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Slide 2 Set - 4 Explaining Motion Slide 3 What is the difference between speed and velocity? A. The two are the same. B. Velocity relates to instantaneous speed, but not to average speed. C. Velocity is the speed and the direction the object is traveling. D. Velocity relates to invisible objects like atoms, while speed relates to visible objects like cars. Slide 4 What is the difference between average speed and instantaneous speed? A.Average speed is the speed of an average runner and instantaneous speed is the speed of a very fast runner. B.Instantaneous speed is the average speed of a very small portion of the trip. C.Average speed is calculated over many trips, but instantaneous speed is calculated during one trip. D.They're the same thing. Slide 5 Why do we care about motion? Because we all move in various ways. Our cars move and they move us. Our friends move. Music is sound and sound moves through the air. We need these concepts to really understand what music is and how it works. Slide 6 The next slide gives an example of why we need this stuff to understand music. Slide 7 The Ear Responds to Pressure A force on the membrane A movement inside the ear Translation into the brain Music ! Slide 8 If you drop a piano out of a 20 story building How long will it take to hit the ground? How fast will it be moving? After it hits the ground.. how difficult will it be to play it? Slide 9 This chapter Mostly physics Needed for understanding of many concepts in music. Slide 10 IntroductionExplaining Motion In physics, to explain something means to create a model that can predict the outcome of experiments. Motions appear to be reproducible; that is, if we start out with the same conditions and do the same thing to an object, we get the same resulting motion. The same motion occurs regardless of: when the experiment is done, and where the experiment is done. This reproducibility is a necessary condition for attempting to search for a set of rules that nature obeys. Rules of nature might be difficult to find, but they do not change. Slide 11 Translation Under identical and repetitive conditions, the same outcome will always occur. Physical motion is PREDICTABLE based upon certain laws of motion. There are three of them that are referred to as NEWTONS LAWS. Slide 12 Do Objects Tend to Rest? Give your book a brief push across a table. Although the book starts in a straight line at some particular speed, it quickly slows and stops. If you epeat this book-pushing experiment on a surface covered with ice. The book would travel a much greater distance before coming to rest. The ice is slicker than the desktop. Different surfaces interact with the book with different strengths. What would happen to the book if the surface were perfectly slick? The book would not slow down at all; it would continue in a straight line at a constant speed forever. Slide 13 Galileo Slide 14 The man Galileo of Pisa Born in Pisa (1564) Thought the Church had become sterile and began to translate it nto modern music. His work began the development that culminated in ITALIAN OPERA! Smart Dude! Slide 15 Galileo Enrolled in medicine but switched to Mathematics. At the age of 25, he was appointed Chair of Mathematics at Padula. In 1610 Developed the telescope Observed Mountains on the moon Moons of Jupiter Phases of Venus Slide 16 Galileo From his OBSERVATIONS, he favored the Copernican world view that the Earth orbited around the sun rather than the other way around. This created big conflicts with the church. Eventually, he was confined to his home where he died in 1642. Slide 17 Galileos Thought Experiment Galileo noted that a ball rolling down a slope speeds up. Conversely, if the ball rolls up the slope, it naturally slows down. The ball experiences an interaction on the falling slope that speeds it up and an interaction on the rising slope that slows it down. Now, Galileo asked himself, what would happen to the ball if it were placed on a level surface? Nothing. Because the surface does not slope, the ball would neither speed up nor slow down; the ball would continue its motion forever. FOREVER ??? Slide 18 The importance of TIME in Galileos Experiments Pendulum Acceleration . WHY?? The red dots represent the positions after equal time intervals. What can we say about this motion? Slide 19 The Tower?? Aristotle claimed that a heavier object will hit the ground sooner than a light object dropped at the same time. Galileo did the experiment and proved Aristotle wrong. There is no evidence to prove that Galileo actually did this experiment. But he may have! Slide 20 What he would have found had he done the experiment: The longer the object fell, the faster it went. The weight (to be more carefully defined shortly) of the object didnt matter. The size of the object MAY have mattered. Slide 21 Sort of Slide 22 More importantly For every second a falling object falls (vertically), its speed increases by about 10 meters per second (or 32 ft/sec). This only works if air resistance can