SPH4UHW1

**Physics 4U Homework Spring 2013**
=Date= ||= =Class Topic and Notes Summary= || =Homework/Handouts= || Lowest test will be dropped if you complete all quizzes and summative assignments (quiz marks do NOT count toward your grade). Due Dates for tests and summatives are always announced at least one week in advance and you are encouraged to finish work before due dates. Due Dates will be strictly enforced. If you are gone the day of a test or summative, you will receive a score of ZERO, unless you have made arrangements in advance. You will appreciate this thoughtfulness on my part when you go to university next year. **Introduction to Fermi Questions:** How long would our class be able to survive in the classroom with only that amount of air available? What assumptions and calculations can we make to get a reasonable answer? Work through sections 1.1, 1.2, 1.4. Focus on precision with calculated values. The rule for addition and subtraction says that the number of decimal places in the answer is equal to the number of decimals in the least precise number in the question. The rule for multiplication and division is that the number of digits in the answer (ignoring leading and trailing zeros) is equal to the number of digits in the least precise number in the question. || || intro to Fermi questions - the point is to determine a reasonable answer to a complicated problem without going to google to get information. We are trying to determine if the answer is closer to 10, 100, 1000 ,1 million, 1 billion. Students choose a problem from the handout to present to the class on Friday. A sample will be done in class. Note that a Fermi problem should NOT require additional research; it should be based on REASONABLE ASSUMPTIONS, ESTIMATES, and SIMPLE CALCULATIONS. Proportioning - determining the relationship between two variables - use a quick sketch and then try to match the data to one of the five standard power functions - cubic, quadratic, linear, rational (1/x and 1/x²) ||
 * =Today's=
 * Jan 29 || **How to earn your mark in this class:** Unit tests (6 or 7); unit summative assignments (3 or 4 - weighted as one or two tests);
 * Jan 29 || **How to earn your mark in this class:** Unit tests (6 or 7); unit summative assignments (3 or 4 - weighted as one or two tests);
 * Unit 1 outline - measurement and analysis **
 * Jan 30 || review of homework problems - what to do with zeros (how to determine if they are significant) The question of how to know if zeros are significant is answered at the [|University of Guelph - Physics] page.

p 25-26 # 1-3 p 30 # 2,3 Fermi: how many pizzas were eaten in Canada last night? || 1. Use log graph paper to sketch the data - the measured slope of the line is the exponent (gives approximate answer) 2. Calculate the slope using logs of the original data m = (log y 2 - log y 1 ) / (log x 2 - log x 1 ) (gives more exact answer) For example, given the following data, can you sketch the data on log graph paper, estimate the slope (power) and then determine the equation that best fits the data: a) (2, 18.8) (4, 65.5) (6,135.8) (8, 228.0) b) (1, 500) (3, 32.1) (5, 8.9) (7, 3.8) Work through problems - answers are y = 5.4x 1.8 y = 500 / x 2.5 Other data sets to practice with: 1. (2, 7.798) (3, 15.535) (4, 25.335) (5, 37.022) y = 2.4 x 1.7 2. (2, 70.31) (3, 247.01) (4, 602.84) (5, 1203.98) y = 8.2 x 3.1 ||
 * Jan 31 || Take up relationships from p 25 and 30 - here is a sheet with lots of variety in functions Intro to relationships where the exponent is not a whole number - use logs to determine the power:

[|how to graph with log-log paper] || Ex: If you expect a value of 29.9 m/s and get an experimental value of 26.2 m/s, your absolute and relative errors are:__ Two minute review of log calculations and introduction to absolute/relative errors Fermi Question preparations. Need to identify your assumptions and process - students will identify strengths and weaknesses of the method. Quiz 1 - data analysis - This is to be handed in first thing Monday so that I can return them during class - remember: this is a learning tool which will prepare you better for ** Wednesday's test **. || || Presentation of Fermi Problems - your task is to list your assumptions and have the class calculate the correct power of 10. The class may also want to challenge one or more of your assumptions. ||  || Review for test - hand back quizzes Hand out summative assignment #1 - due Feb 19 by end of school day || || - graphs of distance vs time and speed vs time - review of kinematic formulas and acceleration - algebraic motion problems - projectile motion We start by deriving the kinematic formulas from simpler equations for uniform motion: start with d = v * t v = (vi + vf) / 2 a = (vf - vi)/t = Δv / Δt and end with d = vi t + ½ a t² and vf² = vi² + 2ad || Do the problems (below) from p 46, 52, and 54. Then derive one more kinematic formula: d = vf t - ½ a t² ||
 * Feb 1 || Absolute and Relative errors in physics - absolute is how far away your experiment or measurement is from the expected (theoretical or predicted) value; relative is how far you are away as a percentage of the expected value.
 * Feb 4 || Collect quizzes - to return tomorrow
 * Feb 5 || Fermi Problems continued
 * Feb 6 || Test - whole class - when you finish, you should work on the summative assignment ||  ||
 * Feb 7 || Begin unit two - start with a review of motion
 * || For Students going on the Dominican trip, you should finish the spreadsheet and graphing work for the summative assignment. You should also work through the problems based on graphs and the kinematics problems

