force of gravity at the Moon’s surface is only about 16 percent as large as the force of Earth’s gravity. So your weight on the Moon is less than your weight on Earth. Mass, on the other hand, is a measure of the amount of matter in an object. It is constant no matter where you are. An astronaut would have the same mass on Earth as on the Moon. How are mass and weight different? Recall that mass is a measure of inertia, which is how hard it is to change the motion of an object. Think of how hard it would be to stop a 130-kg football player rushing at you. Now suppose you were in outer space. If you were far enough from Earth, the force of Earth’s gravity would be weak. Your weight and the football player’s weight would be small. If he were moving toward you, he would be just as hard to stop as on Earth. He still has the same mass and the same inertia, even though he is nearly weightless. 166 CHAPTER 6 Newton’s Laws of Motion Friction Rub your hands together. You can feel a force between your hands, slowing their motion. If your hands are covered in lotion, making them slippery, the force is weaker. If anything gritty or sticky is on your hands, this force increases. Friction is a force that resists motion between sufaces that are touching. Friction always is present when two surfaces of two objects slide past each other. To keep the objects moving, a force has to be applied to overcome the force of friction. However, friction is also essential to everyday motion. How hard would it be to move without friction? When you walk up a ramp, friction prevents you from sliding to the bottom. When you stand on a skateboard, friction keeps you from sliding off. When you ride a bike, friction enables the wheels to propel the bike forward. Friction sometimes can be reduced by adding oil or grease to the surfaces, but it always is present. There are several types of friction, and any form of motion will include one or more of them. Static Friction Gently push horizontally on this book. You should be able to push against it without moving it. This is because of the static friction between the cover of the book and the top of the desk. Static friction hinders a stationary object from moving on a surface when a force is applied to the object. When you stand on a slight incline, you don’t slide down because of the static friction between your shoes and the ground. When you carry a tray of food to a table and stop to sit down, Newton’s first law predicts that food on the tray will keep moving and slide off the tray. Happily, static friction keeps the food on the tray, allowing you to sit down and enjoy your meal. This is similar to the example shown in Figure 13. Figure 13 The rubber mat increases the static friction acting on the computer. This static friction keeps the computer from sliding. Without static friction, what would happen when the cart stopped? Computer Rubber mat Cart SECTION 3 Newton’s Second Law 167 Sliding Friction Push on your book again. Notice that once the book is in motion and leaves your hand, it comes to a stop. Sliding friction is the force that slowed the book down. Sliding friction occurs when two surfaces slide past each other. To keep the book moving, you have to keep applying a force to overcome sliding friction. The friction between a skier and the snow, a sliding baseball player and the ground, and your shoes and the skin where a blister is forming are examples of sliding friction. When you apply the brakes to a bike, a car, or the skateboard shown in Figure 14, you use sliding friction to slow down. Rolling Friction A car stuck in snow or in mud spins its wheels but doesn’t move. Rolling friction makes a wheel roll forward or backward. If the rolling friction is large enough, a wheel will roll without slipping. The car that is stuck doesn’t move because mud or snow makes the ground too slippery. Then there is not enough rolling friction to keep the wheels from slipping. Because rolling friction is the force that enables a wheel to roll past a surface, the force of rolling friction is in the same direction that the wheel is rolling. If the wheel is rolling forward, the rolling friction force also points forward, as shown in Figure 15. Some of the ways that static, sliding, and rolling friction are useful to a bike rider are shown in Figure 16. Figure 14 Sliding friction between the rider’s shoe and the sidewalk slows the skateboarder down. What kind of friction is used when the skateboarder pushes off to start moving? Motion of tire Figure 15 Rolling friction is needed for this wheel to roll forward. Without friction, it would slide along the street. 