This Document Contains Chapters 1 to 3 Chapter 1 What is Science? Contents Objects and Properties Quantifying Properties Measurement Systems Standard Units for the Metric System Length Mass Time Metric Prefixes Understandings from Measurements Data Ratios and Generalizations The Density Ratio Symbols and Equations The Nature of Science The Scientific Method Explanations and Investigations Scientific Laws Models and Theories Science, Nonscience, and Pseudoscience From Experimentation to Application Science and Nonscience Pseudoscience Limitations of Science Overview Students begin by considering their immediate environment, and then logically proceed to an understanding that science is a simple, clear, and precise reasoning and a way of thinking about their environment in a quantitative way. Within the chapter, understandings about measurement, ratios, proportions, and equations are developed as the student learns the meaning of significant science words such as “theory,” “law,” and “data.” The chapter develops a concept of the nature of scientific inquiry and presents science as a process. It distinguishes science from nonscientific approaches. It also identifies pseudoscience as a distortion of the scientific process. Suggestions 1. To begin the discussion ask the class their definition of science, accepting all answers. Consider the natural sciences as the study of matter and energy in living and nonliving systems, applied sciences (engineering), and social sciences in the discussion. 2. When discussing the meaning of concept, point out that different levels of thinking exist. Lower levels are not necessarily incorrect but are incomplete compared to higher levels. For example, a young child considers a “dog” to be the short brown furry animal that lives across the street. Later, the child learns that a dog can be any size (within limits) with highly variable colors, and in fact, dogs come in many sizes, colors, and patterns of colors. Still later, a dog (Canis familiaris) is understood to be a domestic mammal closely related to other animals (the common wolf). Each of these generalizations represents a concept, but at different levels of understanding. This discussion of levels of conceptualization will be useful later as a comparison when students argue a concept of something from a lower level of understanding. Many nonscience students have an understanding of acceleration, for example, as a simple straight-line increase in velocity. This concept is not incorrect (the dog across the street), but it represents an incomplete level of conceptual understanding. 3. To introduce properties and referents, display an unusual rock (not pyrite) or object and ask the class to describe it as if talking to someone on the telephone. Keep track of the descriptive terms, then list them all together and ask the students if they could visualize the object if they heard this description over the telephone. The point about typical, vague everyday communications will be obvious. Ask for a volunteer who is majoring in education (or some other major requiring communications) and who loves coffee to describe the taste of coffee to someone who has never tasted it. The student will have difficulty because of the lack of a referent. The concept of a referent will probably be new to most nonscience students, but it is an important concept that will prove useful to them throughout the course. 4. Many devices are available from scientific equipment companies to demonstrate the metric system of measurement, such as the plastic liter case. It is often useful to call attention to the similarities between the metric prefixes and the monetary system (deci- and dime, centi- and cent, and so forth). If students can make change, they can use the metric system. 5. In developing the concept of a ratio, it is useful to have a set of large blocks that you can actually measure to find the surface area to volume ratio. Show all calculations on an overhead transparency or chalkboard. 6. The development of the concepts of a proportionality statement, an equation, and the meaning and uses of symbols is critical if you plan to use a problem-solving approach. The three classes of equations provide an important mental framework on which future concepts will be hung. A student who does not “understand” density has less of a problem learning that density is a ratio that describes a property of matter. Likewise, a student who does not “understand” an electric field has less of a problem learning that an electric field is a concept that is defined by the relationships of an equation. Identifying equations throughout the course as “property,” “concept,” or “relationship” equations will help students sort out their understandings in a meaningful way. 7. In the discussion of scientific laws, analysis of everyday “laws” can be useful (as well as interesting and humorous). One statement of Murphy’s law, for example, is that “the bread always lands butter side down.” Ask the class what quantities are involved in this law and what the relationship is. Another everyday law is Bombeck’s law: “ugly rugs never wear out.” You could also make up a law — [your name]’s law: “the life span of a house plant is inversely proportional to its cost.” Analysis? For Class Discussions 1. A beverage glass is filled to the brim with ice-cold water and ice cubes floating in the water, some floating above the water level. When the ice melts, the water in the glass will a. spill over the brim. b. stay at the same level. c. be less than before the ice melted. 2. A homeowner wishes to fence in part of the yard with a roll of wire fencing material. If all the roll of material is used in all situations, which shape of fenced-in yard would enclose the greatest area? a. square b. rectangle c. both would have equal areas. 3. Again considering the homeowner and a fence made with a roll of wire fencing material. If all the roll of material is used in all situations, which shape of fenced-in yard would enclose the greatest area? a. right-angle triangle b. rectangle c. the answer will vary with the shape used. 4. Which of the following is usually measured by a ratio? a. The speed of a car. b. The density of a rock. c. Both speed and density are ratios. d. Nothing is measured with a ratio. 5. A 1 cm3 piece is removed from a very large lump of modeling clay with a volume of over 100,000 cm3. Which piece has the greatest density? a. The small piece. b. The large piece. c. Both the large and the small piece have the same density. 