be neglected. The object is said to be UNIFORMLY ACCELERATING. Slide 23 Galileos BIG Contribution OBSERVEMODEL Change Something Slide 24 Part III or IV or Something Slide 25 Reminder.. Exam #1 is on September 24 th. Short answer format 30 to 50 questions not yet sure. Graded by Scantron You might want to think about studying! Or not! Slide 26 Last Time We defined acceleration We applied it to the acceleration of gravity We did a reaction time test You screwed it up We will try again! Slide 27 Acceleration If an object starts with a velocity v 0 and ends with a velocity v f after a time t, then the average acceleration is said to be Units: velocity/time = (m/sec)sec or m/s 2 Slide 28 Some algebra Slide 29 An object is thrown into the air with a velocity of 20 m/s. How long will it take to get to the top of the trajectory? How long back to the thrower? Slide 30 No Surprise: Instantaneous Acceleration Slide 31 Acceleration of gravity ~10 m/s 2 Actually 9.8 m/sec 2 32 ft/sec 2 Slide 32 An object is THROWN vertically down from the top of a building with an initial speed of 20 meters per second. 2 seconds later it will have a speed of A. 30 m/s B. 40 m/s C. 50 m/s D. 60 m/s Slide 33 A woman throws a ball straight up into the air at a speed of 30 m/s. After how many seconds will the ball return to her hands? 3 4 5 6 None of these Slide 34 Did she catch the ball? Of course she did.. She is a woman! Dont be ridiculous, she is a woman! The ball was suddenly beamed up into a passing alien spaceship. Leave me alone it is Monday. Slide 35 Look at the graph: V0V0 VfVf Time t v Area = v x t = distance traveled Distance = v 0 t + (1/2) at 2 Slide 36 Reaction Time Distance = v 0 t + (1/2) at 2 Distance = (1/2) at 2 D = (1/2) gt 2 Slide 37 LETS DO IT AGAIN! Slide 38 REACTION TIME Slide 39 The Modern Explanation Galileo was the first to suggest that constant-speed, straight-line motion was just as natural as at-rest motion. Natural motion is one in which the speed and direction are constant. An interaction with an external agent is required to cause an object to change its velocity. Objects at rest tend to remain at rest. Objects in motion tend to remain in motion. This property of remaining at rest or continuing to move in a straight line at a constant speed is known as inertia. Slide 40 Note- This was later quantified by Sir Isaac Newton This is the next topic Slide 41 The Modern Explanation There is more to inertia than getting things moving. If something is already moving, it is difficult to slow it down or speed it up. An example is drying your wet hands by shaking them. When you stop your hands abruptly, the water continues to move and leaves your hands. In a similar way, seat belts counteract your bodys inertial tendency to continue forward at a constant speed when the car suddenly stops. Slide 42 The Modern Explanation All objects do not have the same inertia. Imagine trying to stop a baseball and a cannonball, each of which is moving at 150 kilometers per hour (about the speed a major- league pitcher throws a baseball). The cannonball has more inertia and, as you can guess, requires a much larger effort to stop it. Conversely, if you were the pitcher trying to throw them, you would find it much harder to get the cannonball moving. Slide 43 Fun Trick with Inertia Slide 44 Newton and Galileos Legacy Although Galileo did not fully explain motion, he did take the first important step and, by doing so, radically changed the way we view the motion of objects. His work profoundly influenced Isaac Newton, the originator of our present- day rules of motion. Slide 45 Sir Isaac Newton Born in 1642 One of the GREATS of physics (on a par with Einstein!) Strange dude rumor is that he died a virgin. Slide 46 Newton Born in England and he was supposed to return and look after the family farm. At age 17 he returned from boarding school he proved to be a total failure at farming. Went to Trinity College, paying his way by waiting on tables and cleaning rooms for faculty and wealthy students. Many students do this today as well. Slide 47 Newton In1667 he published a treatise on infinite series. Developed a reflecting telescope and was elected membership in the Royal Society. Decided that Christianity had deviated from the original teachings of Christ and refused to take the colleges holy orders. He was excused.. The only person ever to have received this allowance. Slide 48 More Newton In 1686 he published his Principia.. Which established the laws of motion in a mathematical way. He developed the calculus while Leibnitz developed a different approach. For years they fought over who was the real inventor! He showed that white light was a mixture of all of the colors of the rainbow. He developed the math to show that the planets and comets rotated around the sun in elliptical orbits. He died in 1727. Slide 49 Newtons First Law Newtons first law of motion. It is also referred to as the law of inertia: -The velocity of an object remains constant unless it is acted upon by an external force. For the velocity of an object to