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Sci 111 Ch1

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Published on December 17, 2008

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Slide 1: Science 111 Dr. Jeff Lewis Winter 2008 Go over syllabi Science 111 : Science 111 Chapter 1 Jeff Lewis ©2008 Ch. 1: Patterns of Motion and Equilibrium : Ch. 1: Patterns of Motion and Equilibrium Read Chapter 1 The text starts with a discussion about the ancient Greek scientist and philosopher Aristotle. Aristotle (384-322 BC) : Aristotle (384-322 BC) The greatest of the ancient Greek scientists. One of his ideas: All matter is composed of four basic substances, earth, air, fire, water (and a fifth element, quintessence, which heavenly objects like the Sun and Moon were made of). How did that work? : How did that work? All substance are some combination of the four elements, such as Steam = fire + water Smoke = air + fire Mud = water + earth Plato expanded on this idea: : Plato expanded on this idea: Each element has a different shape. Fire particles are tetrahedrons with sharp corners, hence painful. It’s a beautiful scheme! The beauty of it may have been convincing then but doesn’t cut it now. Can it be correct? : Can it be correct? What’s wrong with the four elements hypothesis? You can explain things in terms of this model. But it fails to make predictions that can be experimentally verified. Metals : Metals In this model, metals were all believed to be part earth and part water. Lead and gold simply had different proportions of earth and water. So maybe if you add a little water to lead you can turn it into gold! Alchemists : Alchemists Inspired by the four elements hypothesis, alchemists tried for centuries to turn lead into gold. They never succeeded. Mainly because their underlying assumptions (the four elements) was incorrect. Other problems : Other problems Smoke (air + fire), leaves soot on pots, so smoke also contains some earth. No substance was found to be purely one of the four elements. Removing heat (fire) from water changes it into ice (which is lighter than water so it must contain air?). Fundamental Failure : Fundamental Failure The exact proportions of the elements (earth, air, fire, water) was never determined for any substance. An experiment that indicates one ratio of elements would conflict with another experiment. Modern Elements : Modern Elements The Greeks tried to identify the fundamental elements by reason alone. Starting in the 1600s, scientists used the scientific method. They found substances were composed of dozens of fundamental elements, not Aristotle’s four. Modern examples : Modern examples Water is hydrogen and oxygen. Graphite is pure carbon. Diamond is pure carbon (with the carbon atoms in a different pattern). Gold and lead are each pure elements. Today we know of over 100 elements. The Periodic Table : The Periodic Table The Periodic Table The Elements : The Elements Aristotle tried to explain all substances as being composed of four elements. That didn’t work. The 100+ elements of the periodic table do succeed in explaining the underlying composition of all material objects. 100 elements, not 4 : 100 elements, not 4 Was Aristotle crazy to think that all objects could be explained using just four elements? Why are there 100 (or so) elements? Why are some elements common (oxygen, carbon, hydrogen) and others very rare (Dysprosium, Neptunium)? Those are good questions : Those are good questions All the elements are themselves composed of three basic building blocks. Electrons, protons, and neutrons. The number of protons determines how an atom will interact chemically with other atoms. Elements determined by protons : Elements determined by protons Hydrogen atoms always have 1 proton. Carbon has 6. Oxygen has 8. Always! Neptunium has 93 protons which makes it unstable and hence rare. How many elements? : How many elements? The elements of the periodic table are all composed of smaller pieces. There are just three fundamental elements (call them particles to avoid confusion) that make up all matter, the electron, proton, and neutron. Aristotle wasn’t crazy to suggest just four. Complications : Complications Other types of particles have been discovered that aren’t made of electrons, protons, and neutrons, a lot of other particles. Neutrons, protons, and some other particles are now known to be composed of more fundamental “quark” particles. What’s at the bottom? : What’s at the bottom? Today, six types of quarks, the electron, two other electron-like particles, three more particles collectively called