6. The nature of science is such that a. when proven, scientific theories become scientific laws. b. nature behaves as it does because of scientific laws. c. neither of these statements are true. 7. Which of the following statements is most correct? a. Science is always right. b. Nonscientific study has little value. c. Science has all the answers. d. Science seeks to explain natural occurrences. 8. When a scientist sees patterns or relationships among a number of isolated facts, a. laws or principles are developed. b. truth has been reached. c. elaborate tests must be developed to prove the pattern exists. d. as a rule, the pattern must be published. 9. Scientific method involves each of the following except a. systematic search for information. b. observation and experimentation. c. forming and testing possible solutions. d. formulation of laws and principles that control the observed facts. 10. Select the description of a controlled experiment: a. Group I, 50 mice fed, watered, Group II, 25 mice differently fed, watered. b. Group I, 25 mice fed, watered, Group II, 50 mice 1/2 fed, watered. c. Group A, 50 mice fed, watered, Group B, 50 mice fed differently, watered differently. d. Group A, 50 mice fed, watered, Group B, 50 mice fed different food, watered. Answers: 1b (ice floats above the water line because it is less dense; when it melts it occupies the same volume displaced while floating), 2a, 3c, 4c, 5c, 6c, 7d, 8a, 9d, 10d. Answers to Questions for Thought 1. A concept is a generalized mental image of an object or idea. 2. A measurement statement always contains a number and the name of the referent unit. The number tells “how many,” and the unit explains “of what.” 3. The primary advantage of the English system of measurement is that most United States citizens are familiar with the basic units and their sizes. The metric system has the advantage of easily converting the units to a convenient size merely by moving the decimal and using the appropriate prefix with the basic unit. 4. The meter is the metric standard of length and is defined as the distance light travels in a vacuum in 1/299,792,458 seconds. The metric standard of mass is the kilogram, which is defined as the mass of a standard kilogram kept by the International Bureau of Weights and Measures in France. The standard unit of time is the second, which is defined as the time required for a certain number of vibrations to occur in a type of cesium atom. 5. The density of a liquid does not depend upon the shape of its container. Density is a ratio of mass per unit volume. As long as this ratio stays the same the density does not change. 6. A flattened pancake of clay has the same density as a ball of the same clay. Even though the shape of the material has changed, the volume and the mass of the material have not changed. Since density is a ratio of mass per unit volume the density is the same. 7. A hypothesis and a scientific theory are alike in that both are working explanations. A hypothesis, however, usually deals with a narrow range of phenomena, while a theory is a broad working hypothesis that forms the basis for thought and experimentation in a field of science. 8. A model is a mental or physical representation of something that cannot be directly observed. A simpler representation of a complex phenomenon is also a model. A model is used as an easily visualized and understood analogy to some behavior or system that is not directly observable or is very complex. 9. Theories do not always enjoy complete acceptance but are rarely rejected completely. The better a theory explains the results of experiments and correctly predicts the results of new experiments, the greater the degree of acceptance. Theories that do not conform with experiments are usually modified and gain wider acceptance. 10. Pseudoscience is a methodology, presentation, or activity that appears to be or is presented as being scientific, but is not supportable as valid or reliable. It can be identified by the following characteristics: a lack of valid substantiation of claims, untestable hypotheses, unwillingness to submit to rigorous testing, or inability to repeat the experiments. Group B Solutions 1. Answers will vary. In general, mass and weight are proportional in a given location, so Kilograms can be converted to grams by the procedure described in the appendix A of the text. 2. Since density is given by the relationship m/V, then 3. The volume of a sample of copper is given and the problem asks for the mass. From the relationship of m/V, solving for the mass (m) tells you that the density () times the volume (V) gives you the mass, m = V. The density of copper, 8.96 g/cm3, is obtained from table 1.3 in the text, and 4. Solving the relationship m/V for volume gives V = m/, and The answer is rounded up to provide two significant figures, the least number given in the density of 0.92 g/cm3. This assumes that 5,000 grams of ice means exactly 5,000 grams, that is, that 5,000 has four significant figures. 5. A 50.0 cm3 sample with a mass of 51.5 grams has a density of According to table 1.3, 1.03 g/cm3 is the mass density of seawater, so the substance must be seawater. 6. The problem asks for a mass, gives the mass density of gasoline, and gives the volume. Thus, you need the relationship between mass, volume, and mass density. The volume is given in liters (L), which should first be converted to cm3 because this is the unit in which density is expressed. The relationship of m/V solved for mass is V, so the solution is The answer is rounded up to provide three significant figures, the number of significant figures given in the density and volume measurements. The answer of 64,300 g is correct, but usually it is better to express the answer using “standard” conventions being used. Using scientific notation would be better yet because of ease of showing significant figures and the ease of performing mathematical operations. 