168 CHAPTER 6 Newton’s Laws of Motion Rolling friction VISUALIZING FRICTION Figure 16 riction is a force that opposes motion. But sometimes friction can be used to your advantage. For example, you could not ride a bicycle without friction. A: The rolling friction between the tires and the pavement pushes the bottom of the tires forward; this helps rotate the tires and propels the cyclist forward. B: Brake pads push against the rim of the tire; this creates sliding friction, which slows the wheel. C: Bicycle pedals have a rough surface that increases static friction and keeps the cyclist’s feet from slipping off. F A B C SECTION 3 Newton’s Second Law 169 Air Resistance Do you know why it Gravity Air resistance Figure 17 Gravity and air resistance are the forces acting on a parachutist. When the forces balance each other, the parachutist falls at a constant velocity. is harder to walk in deeper water than in shallow water? It’s because the deeper the water is, the more of it you have to push out of your way to move forward. You usually do not realize it, but the same is true for walking on dry land. To move forward, you must push air out of your way. Unless you’re in a hurricane, it is much easier to walk through air because the molecules in air are farther apart than water molecules are. Molecules in air collide with the forward-moving surface of an object, slowing its motion. This is called air resistance. Air resistance is less for a narrow, pointed object than for a large flat object. Air resistance also increases as the speed of an object moving through the air increases. Because air resistance is a type of friction, it acts in a direction opposite to the motion of an object through the air. Before the sky diver in Figure 17 opens the parachute, his air resistance is small. The force of air resistance is upward, but is not large enough to balance the downward force of gravity. As a result the sky diver falls rapidly. When he opens his parachute the air resistance is much greater because the parachute has a large surface area. Then the force of air resistance is large enough to slow his fall and balance the force of gravity. Section Assessment 1. A ball has a mass of 2 kg. What is the force due to gravity on the ball (its weight)? 2. An angled conveyor belt lifts a box to a shipping area. What force keeps the box from sliding off the belt? 3. Compare the acceleration of an object acted on by forces of 1 N and 2 N. 4. What factors influence air resistance? 5. Think Critically The following forces act on an object: 3 N left, 2 N up, 1 N right, 2 N down. What is the total force on the object? Give the size and direction. 170 CHAPTER 6 Newton’s Laws of Motion 6. Concept Mapping Make a spider concept map about the types of friction. Include static friction, sliding friction, rolling friction, and air resistance. For more help, refer to the Science Skill Handbook. 7. Using an Electronic Spreadsheet Calculate the acceleration of a 40-kg sled acted on by a 20 N force. Then,if the sled starts from rest,use a computer spreadsheet to calculate the speed of the sled every second. For more help, refer to the Technology Skill Handbook. Static and Sliding Friction S tatic friction can hold an object in place when you try to push or pull it. Sliding friction explains why you must continually push on something to keep it sliding across a horizontal surface. In this activity, you’ll measure and compare static and sliding friction. What You’ll Investigate How do different types of friction compare? Materials spring scale block of wood or other material tape Goals ■ Observe static and sliding friction. ■ Measure static and sliding friction. ■ Compare and contrast static and sliding friction. Safety Precautions Procedure 1. Attach a spring scale to the block and set it on the table. Experiment with pulling the block with the scale so you have an idea of how hard you need to pull to start it in motion and continue the motion. 2. Measure the force needed to start the block in motion. This is the force of static friction. 3. Measure the force needed to keep the block moving at a steady speed. This is the force of sliding friction on the blocks. 4. Repeat steps 2 and 3 on a different surface, such as carpet. Record your measurements in your Science Journal. Conclude and Apply 1. Compare the forces of static friction and sliding friction on both horizontal surfaces. Which force is greater? 2. On which horizontal surface is the force of static friction greater? 3. On which surface is the force of sliding friction greater? 4. Which surface is rougher? How do static and sliding friction depend on the roughness of the surface? 5. Explain how different materials affect the static and sliding friction between two objects. Compare your conclusions with those of other students in your class. For more help, refer to the Science Skill Handbook. ACTIVITY 171 SECTION Newton’s Third Law Action and Reaction Interpret motion using Newton’s third law. ■ Analyze motion using all three laws. ■ Vocabulary third law of motion Newton’s three laws together will help you understand motion. When you push off the side of a pool, you accelerate. By Newton’s laws of motion, when you accelerate, a force must be exerted on you. Where does this force come from? Newton’s first two laws explain how forces acting on a single object affect its motion. The third law describes the connection between the object receiving a force and the object supplying that