remain constant, its speed and its direction must both remain constant. Slide 50 Newtons First Law Remember: Velocity can be ZERO Therefore Newtons first law also says that: an object at REST (not moving) will stay at rest. Slide 51 Newtons First Law: Force?? The first law incorporates Galileos idea of inertia and introduces a new concept, force. A book sliding across the table slows down and stops because there is a force (called friction) that opposes the motion. Similarly, a falling rock speeds up because there is a force (called gravity) acting on it.. Slide 52 What Are Forces? Casually speaking, a force is a push or a pull. We dont actually see forces. We see objects behave in a certain way, and we infer that a force is present. The direction of the force is as important as its size, in the way they make objects behave. Therefore, we treat forces as vectors. Slide 53 Whats Up?? Supermans WEIGHT No force UP! Slide 54 A guy is pulling his girlfriend on a sled at constant velocity. Lets discuss the FORCES that are acting. Slide 55 Question #1: What object are we talking about? The Guy? The Girl? We must apply our ideas to only ONE object at a time, or an appropriate combination of objects that are functioning as a single body. We choose the girl & sled Slide 56 The (Girl + Sled) since they move together! The Pull Friction Weight of the girl AND the sled Something NEW: The force the earth pushes up with! We call it the NORMAL FORCE Slide 57 Normal? W N The two are equal but opposite in direction. Gravity N=W Slide 58 FREE BODY DIAGRAM of the (Girl + Sled) since they move together! components EQUAL Slide 59 Balanced & Unbalanced Forces Remember that Newtons first law refers to the unbalanced force. In many situations there is more than one force on an object. When two forces of equal size act along a straight line but in opposite directions, they cancel each other. There is an unbalanced force only if the sum of the forces is not zero. Slide 60 Balanced & Unbalanced Forces When we observe an object with no acceleration, we infer that there is no unbalanced force on that object. If you see a car moving at a constant speed on a level, straight highway, you infer that the frictional forces balance the driving forces. What is the net force acting on an airplane in level flight flying at 500 mph due east? Because the speed and direction are constant, there is no acceleration, and the net force must be zero. Slide 61 Adding Vectors Mathematicians have developed rules for combining vector quantities such as displacements, velocities, accelerations, or forces. In this chapter you will learn to combine vectors using a graphical method and the scale shown in the next slide. Slide 62 Vector Shorthand In texts, vectors are represented by boldface symbols (such as F). When writing by hand about vectors, you use an arrow over the symbol (such as F ). The magnitude of the vector quantity is represented by an italic symbol. Therefore, a force is written as F, and its magnitude is written as F. Slide 63 Drawing Vectors Accurately To complete this representation, we assign a convenient scale to our drawings. Here, one centimeter on paper represents 20 meters on the ground. We can represent any vector by an arrow; its length represents the magnitude of the quantity, and its direction represents the direction of the quantity. Slide 64 Tail-to-Tip Vector Addition When you are given a list of directions, each succeeding arrow is drawn beginning at the head of the previous arrow. The arrow drawn from the tail of the first arrow to the head of the last arrow represents the vector sum. You can determine the direction and magnitude of this last vector, the sum, with a ruler and a protractor. In this way the three forces acting on the ball (a) can be added to find the net force (b). Note that you dont have to start with F 1. The order in which the forces are added doesnt matter; you could choose F 2 or F 3. Try it! Slide 65 Adding Vectors F1F1 F2F2 F3F3 F3F3 F1F1 F1F1 F2F2 SUM The Same Diagram Slide 66 Vectors we have used: Position (Not too often in this class) Velocity Acceleration Force Any others??? Slide 67 Summary: Newtons FIRST Law Objects in motion tend to remain in motion unless acted upon by an external force. Objects at rest tend to remain at rest unless acted upon by an external force Slide 68 Do objects at rest have a velocity?? Slide 69 Newtons Second Law The acceleration of an object is proportional to the net force acting on it. Twice the force produces twice the acceleration. The direction of the acceleration is always in the direction of the net force. Two springs pulling side by side exert twice the force of one spring pulled by the same amount. Thus, they produce twice the acceleration. Slide 70 Newtons Second Law Mass and acceleration are inversely proportional. Inversely indicates that the changes in the two values are opposite each other. If the mass is increased by a certain multiple, the acceleration produced by the force is reduced by the same multiple. Slide 71 Newtons Second Law Newton put