7. From table 1.3, the density of iron is given as 7.87 g/cm3. Converting 2.00 kg to the same units as the density gives 2,000 g. Solving m/V for volume gives 8. The length of one side of the box is 1.00 m. Reasoning: Since the density of water is 1.00 g/cm3, then the volume of 1,000,000 g (1,000 kg) of water is 1,000,000 cm3. A cubic box with a volume of 1,000,000 cm3 is 100 cm (since 100 100 100 = 1,000,000). Converting 100 cm to m units, the cube is 1.00 m on each edge. 9. The relationship between mass, volume, and density is m/V. The problem gives a volume, but not a mass. The mass, however, can be assumed to remain constant during the compression of the bun so the mass can be obtained from the original volume and density, or A mass of 36 g and the new volume of 195 cm3 mean that the new density of the crushed bread is 10. According to table 1.3, lead has a density of 11.4 g/cm3. Therefore a 1.00 cm3 sample of lead would have a mass of Also according to table 1.3, iron has a density of 7.87 g/cm3. To balance a mass of 11.4 g of lead, a volume of this much iron would be required: For Further Analysis 1. Answering this question requires the critical thinking skills of clarifying values and developing criteria for evaluation. Answers will vary. 2. This question requires students to explore beliefs and evaluate arguments. Answers will vary. 3. This requires the student to evaluate a concept, comparing the concept with the real world. The evaluation should note that density is a mass over volume ratio and larger and larger volumes with the same mass reduces the density. 4. Thinking precisely, the student will realize that doubling a quantity that is squared will result in a four-fold increase. 5. Thinking precisely and evaluating critical vocabulary is required. Answers will vary. 6. Thinking precisely and evaluating critical vocabulary is required. Answers will vary. 7. Exploring arguments and clarifying issues is required. Answers will vary. Chapter 2 Motion Contents Describing Motion Measuring Motion Speed Velocity Acceleration Forces A Closer Look: A Bicycle Racer’s Edge Horizontal Motion on Land Falling Objects Compound Motion Vertical Projectiles Horizontal Projectiles Laws of Motion Newton’s First Law of Motion Newton’s Second Law of Motion Weight and Mass Newton’s Third Law of Motion Momentum Conservation of Momentum Impulse Forces and Circular Motion Newton’s Law of Gravitation Earth Satellites Weightlessness A Closer Look: Gravity Problems Overview This chapter primarily contains the patterns of motion developed by Isaac Newton (A.D. 1642–1727). Newton made many contributions to science, but his three laws of motion and his law of gravitation are the most famous. The three laws of motion are concerned with (1) what happens to the motion of a single object when no unbalanced forces are involved, (2) the relationship between the force, the mass of an object, and the resulting change of motion when an unbalanced force is involved, and (3) the relationship between the force experienced by two objects when they interact. The laws of motion are universal, that is, they apply throughout the known universe and describe all motion. Throughout the universe mass is a measure of inertia, and inertia exists everywhere. A change of motion, acceleration, always results from an unbalanced force everywhere in the known universe. Finally, forces of the universe always come in pairs. Of the two forces one force is always equal in magnitude but opposite in direction to the other. The law of gravitation is also applicable throughout the known universe. All objects in the Solar System — the sun and the planets, the earth and its moon, and all orbiting satellites — obey the law of gravitation. Relativistic considerations should not be mentioned at this time. Concentrate on Newton's laws of motion, not Einstein's modifications of them. The key to understanding patterns of motion is to understand simultaneously the ideas represented in the three laws of motion. These areas follow: 1. Inertia is the resistance to a change in the state of motion of an object in the absence of an unbalanced force. An object at rest remains at rest and an object moving in a straight line retains its straight-line motion in the absence of an unbalanced force. The analysis of why a ball moving across a smooth floor comes to a stop, as presented in the previous chapter, is an important part of the development of this concept. Newton's first law of motion is also known as the law of inertia. 2. Mass is defined as a measure of inertia, that is, a resistance to a change in the state of motion of an object. Thus the greater the mass the greater the resistance to a change in the state of motion. Acceleration is a change in the state of motion of an object. According to the definition developed in the previous chapter, an object that speeds up, slows down, or changes its direction of travel is undergoing an acceleration. Students who have difficulty accepting the meanings of mass and acceleration often have less difficulty if they are told these are definitions of the quantities. A force is a push or a pull that is capable of causing a change in the state of motion of an object, that is, capable of producing an acceleration. The resulting acceleration is always in the same direction as the direction of the applied force. Newton's second law of motion is a relationship between mass, acceleration, and an unbalanced force that becomes clear when the conceptual meaning of these terms is understood. The relationship is that the greater the mass (inertia), the greater the force required to bring about a change in the state of motion (acceleration). In symbol form the relationship is a F/m, or the more familiar F ma. Since a newton of force is defined in terms of a certain mass (1 kg) and a certain acceleration (1 m/s2), the units are the same on both sides and the relationship becomes an equation, or F = ma. This is an example of an equation that defines a concept (see chapter 1). 3. A single force never occurs alone; a force is always produced by the interaction of two or more objects. There is always a matched and opposite force that occurs at the same time, and Newton's second law of motion is a statement of this relationship. Suggestions 1. The need for precision and exact understanding should be emphasized as the various terms such as speed, velocity, rate, distance, acceleration, and others are presented. Stress the reasoning behind each equation, for example, that velocity is a ratio that describes a property of objects in motion. Likewise, acceleration is a time rate of change of velocity, so vf - vi/t not only makes sense but can be reasoned out rather than memorized. Students are sometimes confused by the use of the symbol “v” for both speed and velocity. Explain that speed is the same quantity as velocity but without direction, so the same symbol is used to simplify things. On the point of simplifying things, avoid the temptation to use calculus in any explanation or discussion. 