Clickers Registration Roll Call Today If you do not see your name then either: 1) You successfully registered your clicker during the roll call on tuesday OR 2) You added the course and your name was not yet in the system as of Jan. 20. If this is the case, please see me after class. Announcements: HW#2 is due Wednesday 1/28 by 8:00 am Extra Credit essay #1 on the LONCAPA website is due tomorrow at 8:00 am Loose ends from lecture 2 Law of Inertia (Newton s 1st Law) What is Force? Introduction ISP209s9 Lecture 3-1- ISP209s9 Lecture 3-2- Adding and Subtracting 2 Vectors Adding and Subtracting 2 Vectors Example 1: Imagine two vectors (A and B)represent two walks, one in one direction and the other in another direction. A negative sign means "go the opposite direction the arrow shows". The resultant vector (C) points from your original starting point to where you ended up at the end of the second walk. ISP209s9 Lecture 3-3- ISP209s9 Lecture 3-4-
Adding and Subtracting 2 Vectors Motion Example 2: Position location relative to the center of a coordinate system. Displacement the difference between two positions Velocity rate of change of position. This means changing direction as well. Acceleration rate of change of velocity. If either the magnitude of the velocity or its direction are changing, the object is accelerating. ISP209s9 Lecture 3-5- ISP209s9 Lecture 3-6- Speed from a distance versus time plot Example: Motion of a car as a function of time: Speed versus distance plot Example: Motion of a car as a function of time. What is the average speed at 2.5 min? x f " xi 0.75miles " 0.25miles miles 60min miles v = = = 0.56! = 33.6 t " t 2.7 min" 1.8min min h h f i ISP209s9 Lecture 3-7- We can get this graph from this one by repeating the previous calculation for several different times and plotting the points ISP209s9 Lecture 3-8-
A pictorial way to calculate rates of change d2! d1 6! 2 m = speed = = = 0. 59 m t! t 9.3! 2.5 s 2 1 Draw a line tangent to the curve at the time you want. The line can be any length. Mark two points on the line and record the values. Calculate the slope of the tangent line ISP209s9 Lecture 3-9- Homework Problem Traveling Car 1st sketch the speed vs. time graph Next, use the speed graph to sketch the acceleration vs. time graph ISP209s9 Lecture 3-10- History of our effort to understand motion Aristotle(384 BC 322 BC) Natural motions: items seek their natural locations Violent motions like moving across the room require an agent Galileo (1564-1642) Tried to deduce the laws of motion from experiments Introduced the concept of inertia. (Inertia is not a well defined concept.) Isaac Newton (1643-1727) Formulated laws that govern planetary motion and most ** motion we see in our daily lives Invented Calculus along the way Many view Newton (along w/einstein) as the greatest ever Problems with Aristotle s Theory Now, throw a ball across the room. Once it leaves your hand, what keeps it moving? Aristotle says there must be a constant force to keep it in motion. Aristotle also believed heavier objects fall faster. It all sounds reasonable, yes? ** Except for the very small (Quantum Mechanics) and fast (Special Relativity) ISP209s9 Lecture 3-11- ISP209s9 Lecture 3-12-
Galileo s Thought Experiment Let a ball roll down an incline; it will speed up. Let it roll up the incline; it will slow down. In between, on a perfectly flat surface with no friction, the ball will keep rolling at a constant speed forever. ISP209s9 Lecture 3-13- Galileo and the Scientific Method Galileo s method: Experimentation, to test a specific hypothesis -E.g., Aristotle s theory of motion Idealization, to eliminate side effects that may mislead -E.g., air resistance and friction Consider only one question at a time - E.g. speed of falling objects of different masses Quantitative methods: precise measurement - E.g., timing the fall of different objects from a tower ISP209s9 Lecture 3-14- The Law of Inertia Imagine we could turn off air resistance, friction, and gravity. How would things move? Descartes had the answer (which Newton took as his first principle of motion): The Law of Inertia: A body that is subject to no external influences (also called external forces) will stay at rest if it was at rest to begin with and will keep moving if it was moving to begin with; in the latter case, its motion will be in a straight line at an unchanging speed. In other words, all bodies have inertia. ISP209s9 Lecture 3-15- The Law of Inertia For example, if you are driving a car on an icy road a VERY icy road and try to stop or turn, you will find that your car continues to go in a straight line, as there is little friction. You can also watch videos of astronauts things will float around until somebody grabs them, or they run into the wall. ISP209s9 Lecture 3-16-