the two preceding ideas together into his second law of motion. The net force on an object is equal to its mass times its acceleration and points in the direction of the acceleration. Slide 72 Conceptual Question on the 2 nd Law A crate falls from a helicopter and lands on a very deep snowdrift. The snow slows the crate and eventually brings it to a stop. During the time that the crate is moving downward through the snow, is the magnitude of the upward force exerted on the crate by the snow greater than, equal to, or less than the magnitude of the gravitational force acting downward on the crate? Slide 73 Answer to the Conceptual Question Because the crate is moving downward, its velocity is pointing down. Because the crate is losing speed, its acceleration must be pointing in the opposite directionthat is, up. The net force always points in the same direction as the acceleration. Therefore, the force acting upward on the crate must be larger than the force acting downward. Thus, the snow exerts the greater force. Slide 74 Defining Units of Mass and Force In the previous chapter, we have defined a measure for acceleration, but not as yet for mass and force. Historically, a certain amount of matter was chosen as a mass standard. The mass of a liter of water has a mass of 1 kilogram. The force needed to accelerate a 1-kilogram mass at 1 (meter per second) per second is called 1 newton (N), in honor of Isaac Newton. In using any rule of nature, we must use a consistent set of units. Slide 75 Newtons Second Law - UNITS F = m a Newtons Kilograms Meters/second 2 Slide 76 Everything in this course is pretty much based on F=ma Slide 77 Meters/second 2 Can be written as (meter/second)/second Consider an object accelerating at 10 (meters/second)/second Every second its velocity increases by 10 m/s. Slide 78 Example At t=0 (what does this mean???), an object is moving at 15 m/s and is accelerating at 10 m/s 2. What is its velocity as a function of time?? Slide 79 The results Time (seconds)Velocity 015 125 235 345 455 565 675 785 Slide 80 The Graph Slide 81 Numerical Question on the 2 nd Law What is the net force needed to accelerate a 5-kg object at 3 m/s 2 ? When accelerations are measured in (meters per second) per second, as they are here, the masses must be in kilograms and the forces in newtons. A newton can be written as kg m/s 2. Applying the second law, we have Slide 82 Mass Weight Mass is often confused with weight. They are proportional to each other. Our weight depends on where we are. We compress the spring in a bathroom scale because Earth is attracting us. If we were on the Moon, our weight would be less because the Moons gravitational force on us would be less. Our mass, however, is not dependent on our location in the Universe. It is a constant property that depends only on how much there is of us. Slide 83 Consequence: Does the 2 nd Law Apply in Space? Being weightless does not mean that you are massless. Imagine a huge truck in outer space hanging from a spring scale. Although the scale would read zero, if you tried to kick the truck, you would find that it resisted moving. Weight can be expressed in newtons to clear up misunderstandings. A 1-kilogram mass near Earths surface has a weight of 9.8 newtons, or about 2.2 pounds. Therefore, a pound of butter has a weight of 4.5 newtons and a mass a little less than kilogram. Slide 84 Weight as a Force Lets represent the acceleration due to gravity by the symbol g, where weve used a vector to indicate both the size and direction. If we then replace the net force F net by the weight W, we obtain: General equation of the 2 nd Law Re-stated in gravitational terms Slide 85 How Much Do You Weigh? (Remember, mass cannot be expressed in newtons; weight can.) Calculate the weight of a child with a mass of 25 kg. Obtain the mass of a dog that has a weight of 150 N. Slide 86 Introducing Free-Body Diagrams Imagine that you are pulling your little sister on a sled and that the sled is speeding up. There are many forces acting on the sled. The rope is exerting a tension on the sled, pulling it forward. Earth is pulling down on the sled with a gravitational force. The snow is pushing up on the sled with a force commonly called a normal force. (Normal means perpendicular, and this force acts perpendicular to the surface between the sled and the snow.) Your sister is pushing down on the sled with a normal force, and the snow is resisting your efforts with a frictional force that acts parallel to the surface of the snow. Slide 87 Introducing Free-Body Diagrams Which of these forces do we use in Newtons second law? F net = ma ActorDirection RopeForward EarthDownward SisterDownward SnowBackward SnowUpward F net, the net force, is the vector sum of all the forces acting on the sled. It is important, therefore, to correctly identify all the forces acting on an object when analyzing its motion. We identify the forces by drawing a free- body diagram. Slide 88 Free Fall RevisitedF net Objects falling on Earth dont fall in a vacuum but through air. Thus, in realistic