2. Students are generally interested in “relative to what” questions concerning motion. For example, what is the speed of an insect flying at 5 mph from the front to the back of a bus moving at 50 mph? What do you observe happening to an object dropped inside an airplane moving at 600 mph? What would an observer outside the airplane observe happening to the object? 3. The discussion of what happens to a ball rolling across the floor is an important one, and many students who think from an “Aristotelian framework” are surprised by the analysis. When discussing the role of friction and objects moving on the earth’s surface, it is often interesting to ask why planets do not stop moving around the sun. Spur on the discussion by answering with another question, Why should they stop? It might be helpful to review the meaning of vector arrows that represent forces. 4. Another way to consider acceleration is to ask, How fast does “how fast” change? If students have learned the concept of a ratio they will understand the concept of uniform straight-line motion. The acceleration concepts, however, require the use of a ratio within another ratio, that is, a change of velocity (a ratio within) per unit of time (the acceleration ratio). This understanding is necessary (along with some basic math skills) to understand the meaning of such units as m/s2. 5. Demonstrations that illustrate the characteristics of projectile motion are illustrated in several devices found in scientific catalogs. Among the most impressive is the “monkey and hunter” demonstration. Students enjoy this demonstration along with the humor the instructor can induce while performing it. 6. There are many demonstrations and devices available from scientific suppliers that readily illustrate the laws of motion. However, none seems better than the personal experiences of students who have stood in the aisle of a bus as it starts moving, turns a corner, or comes to a stop. Use the three laws of motion to analyze the inertia, forces, and resulting changes of motion of a student standing in such an aisle of a bus. 7. Stress that weight and mass are two entirely different concepts. You will probably have to emphasize more than once that weight is another name for the gravitational force acting on an object, and that weight varies from place to place while mass does not. Use the second law of motion to show how weight can be used to calculate mass. A large demonstration spring scale calibrated in newtons can be used to show that a 1 kg mass weighs 9.8 N. Other masses can be weighed to show that weight and mass are proportional in a given location. 8. In solving problems involving the third law of motion, it is helpful for students to realize that a change in the state of motion always occurs in the same direction as the direction of an applied force. If you apply an unbalanced force on a ball toward the North, you would expect the ball to move toward the North. Thus if one starts walking toward the North a force must have been applied in the same direction. The foot pushed on the ground in the opposite direction, so it must be that the equal and opposite force of the ground pushing on the foot is what caused the motion toward the North. It seems almost anthropomorphic to state that the ground pushed on a foot, but no other answer is possible with this analysis. The next step, so to is to realize that since the force of the foot on the ground equals the force of the ground on the foot (third law). Then the mass of the earth times the acceleration of the earth (second law) must equal the mass of the person times the acceleration of the person (ma = ma). This means at least two things: (1) that the earth must move when you walk across the surface (earth's acceleration must be greater than zero) and (2) that the earth would move with the same acceleration as the person if both had the same mass. Students are making progress when they can understand or make this kind of analysis. 9. A large coffee can attached to a strong cord and filled with water makes an interesting demonstration of centripetal force and inertia when whirled overhead. Practice this, however, before trying before a class. 10. More demonstrations: (a) Show the stroboscopic effect as a means of measuring motion. Use a strobe light or hand stroboscopes, for example, to “stop” the motion of a spinning wheel of an upside-down bicycle. (b) Roll a steel ball down a long ramp and mark the distance at the end of each second. Plot distance vs. time and distance vs. time squared to verify the acceleration equation. (c) Crumple a sheet of paper tightly into a small ball. Drop the crumpled ball and a sheet of uncrumpled paper from the same height. Discuss which is accelerated at 9.8 m/s2 and the roll of air resistance. (d) Use the commercial apparatus that shoots or moves one ball horizontally and drops another ball vertically at the same time. A single “click” means that both balls hit the floor at the same time. This illustrates the independence of velocities. (e) Drop a small steel ball from the highest place practical into a tub of water. Make sure this is done on a day without wind and with no person near the tub. Time the fall with a stopwatch. Measure the vertical distance accurately, then find g from d = 1/2gt2. (f) Use a spring scale to show that a 1.0 kg mass weighs 9.8 N. Use other masses to show that the weight of an object is always proportional to the mass in a given location. (g) Use an air track to illustrate Newton’s first and second law of motion. If an air track is not available, consider a slab of ice or dry ice on a smooth demonstration table top. Wood blocks can be set on the ice to add mass. (h) Will a jet plane backed up to a brick wall take off faster than one out in the open? Compare the jet plane to a balloon filled with air, that is, the balloon is propelled by a jet of escaping air. Thus the movement is a consequence of Newton’s third law and the brick wall will make no difference–a jet plane backed up to a brick will take off the same as an identical jet plane out in the open. (i) Seat yourself on a small cart with a CO2 fire extinguisher or a bottle of compressed air from the shop. Hold the device between your feet and legs with the escape valve pointed away from your body. With the way clear behind you, carefully discharge a short burst of gas as you accelerate. This attention-grabber affords an opportunity to review all three of Newton’s Laws of motion. (j) Demonstrate that the acceleration of a freely falling object is independent of weight. Use a commercial “free-fall tube” if one is available. If not, try a large- diameter 1 meter glass or plastic tube with a solid stopper in one end and a one- hole stopper in the other. Place a coil and a feather in the tube, then connect the one-hole stopper to a vacuum pump. Invert the tube to show how the coin and feather fall in air. Pump air from the tube, then again invert to show the coin and feather in free fall. For Class Discussions 1. Neglecting air resistance, a ball in freefall will have a. constant speed and constant acceleration. b. increasing speed and increasing acceleration. c. increasing speed and decreasing acceleration. d. increasing speed and constant acceleration. 