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## Set - 4

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**Set - 4**Explaining Motion**What is the difference between speed and velocity?**• The two are the same. • Velocity relates to instantaneous speed, but not to average speed. • Velocity is the speed and the direction the object is traveling. • Velocity relates to invisible objects like atoms, while speed relates to visible objects like cars.**What is the difference between average speed and**instantaneous speed? • Average speed is the speed of an average runner and instantaneous speed is the speed of a very fast runner. • Instantaneous speed is the average speed of a very small portion of the trip. • Average speed is calculated over many trips, but instantaneous speed is calculated during one trip. • They're the same thing.**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.**The next slide gives an example of why we need this stuff to**understand music.**The Ear**• Responds to Pressure • A force on the membrane • A movement inside the ear • Translation into the brain • Music !**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?**This chapter**• Mostly physics • Needed for understanding of many concepts in music.**Introduction—“Explaining 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.**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 NEWTON’S LAWS.**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.**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!**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**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.**Galileo’s 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 ???**The importance of TIME in Galileo’s Experiments**The red dots represent the positions after equal time intervals. What can we say about this motion? Pendulum Acceleration …. WHY??**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!**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 didn’t matter. • The size of the object MAY have mattered.**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.**Galileo’s BIG Contribution**OBSERVE MODEL Change Something**Acceleration**• If an object starts with a velocity v0 and ends with a velocity vf after a time t, then the average acceleration is said to be • Units: velocity/time = (m/sec)sec or m/s2**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?**AGAIN:Acceleration of gravity**• ~10 m/s2 • Actually 9.8 m/sec2 • 32 ft/sec2**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 • 30 m/s • 40 m/s • 50 m/s • 60 m/s**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**Look at the graph:**Vf v Area = v x Dt = distance traveled V0 Dt Time t Distance = v0t + (1/2) at2**Reaction Time Experiment**• 2 People • One holds the meter stick • The second has hand at the bottom • When the first person releases the meter stick, the second catches it as fast as possible. • From the distance, we can calculate reaction time.**Reaction Time DROP THE RULER**Distance = v0t + (1/2) at2 Start from rest so Distance = (1/2) at2 D = (1/2) gt2**REACTION TIME**Minus Signs Are Important**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.**INERTIA**Is Important!**Note-**• This resistance to changes in motion was later quantified by Sir Isaac Newton • This is the next topic**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 body’s inertial tendency to continue forward at a constant speed when the car suddenly stops.**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.**Newton and Galileo’s 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.**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.**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.**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 college’s holy orders. • He was excused .. The only person ever to have received this allowance.**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.**Newton’s First Law**• Newton’s 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.**Newton’s First Law**• Remember: • Velocity can be ZERO • Therefore Newton’s first law also says that: an object at REST (not moving) will stay at rest.**Newton’s First Law: Force??**• The first law incorporates Galileo’s 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. .