force. According to the third law of motion, forces always act in equal but opposite pairs. This often is restated—for every action, there is an equal but opposite reaction. For example, if object A exerts a force on object B, then object B exerts a force of the same size on object A. What relationship does the third law of motion describe? Figure 18 Notice that when you walk, you push backward on the ground, yet you move forward. This is because when you push back on the ground, the ground exerts an equal force forward on you. Your force 172 The Third Law in Action Newton’s third law means that when you lift your book bag, your book bag pulls back. When you jump, you push down on the ground, which pushes up on you. When you walk, you push back on the ground, and the ground pushes forward on you. When you throw a ball, you push forward on the ball and it pushes back on your hand. Figure 18 shows that when you exert a force on the floor, the floor exerts an equal force on you in the opposite direction. The same is true for any two objects, regardless of whether the force between the objects is a contact force or a long-range force. For example, if you Reaction place two bar magnets with opposite force poles facing one another, they will move toward each other. Each magnet applies a force to the other, even though they are not in direct contact. No matter how one object exerts a force on another, the other object always exerts an equal force in the opposite direction. CHAPTER 6 Newton’s Laws of Motion Figure 19 Static friction between your shoes and the ground makes it possible to push a heavy door forward. Without static friction, pushing the door would make you slide backwards. How can anything move? Action and reaction forces are not the same as balanced forces. Recall that balanced forces are forces that act on the same object and cancel each other. Action and reaction forces act on different objects. When you kick a soccer ball, your force on the ball equals the ball’s force on you. The harder you kick, the greater the force the ball exerts on your foot. A hard kick can hurt because the ball exerts a large force on your foot. Unlike balanced forces, action and reaction forces can cause the motion of objects to change. How do balanced forces differ from action and reaction forces? Using Friction When you push a heavy door, as in Figure 19, you exert a force on the door to move it. The door exerts an equal force back on you. Why don’t you move? When you push on the door, your feet are touching Earth and static friction keeps you from sliding. The reaction force is exerted on you and Earth together. The door can’t push enough on you and Earth to move you back. If you wear slippery shoes or if the ground is slippery, you might not be able to open a heavy door. The force exerted by the door on you would cause your feet to slip out from under you. Static friction hinders you from moving when you throw a ball or pull a book off a shelf. However, if you throw a heavy ball while standing on ice, you will slide in the opposite direction to the direction you threw the ball. SECTION 4 Newton’s Third Law 173 Doing the Math If a 50-kg person in the middle of an ice- Observing the Laws of Motion Procedure 1. Incline one end of a board to a height of 20 cm. 2. Lay a meterstick on the floor with one end flush to the board, and place a softball where the board and meterstick meet. 3. Hold a baseball 10 cm up the slope and roll it into the softball. Measure the distance the softball is pushed. 4. Repeat step 3 from different heights. skating rink pushes a 20-kg box with a force of 10 N, what will the acceleration of each be? According to Newton’s third law, the forces are equal. Use the second law to find the accelerations. Find the acceleration of the box. force acceleration mass (10 N) a (20 kg) a 0.5 m/s2 Find the acceleration of the person. force acceleration mass (10 N) a (50 kg) a 0.2 m/s2 Analysis 1. Compare the distances the baseball pushed the softball. 2. Use the laws of motion to explain your results. If the same force is applied to two different objects, the one with the larger mass has a smaller acceleration. Figure 20 the ground. According to the third law, you aren’t just pulled toward Earth—Earth also is pulled toward you. When you jump into a swimming pool, how far does Earth move? The force you exert on Earth is the same as the force Earth exerts on you. However, Earth is trillions of times more massive than you are. Because Earth has such a large mass, the pull you exert on it isn’t noticeable. The motion of these galaxies can be explained by Newton’s laws of motion. Gravity and the Third Law Gravity is pulling you down to Newton’s laws of motion apply to all objects, including the distant galaxies shown in Figure 20. Just as the Sun exerts a gravitational force on Earth, Earth exerts an equal and opposite force on the Sun. This force causes a small variation in the Sun’s motion. Variations like this can be used to find planets outside Earth’s solar system. These planets do not reflect enough light to be observed directly by scientists on Earth. By observing small variations in the motions of a star, they are able to determine whether a star is being affected by the force of an orbiting planet. 