2. Neglecting air resistance, a ball rolling down the slope of a steep hill will have a. constant speed and constant acceleration. b. increasing speed and increasing acceleration. c. increasing speed and decreasing acceleration. d. increasing speed and constant acceleration. 3. Neglecting air resistance, a ball thrown straight up will come to a momentary stop at the top of the path. What is the acceleration of the ball during this stop? a. 9.8 m/s2. b. zero. c. less than 9.8 m/s2. d. more than 9.8 m/s2. 4. Neglecting air resistance, the ball thrown straight up comes to a momentary stop at the top of the path, then falls for 1.0 s. What is speed of the ball after falling 1.0 s? a. 1 m/s b. 4.9 m/s c. 9.8 m/s d. 19.6 m/s 5. Neglecting air resistance, the ball thrown straight up comes to a momentary stop at the top of the path, then falls for 2.0 s. What distance did the ball fall during the 2.0 s? a. 1 m b. 4.9 m c. 9.8 m d. 19.6 m 6. A ball is thrown straight up at the same time an ball is thrown straight down from a bridge, with the same initial speed. Neglecting air resistance, which ball would have a greater speed when it hits the ground? a. The one thrown straight up. b. The one thrown straight down. c. Both balls would have the same speed. 7. After being released, a ball thrown straight down from a bridge would have an acceleration of a. 9.8 m/s2. b. zero. c. less than 9.8 m/s2. d. more than 9.8 m/s2. 8. A gun is aimed at an apple hanging from a tree. The instant the gun is fired the apple falls to the ground, and the bullet a. hits the apple. b. arrives late, missing the apple. c. may or may not hit the apple, depending on how fast it is moving. 9. You are at rest with a grocery cart at the supermarket, when you apply a certain force to the cart for a short time and acquire a certain speed. Suppose you had bought more groceries, enough to double the mass of the groceries and cart. Neglecting friction, doubling the mass would have what effect on the resulting final speed if you used the same force for the same length of time? The new final speed would be a. one-fourth. b. one-half. c. the same time. d. doubled. e. quadrupled. 10. You are moving a grocery cart at a constant speed in a straight line down the aisle of a store. The forces on the cart are a. unbalanced, in the direction of the movement. b. balanced, with a net force of zero. c. equal to the force of gravity acting on the cart. d. greater than the frictional forces opposing the motion of the cart. 11. Considering the gravitational attraction between the Earth and Moon, the a. more massive Earth pulls harder on the less massive Moon. b. less massive Moon pulls harder on the more massive Earth. c. attraction between the Earth and Moon and the Moon and Earth are equal. d. attraction varies with the Moon phase, being greatest at a full moon. 12. You are outside a store, moving a loaded grocery cart down the street on a very steep hill. It is difficult, but you are able to pull back on the handle and keep the cart moving down the street in a straight line and at a constant speed. The forces on the cart are a. unbalanced, in the direction of the movement. b. balanced, with a net force of zero. c. unbalanced if there is a massive load of groceries. d. equal to the force of gravity acting on the cart. e. greater than the frictional forces opposing the motion of the cart. 13. Which of the following must be true about a horse pulling a buggy? a. According to the third law of motion, the horse pulls on the buggy and the buggy pulls on the horse with an equal and opposite force. Therefore the net force is zero and the buggy cannot move. b. Since they move forward, this means the horse is pulling harder on the buggy than the buggy is pulling on the horse. c. The action force from the horse is quicker than the reaction force from the buggy, so the buggy moves forward. d. The action-reaction force between the horse and buggy are equal, but the resisting frictional force on the buggy is smaller since it is on wheels. 14. Suppose you have a choice of driving your speeding car head on into a massive concrete wall or hitting an identical car head on. Which would produce the greatest change in the momentum of your car? a. The identical car. b. The concrete wall. c. Both would be equal. 15. A small, compact car and a large sports utility vehicle collide head on and stick together. Which vehicle had the larger momentum change? a. The small, compact car. b. The large sports utility vehicle. c. Both would be equal. 16. Again consider the small, compact car and large sports utility vehicle that collided head on and stuck together. Which experienced the larger deceleration during the collision? a. The small, compact car. b. The large sports utility vehicle. c. Both would be equal. Answers: 1d, 2c (a = g straight down, but decreases to zero on a level surface), 3a (acceleration is a rate of change of velocity and gravity is acting, F = ma, so a must be occurring), 4b (initial speed was zero, average speed is one-half of final speed), 5d, 6c, 7a (after release only gravity acts on ball), 8a (the apple and bullet accelerate downward together, no matter how fast the bullet is moving), 9b, 10b, 11c, 12b, 13d, 14c, 15c, 16a. Answers to Questions for Thought 1. The speed of the insect relative to the ground is the 50.0 mi/h of the bus plus the 5.0 mi/h of the insect relative to the bus for a total of 55 mi/h. Relative to the bus alone the speed of the insect is 5.0 mi/h. 2. After it leaves the rifle barrel, the force of gravity acting straight down is the only force acting on the bullet. 3. Gravity does not depend upon some medium to convey its “force at a distance,” so it can operate in a vacuum. 4. Yes, the small car would have to be moving with a much higher velocity, but it can have the same momentum since momentum is mass times velocity. 