I expect that you will have to catch up on at least one day of work on projectiles, but if you take care of the other work beforehand, you should not have too much to finish when you get back. || p 46 #1-4, p 52 #2,3, p 54 a-d p 59,60 # 1-4, p 73 # 1-4 79 # 18 a-f, 19(sketch d-t and v-t graphs), 22 a,e, 24 b,e, 25 || With graphing problems, you are often asked to find the distance when given a velocity-time graph; you are often asked to find the speed when given a distance-time graph. As we will see in the next few classes, the ties in very nicely with what you have learned about the derivative function in calculus. ||  || Plus p 59 & 60 - questions with four graphs. ||  || 1. If you are given a graph of distance vs time and need to answer question about the object's speed: - you can use the graph data and log calculations to find the equations for distance and for speed - you can use tangents on the d vs t graph to find values for the speed vs time graph - you can use average speed calculations (total distance/total time) to find vf, a, etc 2. If you are given the equation for a distance vs time graph - say d = 2t²: - you can fit the equation to the kinematic formulas and find vf, a, etc - you can use the derivative from calculus to find the slope at any point [d'(t) = v(t)] 3. If you are given a graph of speed vs time and need to answer questions about the object's distance: - you can use the given data to find a, vi or vf, and d, and then make a graph 4. If you are given the equation for a speed vs time graph - say v = 30 - 5t: - you can fit the equation to one of the kinematic forms - you can use calculus, since the speed function is the derivative of the distance function (see above) || you need to come tomorrow ready to move on past the graphing section of the unit this includes all work from yesterday. || in many cases, you should be able to determine the equation for the graph and match it to one of the kinematic formulas. i encourage you to use calculus - derivatives or antiderivatives - to solve graphs for speed or distance. last day of work on graphs - pay special attention to problem 25 - don't just plug in 60 sec and say the answer works; get two equations for distance and solve for the time at which they are equal - which must be 60 sec. || p 67, graph p 79 # 8, 22-25 finish summative assignment for graphs - good for quiz || Homework questions - in problem 25, rather than verifying that the answer is 60 seconds, set up equations that can be solved to show that the answer is 60 seconds. And pay attention to the difference between verifying (plugging in) and proving (algebraically or otherwise) Use calculus methods to find the instantaneous rate of change (speed) or an object that is accelerating - do this with both a specific function (d = 2t² +1) and with the general kinematic formula (d = vi t + ½at²) Today we do a review of calculations with the kinematic formulas. We call this kinematics in one dimension, since tomorrow we start looking at projectiles: objects that have motion in two dimensions (x and y). || - due Thursday p 79 # 26, 28, 29, 30, 32, 33, 36, 39, 40, 49, 50 || - Case 1 (upward angle from elevated starting point) Keys: - an object projected at an angle has a speed in BOTH the x and y directions (based on work with vectors) - gravity only affects the vertical motion of a projectile; not the horizontal motion; the motions are independent - should be able to find the total time in the air using kinematic formulas (keep track of directions: up = positive, down = neg) - use calculated time to find the horizontal distance traveled (dx = vx * t) Ex: find the range (horizontal distance) for a cannonball that is fired at 25 m/s at a 30 degree angle from the top of a 20 m high cliff. Note that it is helpful to treat the starting point as the origin (0,0) and to define anything upwards as positive and anything downwards as negative. The range is 79 m. dy = vi t + ½at² becomes -20 = 12.5 t + ½(-9.8)t², where all numbers refer to vertical speeds and distances. Part B - what if we give you the range but not the initial speed? h = 20 m, dx = 120m, angle = 30 degrees it is harder to solve for v than to solve for dx or dy. We won't even start solving for the angle. Part C - what if we give the range but not the initial height? v = 25 m/s, angle = 30 degrees, dx = 100 m here's a link to an online lesson for horizontal projectiles [] ||  || Is this an easier case than yesterday's case? Case # 3 - what if the projectile is fired downward, rather than upward? Case # 4 - what if the landing spot of the projectile is above rather than below the starting point? what if the landing spot is at the same level as the starting point? I want you to see that cases 2, 3, and 4 are all variations (usually simpler ones) of the original case. The GENERAL formulas for projectile motion: vertical distance -dy = VsinØ * t - 4.9 t² horizontal distance dx = VcosØ * t  Special Cases: - horizontal projectile - Ø = 0, so Vy=0 and Vx = V - downward projectile - Vy is negative - equal start and end heights - dy = 0 ||
 * || SNOW DAY - You should be working on at least one of the following today: either spend an hour working on the summative assignment OR spend that hour going through the problems already assigned (46, 52, 54) and new problems on graphs (59,60)
 * Feb 12 || For tomorrow, you need to finish p 46, 53, and 54 (already assigned)
 * Feb 13 || Graphs of distance vs time and speed vs time
 * Feb 14 || Review of graphs for speed vs time and distance vs time.
 * Feb 19 || Summative assignment due date - DR participants have until next Monday to finish.
 * Feb 20 || Intro to projectiles - the curved path of an object under the influence of gravity.
 * Feb 21 || Projectile motion - Case # 2 - what if the projectile is fired horizontally? what changes in our equations?