174 Combining the Laws The laws of motion describe how an object moves when forces act on it. The object might be a football, a planet, or a bone in your arm. Consider what happens during a jump, as shown in Figure 21. First, you push down on the ground. According to the third law of motion, the ground pushes up on you with an equal and opposite force. The force you exert on the ground does not cause a noticeable acceleration to Earth. However, the force the ground exerts on you gives you an acceleration upward. Two forces act on you—gravity pulls you down, and the force from your jump pushes you up. The overall force is upward. As the second law predicts, you accelerate upward as your foot pushes against the ground. When your feet leave the ground, gravity is the only force acting on you. Again according to the second law, you accelerate in the direction of this unbalanced force. The downward acceleration slows you until you stop at the top of your jump and then causes you to increase your speed downward until you reach the ground. When your feet hit the ground, the ground exerts an upward force on you. The force must be greater than the downward force of gravity to slow you down. When you stop accelerating, all the forces on you are balanced. As the first law predicts, you remain at rest. Section Figure 21 A simple jump includes all of Newton’s laws. What forces are acting in each part of this jump? How do they affect your motion? Assessment 1. What are the action and reaction forces on this book when it rests on your hands? 2. You jump from a boat and the boat moves back as you move forward. Explain. 3. Explain how action and reaction forces differ from balanced forces. Use an example. 4. Suppose you face a child, half your mass, on ice. If you push the child, who will have the greater acceleration? By how much? 5. Think Critically When you hit a baseball with a bat, what does the ball exert a force on? What change in motion does this cause? 6. Comparing and Contrasting Compare and contrast the first two laws of motion with the third law of motion. For more help, refer to the Science Skill Handbook. 7. Solving One-Step Equations Your mass is 60 kg. A skateboard’s mass is 3 kg. If you stand on the ground and push the skateboard away with a force of 6 N, what is the force on the board? Does it accelerate? How fast? What is the force of the board on you? Do you accelerate? If so, how fast? For more help, refer to the Math Skill Handbook. SECTION 4 Newton’s Third Law 175 Balanced and Unbalanced Forces N ewton’s laws tell you that to change the velocity of an object, there must be an unbalanced force acting on the object. Changing the velocity can involve changing the speed of the object, changing the direction of motion, or changing both. How can you apply an unbalanced force to an object? How does the motion change when you exert a force in different ways? Recognize the Problem What types of forces will change the speed of an object’s motion, the direction, or both? Thinking Critically How could you exert a force on a block to affect its speed? Its direction? Goals Possible Materials ■ Describe how to create balanced block book and unbalanced forces on an object. ■ Demonstrate forces that change the speed and the direction of an object’s motion. Safety Precautions 176 CHAPTER 6 Newton’s Laws of Motion strings (2) spring scales (2) Data Source Go to the Glencoe Science Web site at tx.science.glencoe.com for data from other students. Planning the Model 1. Choose an appropriate object and describe how you plan to exert forces on the object. 2. List several different ways to exert forces or combinations of forces on the object. Think about how strong each force will need to be to change the motion of the object you will use. Include at least one force or combination of forces that you think will not change the object’s motion. 3. When are the forces balanced and when are they unbalanced? Predict which forces will change the object’s direction, its speed, both, or neither. Check the Model Plans 1. Make sure that your teacher approves your plans before going any further. 2. Compare your plans for exerting forces with those of others in your class.Discuss why each of you chose the forces you chose. Making the Model 1. Set up your model so that you can 2. Exert each of the forces in turn and exert each of the forces that you listed. record how it affects the object’s motion. Analyzing and Applying Results 1. For each of the forces or combinations of forces that you applied to the object, list all of the forces acting on the object. Was the number of forces acting always the same? Was there a situation when only a single force was being applied? Explain. 2. What happened when you exerted balanced forces on the object? Were the results for unbalanced forces the same for different combinations of forces? Why or why not? 3. Were your predictions correct? 