situations, a falling object has two forces acting on it simultaneously: the weight acting downward, and the air resistance acting upward. And the greater the speed, the greater the air resistance. Slide 89 Free Fall RevisitedTerminal Speed With these facts in mind, consider the downward motion of a falling rock. Initially, it falls at a low speed, and the air resistance is small. Because there is a net force, the rock accelerates, thus increasing its speed. As the rock speeds up, however, its weight remains constant while the air resistance increases. Thus, the net force and the acceleration decrease. The rock continues to speed up but at a decreasing rate. Eventually, the rock reaches a speed for which the air resistance equals the weight. F net = 0. The rock stops accelerating. This maximum speed is called the terminal speed of the object. Slide 90 Terminal Speeds The terminal speeds of different objects are not necessarily equal. Factors include: The shape of the falling object, Its size, Its weight, and Resistive properties of the medium. An object will continue to accelerate until the terminal force is the same size as its weight. The maximum speed of a skydiver near sea level is 190 mphno matter how high up they were when they started! If they fall spread-eagled, this value is decreased. Slide 91 Forces Discouraging Movement Static Friction The static frictional force seems a bit mysterious. Because it is equal to the force you exert: The frictional force is small if you push with a small force (a). If you push with a large force, the frictional force is large (b). It ceases to exist when the applied force is removed. Slide 92 Forces Discouraging Movement Kinetic Friction If your applied force exceeds the maximum static frictional force, the crate accelerates in the direction of your applied force. Although the crate is now sliding, there is still a frictional force (c). The value of this kinetic friction is less than the maximum value of the static frictional force. Unlike air resistance, kinetic friction has a constant value, independent of the speed of the object. Slide 93 Test Static vs. Kinetic Friction With a simple wooden block and a long rubber band, you can verify the behavior of static and kinetic friction. Connect the rubber band to the block with a thumbtack, and slowly pull on the block. The stretch of the band provides a visual indication of the force you are applying. If the block does not move, the static force is equal but opposite in direction to the force of the rubber band. Continue to increase your pull. What happens? Repeat the experiment, with the block sliding across the table at a constant speed. How does the stretch of the rubber band now compare with its maximum stretch in the static situation? Slide 94 Newtons Third Law There is no way to push something without being pushed yourself. For every force there is always an equal and opposite force. If an object exerts a force on a second object, the second object exerts an equal force back on the first object. Forces always occur in pairs. And these forces never act on the same body. Slide 95 I dropped it and the world stood still Consider a ball with a weight of 10 newtons falling freely toward Earths surface. Earth exerts a force W eb on the ball. According to Newtons third law, the ball exerts an equal and opposite force W be on Earth. W eb = W be = 10 N. Earths mass is so large that its acceleration toward the ball is minuscule. Earth does accelerateevery time we drop somethingbut we dont notice it. Slide 96 Another Example When you fire a rifle, it recoils. Third Law: Rifle pushes bullet, bullet pushes rifle. But why doesnt the rifle accelerate as much as the bullet? The force of the bullet on the rifle is the same size but produces a small acceleration because the mass of the rifle is large. The force of the rifle on the bullet produces a large acceleration because the mass of the bullet is small! Slide 97 Without the 3 rd Law, You Cannot Walk In walking you must have a force exerted on you in the direction of your acceleration. And yet the force you produce is clearly in the opposite direction. As you start to walk, you exert a force against the floor (down and backward); the floor therefore exerts a force back, causing you to go forward (and up a little). If you want a clearer demonstration of this, try walking in a rowboat. As the man walks to the left, he exerts a force on the boat that causes the boat to move to the right. Slide 98 Without the 3 rd Law, You Cannot Stand Without the third law, paradoxical events would occur in the Newtonian world view. A person stands on a floor. Because the person is not accelerating, the net force must be zero. Q: What is the force that balances the gravitational force? A: Earth exerts a force W ep on the person, which causes the person to exert a force N pf on the floor. By Newtons third law, the floor exerts an equal and opposite force N fp on the person. Although W ep and N fp are equal and opposite, they are not an actionreaction pair; they both act on the person.