5. A net force of zero is required to maintain a constant velocity. The force of friction is balanced out by the force from the engine as a car drives with a constant velocity. 6. The action and reaction forces are between two objects that are interacting. An unbalanced force occurs on a single object as the result of one or more interactions with other objects. 7. The change of momentum from hitting the ground, or impulse, is the product of the applied force and time that the force is applied. The product of the force and the time is always the same, but both can be varied. Bending your knees has you hit the ground increases the time, therefore reducing the applied force. 8. Your weight can change from place to place because weight is a downward force from gravitational attraction on your mass and the force of gravity can vary from place to place. 9. Nothing! There is no force parallel to the motion to increase or decrease the earth's speed, so the speed remains constant. 10. If you have something to throw, such as car keys or a snowball, you can easily get off the frictionless ice. Since the force you apply to the thrown object results in an equal and opposite force (the third law of motion), you will move in the opposite direction as the object is thrown (the second law of motion). The same result can be achieved by blowing a puff of air in a direction opposite to the way you wish to move. 11. Considering everything else to be equal, the two rockets will have the same acceleration. In both cases, the acceleration results as burning rocket fuel escapes the rocket, exerting an unbalanced force on the rocket (third law) and the rocket accelerates during the applied force (second law). The acceleration has nothing to do with the escaping gases having something to “push against.” 12. The astronaut is traveling with the same speed as the spaceship as he or she leaves. If no net force is applied parallel to the direction of motion of either the astronaut or the spaceship, they will both maintain a constant velocity and will stay together. Group B Solutions 1. The distance that a sound with this velocity travels in the given time is Since the sound traveled from the rifle to the cliff and then back, the cliff must be 172 m/2 = 86.0 m away. 2. 3. 4. 5. The mass of a 39,200 N space probe on the surface of Earth is The probe will have the same mass on Mars. 6. 7. 8. Mass of ball: Momentum of ball: 9. Listing the known and unknown quantities: This is a conservation of momentum question, where the shell and cannon can be considered as a system of interacting objects: The cannon recoils with a velocity of 8 m/s. 10. (a) (b) 11. 12. For Further Analysis 1. Similar – both speed and velocity describe a magnitude of motion, that is, how fast something is moving. Differences – velocity must specify a direction; speed does not. 2. Similar – both velocity and acceleration describe motion. Differences – velocity specifies how fast something is moving in a particular direction; acceleration specified a change of velocity (speed, direction, or both). 3. This requires a comparison of beliefs and an analysis and comparison with new contexts. Answers will vary, but should show understanding of Newton’s three laws of motion. 4. This question requires both clarifying beliefs and comparing perspectives. Answers will vary. 5. Requires refining of understanding. Mass is a measure of inertia, meaning a resistance to a change of motion. Weight is gravitational acceleration acting on a mass. Since gravity can vary from place to place, the weight as a result of gravity will also vary from place to place. 6. Requires clarifying and analyzing several conceptual understandings. Newton’s first law of motion tells us that motion is unchanged in a straight line without an unbalanced force. An object moving on the end of a string in a circular path is pulled out of a straight line by a centripetal force on the string. The object will move off in a straight line if the string breaks. It would move off in some other direction if other forces were involved. Chapter 3 Energy Contents Work Units of Work Power Motion, Position, and Energy Potential Energy Kinetic Energy Energy Flow Energy Forms Energy Conversion Energy Conservation Energy Transfer Energy Sources Today Petroleum Coal Moving Water Nuclear Conserving Energy Energy Tomorrow Solar Technologies Geothermal Energy Hydrogen Overview Energy is generally a difficult subject for many nonscience students because it is an abstract concept. This chapter begins with the more easily visualized concepts of work and power, develops two general aspects of energy (position and motion) based on concepts learned in previous chapters, and then uses these aspects as a basis for a conceptual scheme for understanding energy. This scheme is then applied in considering the energy sources used today. Work and energy are closely related concepts. Work is defined in this chapter by using the second class of equations (defining a concept; see chapter 1). Work is defined as the product of a force moving through a distance, or W = Fd. Both metric units and English units are presented because both are in everyday use today. The metric unit of work is the newton-meter, which is called a joule. The English unit of work is the foot-pound, which does not have another name. Along with learning the scientific meaning of work, students will need to become accustomed to using the terms in the sense of work accomplished or the potential for doing work, for example, “How much work was done on . . .?” and “How much work can the object now do?” The energy of position, or potential energy, can be measured by how much work is done on an object to give it energy of position or by how much work it can now do because of its position. Since work involves forces and movement through a distance, the variables involved are the force, the movement (acceleration = change of motion), and the mass of the object (a measure of inertia, or resistance to a change of motion). Thus a non-calculus calculation of potential energy can begin with Newton's second law of motion, or F = ma. To obtain an expression of work, both sides of this equation are multiplied by distance, h (for height, which is a vertical distance), which gives Fd = mah. For gravitational potential energy, the acceleration is g and the relationship is W = mgh or PE = mgh. The potential energy unit turns out to be joules, which is the same unit used to do work to create the potential energy to begin