Acceleration and the Law of Inertia The law of inertia tells us that an undisturbed object will keep moving with a constant velocity. If an object s velocity is changing, it is accelerating. Acceleration is the rate of change of velocity: acceleration = (change in velocity)/time Falling Falling objects accelerate as they fall. How do we know this? Hold your book above the floor and let it drop. What is its speed right when you let it go? (Don t throw it!) What is its speed when it hits the floor? ISP209s9 Lecture 3-17- ISP209s9 Lecture 3-18- Falling This diagram shows an object falling. Note that both its distance and its velocity are increasing. From one second to the next, the distance traveled increases, but the change in velocity is the same. Falling We see that the speed is proportional to the time 10 m/s at 1 s, 20 m/s at 2 s, and so forth. What about the distance? Clearly it is not proportional to the time. However, if we look at the pattern of how the distance changes from second to second, we can see that the distance is proportional to the square of the time. ISP209s9 Lecture 3-19- ISP209s9 Lecture 3-20-
Falling The object in the diagram is changing its speed at a rate of 10 m/s per second. Therefore, its acceleration is 10 m/s 2. This is (approximately) the acceleration due to gravity anywhere on the Earth. It does NOT depend on the mass, size, or shape of the object. Aristotle was wrong. Click HERE for a demonstration using a coin and feather ISP209s9 Lecture 3-21- What is a Force? A force is a push or pull. Force is a vector, it has a magnitude and a direction. A better definition is given by Newton s Three Laws of Force (my versions) If the net force on an object is zero the object will not accelerate. The amount of acceleration depends on the mass of the object and the amount of the applied force: F = ma. For every force, there is an equal and opposite force. Improved definition: Force is the rate of change of momentum. ISP209s9 Lecture 3-22- How much force? Neglecting friction from the air, a 80.0 kg professor falls off a bench and accelerates toward the ground at 9.81 m/s 2. What is the magnitude of the force of gravity on the professor? F = mass x acceleration = 80.0 kg x 9.81 m/s 2 = 785. N Force: Why Things Accelerate Undisturbed objects will continue moving in a straight line with constant speed (Law of Inertia, aka Newton s 1st Law ) any change in speed or direction (I.e., acceleration) must require a force. Force is an action, such as a push or pull, rather than a thing. A force is exerted on one object by another. ISP209s9 Lecture 3-23- ISP209s9 Lecture 3-24-
Force: Why Things Accelerate Is it possible to have a force without acceleration? Only if there are two forces that cancel each other out. ISP209s9 Lecture 3-25- Force: Why Things Accelerate If you kick a football, when does it accelerate? If you watch carefully, you will see that the ball only accelerates while your foot is in contact with it. Other forces: friction, air resistance these both act to slow moving objects Gravity: force exerted by the Earth (due to its very large mass) A bit different then the previous examples. Nothing is touching an apple to make it fall. Gravity acts at a distance across space. ISP209s9 Lecture 3-26- Connecting Force and Acceleration Through experimentation, we see that the acceleration is proportional to the force: a! F Connecting Force and Acceleration Inertia is not the same as weight Imagine being in outer space. Nothing has weight, but objects still have inertia they will resist a pull or push. Mass is the quantitative measure of inertia. In the metric system, mass is measured in kilograms. ISP209s9 Lecture 3-27- ISP209s9 Lecture 3-28-
Connecting Force and Acceleration Through experimentation, we see that the same force produces a smaller acceleration of a greater mass. Acceleration is inversely proportional to mass: a! 1/m. Connecting Force and Acceleration So, we have found that acceleration is proportional to force and inversely proportional to mass: a! F/m One newton (N) is defined as the force it takes to accelerate 1 kg at 1 m/s 2 ; using these units, we can write: a = F/m ISP209s9 Lecture 3-29- ISP209s9 Lecture 3-30- What is a force on a deeper level? These laws let us recognize a force, but what causes a force? Modern view is related to Quantum Field Theory. Forces are the result of an exchange of virtual particles that pop in and out of existence from thin air. To understand field theory, we have to talk about energy and quantum mechanics (later in the term). ISP209s9 Lecture 3-31-