do six of the problems, ideally one or more of each case. || Last test topic - algebraic motion problems. || || Test topics - graphs for accelerated motion, kinematic review, projectiles, algebraic motion problems ||   || - identify the forces acting on an object at rest or in motion (gravity, accelerating/decelerating forces, friction, tension), and using free-body diagrams to label the forces, find the net force, and determine the acceleration. - use components (Fx and Fy) to deal with forces acting on an object at an angle or two forces acting at different angles, say the force of gravity that causes an object to slide down an incline - identify the forces acting on a system of masses (2 or 3 attached objects), forces that cause acceleration or deceleration of the entire system; for example: two objects connected by a rope over a pully, or an object on a table that is connected to a falling object ||
 * Feb 22 || Hand back first quiz. Additional questions on projectiles.
 * Feb 25 || Hand in your second unit quiz today so that I can give you feedback tomorrow - Test on Wednesday
 * Feb 26 || Quizzes returned today. We spent most of the time taking up questions from the quiz, from the projectile handout, and from the back of the algebraic motion handout. || [[file:projectilesAnswers.pdf|Answers]] ||
 * Feb 28 || Test on Unit 2 - Whole class ||  ||
 * Mar 1 || Begin new unit on Newton's Laws, Forces, and Systems of Masses - this is a major part of any first-year physics course at university. We look at the following situations:

homework is to do several problems from p 138, 145, and 147 || Today we look at the action-reaction forces between objects in a system. We will use the net force of the system to determine the acceleration of the system. Then we will use that acceleration to find the force applied on each object and the tension between any pair of objects Here is a summary of the four cases we looked at: 1. a block sliding down a frictionless ramp; we decided that it was advantageous to rotate the x-y axis by the angle of the ramp 2. the tension between a car and trailer at the point of contact; the car moves forward, but the trailer resists a change in motion 3. the compression between two boxes that are pushed, one in front of the other. We determined that these 2-object "systems" could best be solved by: a. determining the net force on the system b. determining the acceleration of the system c. apply that acceleration to each mass in the system to find the tension || homework is the two problems on the bottom of today's handout. In the first problem, assume the masses move to the left || The force of friction (see handout): - acts opposite to the direction of the applied force - depends on the type of materials in contact - is largely independent of surface area (think of a shoebox on any face - smaller face = more pressure, larger face = smaller pressure; in general these two cancel out) - is calculated by Ffr = Fn * µ (where µ is the coefficient of static friction - we know that once something starts moving, the coefficient of sliding friction is less than that of static friction) and Fn = Fg*cosØ ||
 * Mar 4 || We will take up some of the introductory problems from p 138, 145, and 147
 * Mar 5 || What happens to our calculations of force, acceleration and tension when we include friction?

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 * Mar 6 & 7 || 3-page handout on pulleys, horizontal systems, and inclined planes - acceleratingSystems.pdf

Here is an applet to demonstrate the effect of friction on systems of masses [] We used this to solve the problem on the board in Tuesday's class. Two new problems for today; 1. 30 degree ramp with 10 kg object resting on it, connected by rope and pulley to a 2 kg object hanging straight down. If we calculate the acceleration without friction, it is about 2.45 m/s². However, if the actual acceleration is only 1.5 m/s², what is the coefficient of friction? (0.134) 2. In an Atwood Machine, the left side has a 3 kg mass with a 1 kg mass suspended below; the right side has a 2 kg mass. Find the acceleration of the system and the tension in both strings. (3.23 m/s², 26.2 N and 6.6 N) Thurs - review of problem B-3 from homework - once you get the acceleration of the system, apply that acceleration to EACH mass. You should be able to calculate the tension in the string by using EITHER FBD. (Tension = 17 N) Two more problems - in which the mass does not affect the outcome: 3. Bartender slides a glass along the countertop with Vi = 1.5 m/s²; if µ = 0.15, find the distance the glass slides before coming to a stop. (0.77 m) 4. A toboggan starts from rest at the top of a 20 degree slope. If µ = 0.1, find the speed after the toboggan has traveled 30 m down the slope. (12.07 m/s - thanks, Kat!) || You will work through many of the problems on the accelerating systems handouts.