neutrinos. All matter is made of these twelve types of particles. Is there something inside them that they are made of? End of our side trip : End of our side trip No one knows. String theory? We are way off topic, let’s get back to the material of chapter one. Some of today’s discussion will be resumed later this quarter or in Science 112. Chapter 1 - Patterns of Motion : Chapter 1 - Patterns of Motion In association with his ideas on the elements, Aristotle devised laws of motion. The ideas are mostly based on common sense. The ideas are mostly wrong!! You may have to struggle to overcome the same misconceptions as Aristotle. Aristotle on Motion : Aristotle on Motion Natural motion occurs based on type of element: earth; downward motion, always towards center of the Earth. fire; upwards towards the Sun and stars. water; in-between earth and fire. air; in-between water and fire. Weight : Weight Heavy objects contain mostly earth with little fire or air. Heavy objects fall downwards because that is the natural motion of the earth within them. Heavier objects will fall downward faster than less-heavy objects. Aristotle says… Violent Motion : Violent Motion Violent motion is due to forces, pushes or pulls. Objects naturally slow and stop when no forces act on them, moving back to their natural level based on the elements within them. Celestial objects are made of the element quintessence and move without forces. Aristotle says… Aristotle’s Legacy : Aristotle’s Legacy Aristotle’s ideas on elements and motions went unchallenged for almost 2000 years. Galileo Galilei (1564-1642) proved Aristotle’s ideas wrong using simple experiments in the early 1600s. Aristotle’s Influence : Aristotle’s Influence Aristotle was possibly the most influential man in human history. Even today, his influence is widespread. For example, consider the common phrase, “learn it by heart”? Why do we say that? Aristotle’s Influence (2) : Aristotle’s Influence (2) Because of Aristotle. In his study of human anatomy, he guessed that the purpose of the heart was to store memories! Just as knowing the true purpose of the heart is important, knowing the correct rules of motion is important. Galileo’s Ideas : Galileo’s Ideas All matter (all elements) obey the same laws and rules. On the Earth, in outer space, on the Moon; the same rules apply everywhere. Natural Motion : Natural Motion Moving objects do not naturally slow and stop. Moving objects will naturally continue to move. Moving objects will slow and stop only if something forces them. Motion naturally continues : Motion naturally continues Aristotle claimed motion can continue only if forced to (violent motion) or briefly after the violent motion as the substance returns to its natural level. That’s completely opposite of what Galileo claims. How could Aristotle be so far wrong? Why objects slow and stop : Why objects slow and stop Moving objects on Earth slow and stop because they are forced to, usually by friction and air-resistance. So what Aristotle thought was natural behavior, Galileo saw as being forced by the surrounding environment. Decreasing Friction : Decreasing Friction When friction is less (like on smooth ice), the moving object continues to move much longer. It was with experiments like this that Galileo determined the correct rule, slowing is always due to interactions with an object’s surroundings. Same rule everywhere : Same rule everywhere In outer space, there is no air-resistance. Objects can move forever. Galileo correctly recognizes this as being the same rule, just a different environment. Gravity : Gravity Why, if I let go of a rock, does it fall down? Aristotle: A rock falls because it is seeking its natural (earth) level. Galileo: The rock falls because a force (gravity from the Earth) is making it move. Aristotle, get out of my head : Aristotle, get out of my head Aristotle’s ideas may seem intuitive, but you have to overcome them. Moving objects naturally want to continue moving. If an object slows, it is always because of some outside influence. Another claim : Another claim As we mentioned earlier, Aristotle also claimed that heavier objects fall faster. Galileo did a famous experiment to test this idea. Slide 39: Not really done at the Leaning Tower of Pisa. Galileo’s Experiment : Galileo’s Experiment Aristotle clearly claimed that heavier objects fall faster. Galileo’s experiment showed that heavier and lighter fall at the same rate. Heck, we can do the experiment right here and now! Do experiment. Aristotle Unchallenged : Aristotle Unchallenged How did Aristotle’s ideas survive so long when they