4. Which of Newton’s laws of motion did you demonstrate in this activity? 5. Suppose you see a pole that is supposed to be vertical, but is starting to tip over. What could you do to prevent the pole from falling over? Describe the forces acting on the pole as it starts to tip and after you do something. Are the forces balanced or unbalanced? Compare your results with those of other students in your class. Discuss how different combinations of forces affect the motion of the objects. ACTIVITY 177 SCIENCE AND Society SCIENCE ISSUES THAT AFFECT YOU! I f you’ve been to an amusement park lately, you’ve seen the change in roller coasters. They’re taller and faster. They swoop through curves and corkscrews, flipping riders upside down and sideways. But while roller coasters are more popular than ever, there are more concerns about their safety. Should there be a limit to the size and speed of roller coasters? Bigger , 178 Dangerous Coasters? There was a sharp rise in the number of amusement park ride injuries during the late 1990s. In 1998 alone, 4,500 injuries (many on coasters) required emergency treatment. This coincides with a time when roller coasters were getting bigger and faster. You can now ride a 30-story-high roller coaster that will drop you downhill at speeds approaching 160 km/h. Some people wonder if high-speed drops and twists put unhealthy stress on the body. “Technology and ride design are outstripping our understanding of the health effects of high forces on riders,” said one lawmaker. Skeptics argue that, even with safety measures, accidents on super coasters are bound to be severe because of their speed and height. So there must be a limit on how high and fast they can be. Safe As Can Be Supporters of the new roller coasters say that, although they receive lots of attention, injuries and deaths are rare when you consider the hundreds of millions of annual rides taken. What’s more, most accidents or deaths result from breakdowns or foolish behavior of riders, not bad design. Experts say the rides are safer now because they’re designed and evaluated by computers. And, they say the ultimate safeguards are Newton’s laws of motion. Designers use these laws to figure out how fast a roller coaster should move around a turn, how tight to make the turn, and how much to bank the coaster tracks to safely balance the forces acting on the rider. When a coaster does a loop, designers want the ride to feel dangerous. But because of the planned speed of the ride and curvature of the track, designers can use the forces of motion and gravity to keep passengers safely in place. Supporters of super coasters also point out that safety depends on following rules. It’s safe to whip around a curve in a rollercoaster car when seated, for example. But standing to horse around might throw your center of gravity above the car’s side, pitching you out. With amusement parks drawing hundreds of millions of visitors yearly, super coasters are not going away. But with accidents increasing, people who design and who ride coasters must consider both safety and thrills. CONNECTIONS Research Choose an amusement park ride. Do research on the Glencoe Science Web site to find out how forces act on you while you’re on the ride to give you thrills, but still keep you safe. Write a report with diagrams showing how the forces work. Share it with the class. For more information, visit tx.science.glencoe.com Chapter XX 6 Study Guide Section 1 Motion 1. Motion occurs when an object changes its position. The position of an object is described relative to a reference point. 2. Distance is the entire path length an object travels. Displacement is the distance and direction from a starting point to an ending point. 3. Speed is the distance divided by the time. Velocity is the displacement divided by the time. Acceleration is the change in velocity divided by the time. An object is accelerating if its speed or direction of motion changes. Which of these football players is accelerating? 3. The first law of motion states that an object will remain at rest or in motion at constant velocity until it is acted upon by an unbalanced force. Section 3 Newton’s Second Law 1. The second law of motion states that an object acted on by an unbalanced force will accelerate in the direction of the force according to the formula acceleration force/mass. 2. An object acted on by an unbalanced force can speed up, slow down, or turn. 3. Friction is a force that resists motion between two surfaces that are touching. Types of friction include static, sliding, and rolling friction. Air resistance acts against objects moving through the air. Section 4 Newton’s Third Law Section 2 Newton’s First Law 1. A force is a push or a pull. 2. Balanced forces cancel each other. Unbalanced forces cause an object’s motion to change. Are the forces on this dancer balanced or unbalanced? Explain. 180 CHAPTER STUDY GUIDE 1. The third law states that forces always act in equal but opposite pairs. What are action and reaction forces in this picture? 