with. Thus from this analysis comes the first idea that work = energy = work, or that both are fundamentally the same thing. The energy of motion, or kinetic energy, can also be measured by how much work is done on an object to give it energy of motion or by how much work it can now do because of its motion. Again, work involves forces and movement through a distance such as are involved in throwing a baseball. The non-calculus relationship again involves the variables in Newton's second law of motion, F = ma. As before, both sides are multiplied by distance to obtain an expression of work, which in this case is the energy of motion, and KE = mad. Now we need to put the distance quantity (d) in terms of a final velocity (vf) for kinetic energy. This requires the use of the first three equations presented in chapter 2: Step 1. The relationship between the average velocity, distance, and time is Step 2. The average velocity quantity and the time quantity could now be substituted for d in KE = mad, but they are still not in terms of a final velocity. First, a final velocity is substituted for average velocity ( ) Step 3. Next a final velocity is substituted for time by rearranging the equation for acceleration Now it is a matter of simple substitution of the solutions in step 2 and step 3 into the rearrangement shown in step 1, or These terms can now be substituted for the d in KE = mad to put the equation in terms of velocity rather than distance, and The a's now cancel and the equation is rearranged to the more familiar expression of kinetic energy, which is The kinetic energy unit turns out to be a joule, which is the same unit used to do the work to create the kinetic energy to begin with. Again you can see that work = energy = work, that is, both energy and work are fundamentally the same thing. The similarities between energy and work are discussed throughout the presentation of the energy flow scheme. Note that many textbooks define heat as a form of energy rather than energy in transit between two forms. Either definition is correct. Considering heat as a form of energy, however, is a conceptual level akin to considering a dog as the animal that lives across the street (see chapter 1 in this manual). Suggestions 1. An important key to understanding the concepts presented in this chapter is understanding the relationship between the work performed to give an object potential or kinetic energy, the energy that the object has by way of its position or motion, and the work that an object can do as a result of its kinetic or potential energy. Use a demonstration spring scale calibrated in newtons to lift a kilogram mass one meter from the floor to a shelf. Show the weight of the mass is 9.8 N, and the work done is 9.8 J in lifting the mass 1 m. Discuss that the work is done against gravity. Now use the equation to show the potential energy of the mass is now 9.8 J as a result of the work done on it. Compare the work done on the mass, the potential energy that the mass has as a result, and the work the mass can now do as a result of its position in the attractive force of earth's gravitational field. 2. Students find it interesting to compare the power ratings in one system of measurement with power ratings in the other. A 1500 W hair dryer, for example, has an English power equivalent of almost 2 hp. A 100 hp car, on the other hand, has a metric power rating of a little less than 75 kW. 3. The expressions of kinetic energy, potential energy, and the law of conservation of energy apply to the conversion of any energy form to another. If the students seem confused by electromagnetic or nuclear interactions, concentrate on mechanical interactions. They can learn the relationships involved in the mechanical interactions and apply the concepts to more abstract materials in later chapters. 4. A swinging pendulum provides a good demonstration of the conversion of potential to kinetic energy and from kinetic to potential energy. A meter stick can be used to show that the bob rises to about the same height as it speeds up, as it descends, then slows as it moves up the other half of the arc of its swing. Conservation laws can also be shown by the popular line of steel balls supported by wires on a frame. When one ball is released to hit the line of balls, it stops while one swings out the other side. If two are allowed to hit the line of balls, they stop while two swing out the other side. These elastic collisions demonstrate both the law of conservation of energy and the law of conservation of momentum. 5. See the September 1978 issue of the American Journal of Physics for an interesting and important article on exponential growth and doubling time as applied to our energy sources today. The article reveals the “best-kept secret of the century” about our energy supplies, a topic that should be discussed if future energy supplies are considered. 6. Additional demonstrations: (a) Use a pendulum to demonstrate conservation of energy as the bob converts potential energy (top of its swing) to kinetic energy (bottom of swing), then back to potential again. Point out that a book falling from a shelf also converts PE (top of fall) to KE (bottom of fall). (b) Support a long piece of transparent tubing in a long arc, then roll marbles down one side to see if they roll to the same height at the other side of the tube. Add a loop or several loops and analyze potential energy and kinetic energy at the beginning and end of each loop compared to the overall length of tubing. (c) A line of steel spheres supported by strings can be used to demonstrate conservation of energy in elastic collisions. One mass pulled back and released will result in one mass leaving the row at the other end. If two are pulled back and released, two will leave the other end and so on. Try pulling one mass back from one side and two back from the other side, releasing all at the same time. (d) If your classroom is above or below street level, you can ask each student to calculate how much work is done bringing books to (or from) class. For Class Discussions 1. A spring-loaded paper clamp exerts a force of 2 N on 10 sheets of paper it is holding together. Is the clamp doing work as it holds the papers together? a. Yes! b. No! 2. An iron cannon ball and a bowling ball were dropped at the same time from the top of a building. At the instant before the balls hit the sidewalk, the heavier cannon ball has greater a. velocity b. acceleration c. kinetic energy d. all of these are the same for the two balls 3. Two students are poised to dive off equal height diving towers to a swimming pool below. Student B is twice as massive as student A. Which of the following is true? a. Student B will reach the water sooner than student A. b. Both students have the same gravitational potential energy. c. Both students will have the same kinetic energy just before hitting the water. d. Student B did twice as much work climbing the tower. 