are so easily disproven? Never tested. Air-resistance and friction make some objects behave as Aristotle claimed. That last comment deserves some further study. The Truth About Falling Objects : The Truth About Falling Objects Objects with the same shape: Heavier object falls faster (only slightly faster if both objects are fairly heavy). Objects with same weight but different shape: Object with less air-resistance falls faster. Different weight and different shape: Complicated, depends on exact weights and shapes. Aristotle and Galileo : Aristotle and Galileo Aristotle was definitely wrong, heavier objects do not always fall faster. Galileo’s experiments proved that Aristotle was incorrect. Galileo realized that the changing speed of the falling object depends on the forces due to the surroundings (gravity, air-resistance). Sec. 1.3 Mass – a Measure of Inertia : Sec. 1.3 Mass – a Measure of Inertia Objects at rest will start to move only if forced to. How quickly the object moves depends on how much force was exerted on it. But even when the forces are the same, some objects will move more than others. Volleyball vs. Cannonball : Volleyball vs. Cannonball Imagine both a volleyball and a cannonball sitting on the ground. You give each a kick, the kicks being equally powerful. The volleyball flies away, the cannonball hardly moves at all. Kick ball : Kick ball Both balls were not moving. Both were kicked. The volleyball was made to move much more than the cannonball. The cannonball seemed not to “want” to start moving. Cannonballs are stubborn : Cannonballs are stubborn Imagine a volleyball flying through the air approaching you at 60 mph. You easily bounce it back the way it came. But a cannonball approaching at that speed, even if you bump it just as hard, will go right through you, won’t change direction. Cannonballs don’t “like” to change direction. Inertia : Inertia The cannonball has more inertia than the volleyball. Inertia is how much resistance an object has to changes in its motion. Objects with more material (heavier objects) have larger inertia. Mass measures the inertia of a body. Mass : Mass Masses in the metric system are measured in kilograms. My mass is about 90 kg. Kilograms; yes, that’s a metric unit. We will review the metric system and basic math in lab. Forces : Forces Forces make things move (or stop moving). We’ll be talking about forces all quarter long. Units of force: Metric system: newtons (N) U.S. system: pounds (lb) Weight : Weight One force we deal with repeatedly is the force due to the gravitational pull of the Earth. Weight is the force due to gravity. For example, my weight is around 883 N or 198 lb. Weight vs Mass : Weight vs Mass Weight and mass are often confused. That is because an object near the surface of the Earth with mass 1 kilogram always has a weight of 10 N or 2.2 lb (more accurately 9.8 N or 2.205 lb). Slide 53: The sack contains 1 kg of material, that’s its mass. The force with which it is pushing down on the scale (due to its weight - the pull of the Earth) is 9.8 N. Weight and Mass : Weight and Mass On Earth, a 1 kg mass always has a weight of 9.8 N = 2.2 lb. So, you often see written that 1 kg = 2.2 lb That’s fine … as long as you understand this is not a true equality, it is a correspond-ence, valid only here on Earth. Different Units : Different Units kg and lb are different types of units, so they can’t be equated. Here’s an analogy, you’re driving on the highway at 60 mph. Every 60 miles will take one hour, 60 mi = 1 hr. Sixty miles “equals” one hour only when traveling at 60 mph, it is not a real equality valid always. On the Moon : On the Moon The gravitational pull of the Moon at its surface is just one-sixth that of the Earth. 1.6 N The bag still has the same mass, 1 kg, because there’s still the same amount of material. But the weight is less. Force, weight, and mass : Force, weight, and mass Forces, weights, and masses are easily confused but their differences are important. Mass measures the amount of material or the amount of inertia, units of kg. Force measures the push or pull acting on an object, units of N (newtons) or lb (pounds). Force, weight, mass (cont.) : Force, weight, mass (cont.) Weight is one type of force - the force of a planet’s gravity pulling downward. Being a force, weight is measured in N or lb. Yes! You are going to be tested on your understanding of weight versus mass. Section 1.4 Net Force : Section 1.4 Net Force Galileo: Motions naturally continue Forces cause changes in motion (cause things to speed up, slow down, or change direction). Both the size (or “magnitude”) and direction of a force will be important. Forces are vectors : Forces are vectors Objects that can be fully described using a single value are called “scalars”. Forces cannot be described using a single value, you need multiple values to represent both the size of the force and the direction of the force. Objects with size and direction are called “vectors”. Test: Scalar or Vector? : Test: Scalar or Vector? The temperature of my coffee. Travel directions. Duration of a trip. Distance from the Earth to the Moon. Reading on your car’s speedometer. The current wind. Test Answers : Test Answers The temperature of my coffee. Scalar Travel directions. Vector (like “go north 5 miles, turn right, etc.) Duration of a trip. Scalar Distance from the Earth to the Moon. Scalar, we use the term “displacement” for distance and direction). Reading on your car’s speedometer. Scalar The current wind. Vector, like 10 mph from N. Again, forces are vectors : Again, forces are vectors The action of one body on another is always some amount of push or pull and some direction of the push or pull. A force is not fully specified unless both magnitude and direction are given. Sometimes, like for weight, we know the direction so we don’t explicitly say it. Adding Forces : Adding Forces When multiple forces all act on the same object, the net result is calculated by adding the forces. The total (or net) force is the sum. Forces are added as vectors, the directions of forces must be taken into account when adding them. Net Force : Net Force Net Zero : Net Zero It is the net force acting on a body that will determine how the body’s motion will change. If the net force is zero (no forces act on the body or all the forces - added as vectors - cancelled each other out) then the object’s motion will not change. Mathematical Formula : Mathematical Formula That the net force is zero can be written mathematically as ? F = 0 The Greek letter capital sigma (?) is the summation sign. F represents force. So this says, the sum of forces equals zero. Equilibrium : Equilibrium Objects for which the net force is zero are said to be in “equilibrium”. An object in equilibrium will not be changing its motion. The most common example of an object in equilibrium is something that is not moving at all. Equilibrium => Constant Motion : Equilibrium => Constant Motion If an object is not moving and continues not to move, it is in equilibrium. A body that moves with constant speed in an unchanging direction is also in equilibrium. A body in equilibrium must have ?F = 0. Using This Result : Using This Result Any body in equilibrium must have ?F = 0. So we have a mathematical relationship between the forces that will always be satisfied when an object is in equilibrium. This enables us to identify forces and solve for their strength. ?F = 0 is a vector formula : ?F = 0 is a vector formula Forces are vectors, ?F is adding all the forces together as vectors. This means that, separately, the up and down forces must add to zero; the left and right forces must add to zero; and the in and out forces must add to zero. Identifying Forces : Identifying Forces To get correct results from ?F = 0, we will have to correctly include all the forces acting on that body and not include forces that don’t act on that body. Fortunately, that’s not very hard. Forces come in two categories, long-range forces and contact forces. Long-Range Forces : Long-Range Forces There are only three common types of long-range forces: Gravitational Electrical Magnetic We won’t deal with electrical or magnetic forces until much later in the quarter. Contact Forces : Contact Forces These are forces on one object due to another because the objects are physically touching each other. [Most contact forces are due to the electrical force acting at short range, but we’ll ignore that.] Examples of Contact Forces : Examples of Contact Forces Support (or “normal”) forces. Frictional forces. “Tension” forces (the pull due contact with a stretched string or rope or cable or…). Spring (or elastic) forces. Physical actions: bumping, pushing, pulling, hitting, etc. Equilibrium of Forces : Equilibrium of Forces So, for any object we see that is in equilibrium (not moving), the forces acting on the object must cancel out (add to zero). This applies in all directions separately, up/down, left/right, forward/backward. Let’s practice now identifying forces. Equilibrium Example : Equilibrium Example Picture a book resting atop a table. What are the forces acting on the book? Gravitational force on book from Earth pulls downward on the book. Contact with