2. Action and reaction forces do not cancel because they act on different objects. FOLDABLES After You Read Use the information on your Foldable and in the chapter to explain Newton’s three laws of motion. Reading &Study & Study Skills Chapter XX 6 Study Guide Complete the following table on the laws of motion. Laws of Motion Law First Statement motion of object and force on object Vocabulary Words acceleration balanced forces displacement first law of motion force friction Third An object will remain at rest or in motion at constant velocity until it is acted upon by an unbalanced force. Describes Relation Between What? a. b. c. d. e. f. Second Using Vocabulary g. second law of motion h. speed i. third law of motion j. unbalanced forces k. velocity Study Tip Draw pictures of difficult concepts described in this chapter. Then label each picture with its concept. This will help you remember the concept more easily. For each set of vocabulary words below, explain the relationship that exists. 1. displacement and velocity 2. force and third law of motion 3. speed and velocity 4. force and friction 5. unbalanced forces and second law of motion 6. balanced forces and first law of motion 7. acceleration and second law of motion 8. acceleration and force CHAPTER STUDY GUIDE 181 Chapter 15 6 Assessment & Choose the word or phrase that best answers the question. 1. Which does NOT change when an unbalanced force acts on an object? A) speed C) mass B) velocity D) motion 2. What force holds you to a sled when it starts moving? A) sliding friction C) air resistance B) static friction D) rolling friction 3. Which would include a direction? A) mass C) velocity B) inertia D) distance 4. What does inertia measure? A) speed C) mass B) force D) acceleration 5. The unbalanced force on a football is 2 N downward. Which way does it accelerate? A) upward B) downward C) doesn’t accelerate D) depends on initial velocity 6. A 50-N force acts on a 4-kg object. What is the acceleration of the object? A) 200 m/s2 B) 25 m/s2 C) 12.5 m/s2 D) the same as its velocity 7. Which of the following indicates that the forces on an object are balanced? A) It is slowing down. B) It is speeding up. C) It moves at constant velocity. D) It turns. 8. Which type of friction is needed to run? A) static friction C) rolling friction B) sliding friction D) air resistance 182 CHAPTER ASSESSMENT Review 9. Carol walks at 0.6 m/s for 60 s. How far does she go? A) 10 m C) 100 m B) 36 m D) 360 m 10. The action force is 3 N left. What is the reaction force? A) 0 N left C) 3 N right B) 3 N left D) 6 N right 11. Explain why gymnasts and climbers put chalk on their hands. 12. Give two examples of rolling friction. 13. A 500-N force is applied to a 10-kg object and a 5-kg object. Which one accelerates faster? Explain. 14. You are skiing down a hill at constant speed. What do Newton’s first two laws say about your motion? 15. How can an object be moving if there is no unbalanced force acting on it? 16. Comparing and Contrasting When you come to school, what distance do you travel? Is the distance you travel greater than your displacement from home? 17. Drawing Conclusions If the gravitational force between Earth and an object always causes the same acceleration, why does a feather drop more slowly than a hammer does? 18. Recognizing Cause and Effect Why does a baseball thrown from the outfield to home plate follow a curved path rather than a straight line? Chapter 15 6 Assessment 19. Concept Mapping Complete the concept maps below for Newton’s laws of motion. Marlena did some research about the speed of sound. The information she gathered is shown in the table below. Newton’s First Law also known as TAKS Practice motion stays the same TEKS 8.2 A, C Speed of Sound in Different Materials Newton’s Second Law acceleration Newton’s Third Law change in motion reaction force force pair acts 20. Making Models Design a model to demonstrate air resistance. Material Speed (m/s) Air 335 Water 1,554 Wood 3,828 Iron 5,103 Stone 5,971 Study the table and answer the following questions. 21. Make a Poster Make a poster identifying all the forces acting in each of the following cases. When is there an unbalanced force? How do Newton’s laws apply? ■ You push against a box; it doesn’t move. ■ You push harder, and the box starts to move. ■ You push the box across the floor at a constant speed. ■ You don’t touch the box. It sits on the floor. TECHNOLOGY Go to the Glencoe Science Web site at tx.science.glencoe.com or use the Glencoe Science CD-ROM for additional chapter assessment. 1. According to this information, in which material is the speed of sound greater than 5,000 m/s? A) water C) air B) wood D) stone 2. A reasonable hypothesis based on these data is that _____ . F) sound travels at the same speed in all materials G) sound travels faster through solids than through liquids and gases H) sound does not travel through gases J) sound travels faster through liquids than through solids and gases CHAPTER ASSESSMENT 183