4. The two students are again poised to dive off equal height diving towers to a swimming pool below. Student B is twice as massive as student A. Just before hitting the water, student B will have a. the same kinetic energy as student A. b. twice as much kinetic energy as student A. c. half as much kinetic energy as student A. d. four times as much kinetic energy as student A. 5. A car is moving straight down a highway under ideal conditions. What factor has the greatest influence on how much work must be done on the car to bring it to a complete stop? a. How fast it is moving. b. The weight of the car. c. The mass of the car. d. The latitude of the location. 6. Two identical cars are moving straight down a highway under identical conditions, except car B is moving three as fast as car A. How much more work is needed to stop car B? a. Twice as much. b. Three times as much. c. Six times as much. d. Nine times as much. 7. Two identical cars start at rest on a long hill, with car B twice as high as car A. How much more work is needed to stop car B at the bottom of the hill? a. Twice as much. b. Three times as much. c. Six times as much. d. Nine times as much. 8. Suppose your grocery cart is moving at a constant momentum in a straight line down the aisle of a store, without friction. How will the speed change as you drop groceries into the moving cart? a. increase b. decrease c. remain the same 9. Again consider your grocery cart that is moving at a constant momentum in a straight line down the aisle of a store, without friction. How will the kinetic energy of the cart change as you drop groceries into it? a. increase b. decrease c. remain the same 10. A water balloon dropped from a dorm window does not break on the sidewalk. From how much higher would you need to drop the balloon to double the speed of impact? a. Twice as high. b. Three times as high. c. Four times as high. d. Eight times as high. Answers: 1b, 2c, 3d, 4b, 5a, 6d (W = KE = 1/2mv2 and 32 = 9), 7a (2mgh = 21/2mv2 = 2W), 8b (constant p with increased m in p = mv), 9b, 10c (v = 2gh). Answers to Questions for Thought 1. Energy is the ability to do work, and doing work on something gives it energy. 2. The work done is equal to the increase in gravitational potential energy. 3. Relative to the bus, the person has no kinetic energy because the person is at rest relative to the bus. Relative to the ground, however, the person does have kinetic energy because the person is moving with the same speed as the bus. 4. Because a time factor is in the rating: a watt is a unit of power, and power is work per unit time. A 100 W light bulb uses energy at a rate of 100 J per s. 5. A kWh is a unit of work, and since energy is the ability to do work, it is also a unit of energy. In terms of units, a watt is a joule per second, and an hour, as a second, is a unit of time. The time units cancel, leaving a unit of a joule, which can be used to measure either work or energy. 6. Energy is eventually converted into unrecoverable radiant energy, so new sources of convertible energy must be found in order to continue performing useful work. 7. If the spring clamp does not cause the paper to move, it is not acting through a distance and no work is done. 8. Fossil fuels contain energy from plants or animals that lived millions of years ago. These plants and animals are known from the fossils they left behind, and the energy in the fuels represents energy stored from these ancient organisms. 9. The machine would not be in accord with the principle of conservation of energy. 10. A joule is one newton-meter. A joule of work is from a force acting through a distance while a joule of energy is the ability to perform one joule of work. The use of the same unit means that work and energy are fundamentally the same thing. 11. The energy required is less on the moon because the weight of the object (the downward force due to gravity) depends upon the force of gravity, which is less on the moon than on the earth. Less energy is needed to do the work of raising the mass on the moon, and the elevated object on the moon has less potential energy as a consequence of the work done. 12. The energy is converted to heat and sound. Group B Solutions 1. 2. 3. 4. 5. 6. 7. The work done on an object to put it in motion or the work done by a moving object as a result of its motion is equal to its kinetic energy, so 8. (a) (b 9. (a) (b) 10. (a) (b) (c) Since the PE lost is equal to the KE gained, then KE = 740 J. 11. Doubling the speed quadruples the kinetic energy. 12. (a) (b) For Further Analysis 1. Analyzing and evaluating the definition of mechanical work shows that work is defined as the product of a force and the distance moved as a result of the force. In other words, movement is part of the definition of work. 2. Similarities – both involve a force moving something through a distance. Difference – power is a time rate of doing work; work by itself does not involve time. 3. This requires analyzing and evaluating an interpretation of work. The correct analysis is that this is a true statement. 4. This requires analyzing, exploring beliefs, and clarifying a conceptual understanding. Answers will vary, but should clarify that work input always equals work output. 5. Reasoning precisely about the equation shows that K.E. varies directly with the mass, but varies with the square of the velocity. Thus, twice the mass requires twice the work (K.E.) to bring a car to a stop, but twice the speed requires four times the work to bring the car to a stop. 6. Generating and analyzing this situation will result in answers that vary. 7. Analysis should show mechanical energy (gravitational), chemical (electromagnetic), radiant (electromagnetic), electrical (electromagnetic), and nuclear (nuclear). 8. Evaluating and analyzing should show that this device does not exist. 9. Evaluating and analyzing should show that such contradictions do not exist. Instructor Manual for Integrated Science Bill W. Tillery, Eldon D. Enger , Frederick C. Ross 9780073512259
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