table pushes upward on the book. No other significant forces. Book is in Equilibrium : Book is in Equilibrium The force of gravity pulling down on the book must be equal in strength (and opposite in direction) to the contact force pushing up on the book. The book is in equilibrium and the forces sum to zero. Gravity is non-contact : Gravity is non-contact Isn’t the table pushing against the book the same as the gravity force? No! The gravitational pull downward on the book is separate, it exists whether the book is in contact with the table or not. Equilibrium requires at least 2 forces : Equilibrium requires at least 2 forces If the table wasn’t there or were to suddenly vanish… There would be only one force acting, gravity from the Earth. The net force would not be zero, we would not have equilibrium, the book would not stay at rest - it would fall downward. Forces come in pairs : Forces come in pairs Contact works both ways, the table pushes on the book and the book pushes on the table. Why didn’t we include that force? Because, to analyze equilibrium of the book we must consider only forces acting on the book! Equilibrium of the Table : Equilibrium of the Table The table is in equilibrium. The forces acting on it are: The book pushing down on the table. Gravity pulling down on the table (the weight of the table). The floor pushing up on the table due to the contact at the floor. Forces on the Table : Forces on the Table These forces must add up to zero. The two acting down must add to equal the one going up. Force from the book Force from the Earth Force from the floor Contact force directions : Contact force directions Okay, gravity always pulls down, but how do we know the force from the book is down and that from the floor is up? Contacting surfaces always push against each other, each pushing the other away. So the book is pushed up and table down. Ladder Example : Ladder Example A ladder is leaning against a wall. Nothing is moving so the ladder must be in equilibrium. So the (vector) sum of forces acting on the ladder must add up to zero. What are those forces? Forces on the ladder: : Forces on the ladder: Contact with left wall, force to right. Contact with floor, upward force. Weight, force downward. Is that it? Ladder Trouble : Ladder Trouble That better not be it! Those three forces do not add up to zero. The vertical forces look okay, one up and one down. But horizontally we have a problem, the wall pushes the ladder right but nothing compensates that pushing left. What is wrong? : What is wrong? Did we include a force that we shouldn’t have? No, those three forces will all be there. Did we leave out a force we should have included? Maybe. Let’s count forces… : Let’s count forces… The forces acting on the ladder should be one for each object it’s physically touching plus one force for gravity (which does not require physical contact). Isn’t this exactly what I had? Contact with the wall, the floor, plus gravity. More than just support : More than just support Our error was the bottom contact. Yes, it can and will exert the upward force we showed. But there will also be a horizontal component to that contact force, usually because of “friction”. Sec. 1.8 The Force of Friction : Sec. 1.8 The Force of Friction When two surfaces press against each other, that contact can result in A support (or normal) force, perpendicular to the surfaces. A force pushing the surfaces apart, preventing them from moving into each other. A frictional force, the rough surfaces don’t allow the objects to slide across each other, there is a resisting force called friction. Friction due to roughness : Friction due to roughness Origin of friction : Origin of friction Surfaces, even those that appear quite smooth, can be very jagged on the microscopic level. The bumps and ridges hit each other and resist motion of one surface across the other - the force of friction. Ladder Solution : Ladder Solution For our ladder, the bottom surface must be rough. There will be a horizontal friction force acting in addition to the vertical support force. It is really just one contact force, with two components. Modified force diagram : Modified force diagram Now we have two vertical forces, one up and one down; and two horizontal forces, one left and one right. All the forces can balance and we can have equilibrium. Ladder: final comments : Ladder: final comments This fits what we know, the bottom surface needs to be rough or the ladder will slip. Should there also be a (vertical) friction force at the wall? There could be, but the ladder can be in equilibrium even if that surface is perfectly smooth (or a wheel at that end will still allow the ladder to be stable). Reminder : Reminder Equilibrium is not just stationary things. Moving things can be in equilibrium. Any object moving in a straight line at constant speed (so its motion not changing in any way) is also in equilibrium. For any object in equilibrium, the net force on it must be zero. Moving Equilibrium Examples : Moving Equilibrium Examples Examples: A hockey puck sliding across the ice is nearly in equilibrium (not quite since there will be a little friction and its speed will gradually slow). A jet flying in steady, level flight. A star floating through space, far from the gravitational pulls of other stars. Section 1.9 Speed and Velocity : Section 1.9 Speed and Velocity Speed is the rate of motion. Speed is calculated as the ratio of distance over time. Speed = Distance / Time Examples: 90 km/hr 50 m/s 2.1 ft/yr Average Speed : Average Speed Average Speed – the total distance traveled divided by the total time taken gives the average speed. Travel may have been sometimes faster and sometimes slower. In fact, maybe the rate of motion was never equal to the average. Instantaneous Speed : Instantaneous Speed The speed traveled at one particular instant. A little tricky to define because calculating speed requires the distance traveled over some period of time. The instantaneous speed is the average speed you would have if you continued to travel at your speed at that instant. More Instantaneous Speed : More Instantaneous Speed Tricky to define but not hard to understand. Your car’s speedometer reads the instantaneous speed. It can tell you what speed you had at any particular instant, like 7:51:03 this morning. It is actually measured by considering the distance you traveled during a short time period. Velocity : Velocity When one specifies not only the rate (speed) of motion but also the direction, we call that the velocity. Velocity is the speed vector. Velocity is a vector, a magnitude and a direction, the magnitude is the speed and the direction is the direction of motion. The speed-velocity trap : The speed-velocity trap Forces are vectors, but we do not give a special name to the magnitude of the force vector. But we do have a special name for the magnitude of the velocity vector – speed. This just reflects usage of the words rather than a deliberate attempt to trick people. Test: Speed of Velocity : Test: Speed of Velocity 55 mph? Speed 1 ft/s downward? Velocity Velocity of 40 m/s? Incorrect usage, velocity must also specify direction. Section 1.10 Acceleration : Section 1.10 Acceleration Acceleration is the rate at which velocity is changing. Acceleration = (change in velocity) / (time for change to occur) Acceleration Examples : Acceleration Examples An object that gains 32 ft/s of speed (maybe from 0 ft/s up to 32 ft/s) in one second has an acceleration of (32 ft/s)/(1 s) = 32 ft/s/s = 32 ft/s2 An object slowing from 50 mi/hr to 40 mi/hr in two seconds has an acceleration of (-10 mi/hr)/(2 s) = -5 mi/hr/s Acceleration is changing velocity : Acceleration is changing velocity Acceleration can be changing speed or changing direction. Any change in the motion is an acceleration. Changes in motion are always due to forces. So, forces cause accelerations. Equilibrium versus Acceleration : Equilibrium versus Acceleration When the forces on an object are balanced, we have equilibrium and the motion of the object does not change. When the forces are unbalanced, the net force causes the motion to change, an acceleration. Acceleration due to Gravity : Acceleration due to Gravity The acceleration due to Earth’s gravity (if that force is the only one acting on an object) is 10 m/s2 = (10 m/s)/s More precisely, 9.8 rather than 10. 10 m/s2 is around (20 mi/hr)/s 32.2 ft/s2 in U.S. units. Falling Acceleration : Falling Acceleration A dropped object accelerates downwards. It gains 10 m/s of downward speed for every second that it falls. We are neglecting air-resistance that slows the rate of acceleration. Slide 112: This is figure 1.23 from page 31. What should the speed say after 3s, 4s, and 5s? Slide 113: The constant gravitational force will cause a con-stant acceleration of 10 m/s/s. Hence the speed increases by 10 m/s each second of falling. t = 3s, v = 30 m/s. t = 4s, v = 40 m/s t = 5s, v = 50 m/s. Every 10 m/s is roughly 20 mph, so a falling object will be moving about 100 mph after falling for 5s (ignoring air resistance). End of Chapter 1 : End of Chapter 1 Stay tuned, the exciting chapter 2 is up next.

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