P 151 problems P 197 problems

|| Accelerating systems - Kahn Academy - listen for ideas that have been taught in class []
 * || ==**Spring Break - Europe Trip - Relax**== ||  ||
 * Mar 18 || ** Whirlwind review of accelerating systems - forces, acceleration, tension, friction **

Tomorrow we will finish up most of the problems on the handouts, Thursday you will have a quiz, and by Friday you will be ready for our next test - which will happen next week Wednesday. ||  || Take up problems from the 3 page handout of accelerating systems. Note that we will NOT have a test problem that involves two different string tensions ||  || Here is an applet to demonstrate the effect of friction on systems of masses [] We will do an activity that allows us to measure the coefficient of friction between two surfaces. If we have time we will look at two cases: a force acting on a mass on a horizontal surface and forces acting on a mass on an incline. ||
 * Mar 19 || General solution for the coefficient of friction problems in which an object slows to a stop, with only friction acting on it: µ = v²/2dg
 * Mar 20 || Review of accelerating systems, tension, and friction

|| - problems that include friction acting on an object - problems that require you to calculate the tension by using free-body diagrams - problems that involve horizontal motion or motion on an angle - word problems on accelerating systems On Friday you will work on a quiz. I will collect these on Monday and return them to you on Tuesday so that you can review them for the quiz. ||
 * Mar 21-22 || Mr Guetter is away at a robotics competition. You have two days in which to review (perhaps learn) the main ideas in this unit:



Quiz answers - 1. 1.375 m/s², 10.6 N; 2. 1.53 m/s², 24.8 N; 3. 1.6 m/s²; 4. µ = 0.003; 5. Ø=14 degrees || Work through the first side of the handout: - find µ given r, m and v - find v given µ and r (mass does not make a difference, right?) - find the min radius of a highway exit ramp that has a speed of 80 km/hr and µ = 1.15 || || then continue with new material on circular motion ||  || Then solve the same problem with a 20 degree banked exit ramp - you should be able to convince yourself that the car can travel faster around a banked corner than around a flat corner and that, if the corner is banked, the required coefficient of friction is less. Note that the centripetal force is given by the sum of Fx and Ffr in this case. Gravity is already pulling the car down the bank; add to that the force of friction from the road pushing against the car tires. || Answers to car problems: 2a. µ = 0.92 2c. v = 34.3 m/s With 20 degree bank: 2a. µ = 0.61 2b. v = 42.1 m/s both of these agree with what we expect. || Transition: a car's centripetal motion around a track is caused by forces pushing the car inward (friction and gravity). The motion of a planet around a star or a moon around a planet is caused by the gravity of the larger body pulling on the smaller body. So instead of Fc = Ffr + Fx for a race car, the relationship is Fc = Fg for a planet or moon around another body ||  || Now we extend this to the orbit of the international space station. From the internet, we found that the time for one orbit is about 93 minutes. Now we can use the Kepler constant to find the orbital radius (6.8 x 10⁶ m) and then we can use calculations of distance/time or Fc = Fg to solve for the speed, which is about 7560 m/s. last problem for today is - find the altitude and speed of a geosynchronous satellite (period = 24 hours). We expect the speed to be less than the ISS and more than the moon. We expect the orbital radius to be more than the ISS and less than the moon. ||  || New problem - number 14 from the problem handout. You can only use the given information, plus the universal gravitational constant. One new problem - introduction to vector calculations with gravity. This is problem 17: where, on a line between the Earth and the moon, will an object experience no NET gravitational force? The distance between Earth and moon is 3.84 x 10⁸ m and the moon has 1.2% of the Earth's mass. || plus problem 17 || We can solve with the actual values for mass and distance OR We can solve using the ratio of masses and the distance as a percent. Our calculation gave us 9.87 % of the distance, away from the moon. We can convert this into an actual distance, which agrees with the answer on the question sheet. Second problem for the day - # 25 on the handout. If we replace the force of gravity between the Sun and the Earth with a steel cable, how thick (diameter) should the cable be? The answer is about 9500 km, which is surprising, given that the diameter of the Earth is about 12,800 km. So it's a really thick wire. So gravity is really, really strong. || You should expect either problem 17 or 25 to appear on the next unit test. Mostly because we spent a lot of time on each of them. || Video from [|The Mechanical Universe] Handout of the Retrograde of Mars Key question is: can we predict the motion of heavenly bodies with the tools given by the earlier scientists/philosophers? discussion of the historical move from a geocentric model of the solar system to a heliocentric model. Notes on worldview/paradigm, anomolies like the regression of mars and the uneven speeds of the planets, the Greek ideas of perfection - resulting in the use of epicycles to explain irregular movement, the invention of the telescope, Kepler's bad idea of using the five platonic solids (and his good ideas of the three laws), and the role of the (catholic) church in maintaining the time-honoured beliefs. The battle is one between experience and investigation, or between tradition vs science. In the end, Copernicus, Kepler, and Galileo are successful, though at a cost, since the church held incredible power over people in the 16th and 17th centuries. ||  || - Greek ideas of perfection in the heavenly realm (Plato, Ptolemy) - Biblical references to Earth's position and movement of the Sun - planets didn't move with constant speed (unable to predict the position at future date) - planets occasionally found in retrograde (need epicycles to account for motion) - invention of telescope and the moons of Mars and Jupiter (not everything orbits the Earth) - Copernicus - "On the Revolutions of the Heavenly Bodies" - 1543 - Galileo - "Dialogue Concerning the Two Chief World Systems" - 1632 - first proposed as a calculation device, rather than statement of fact - role of the church - both in promoting investigation and in enforcing its beliefs - Occam's Razor - "Entities should not be multiplied unnecessarily" - move from theory based on experience to theory based on experiment/data ||  || Joshua - the battle in which the sun stands still for a whole day. How are we to understand this if BOTH the Bible and our interaction with the creation (science) are true? Is there a faithful way to reconcile MY BELIEF that both the Bible and the discoveries of science are correct? John Calvin stated (correctly, to me) that we know God BOTH through his creation and through his word. Vector calculations for force of gravity involving multiple objects Make and analyze a log-log graph of orbital radius vs period of revolution for our solar system. ||  || [|One more article] about planets, the solar system, and cosmology - Neil Turok - Perimeter Institute Quiz on planetary motion - Test on planetary motion - Thursday, April 18 - right after lunch. Hand back summative assignment # 1 - you can earn up to 3/4 of your "lost" points if you redo the assignment and hand in both the old and the new versions. Introduction to summative assignment # 2 - due April 30 || || Problems for test: one on vectors and Fg calculations, one on Kepler's constant, one on Fg=Fc (calculate the speed of a satellite, the mass of the planet, etc). Remember that i will ask you to do a problem like # 17 or 25 as well. Begin new unit on Momentum, Energy and Collisions Collisions - collisions are of two types: elastic (in which both KE and momentum are conserved - we call these "bouncy" collisions) and inelastic (in which only momentum is conserved - we call these "sticky" collisions). Examples: 2 balls hit and bounce off each other (2kg, moving 3 m/s R, 1kg moving 4 m/s L) is an example of elastic collisions; a car of mass 1000kg traveling North collides with a 2000 kg truck traveling East at 25 m/s. The two stick together and travel along the line E38N. How fast was the car going? ||
 * Mar 25 || Introduction to circular motion - we start with the motion of cars on a race track, but the goal is to apply circular motion to the solar system: planetary motion.
 * Mar 26 || Hand back quizzes - test review
 * Mar 27 || Test on Accelerating Systems - 4 problems ||  ||
 * Mar 28 || Review of last problem from intro to circular motion - highway exit ramp
 * Apr 2 || Introduction to planetary motion - as an extension of circular motion.
 * Apr 3 || Take up problem about the speed of the moon in orbit around the Earth. Using the Kepler constant OR using Fc = Fg you should get a speed of about 1025 m/s.
 * Apr 4 || Take up geosynchronous satellite problem - v = 2960 m/s and O.R. = 42,400 km.
 * Apr 5 || Take up weightless point between the Earth and the moon.
 * Apr 8 || Few classes on the history of astronomy and the change from an earth-centred to a sun-centred solar system.
 * Apr 9 || Review of the change from a geocentric to heliocentric model of the solar system:
 * Apr 10 || Review of paradigm shift from geocentric to heliocentric model of the solar systerm
 * Apr 15 || Test is still on Thursday - we finished the unit content last week and reviewed one problem on vector addition of gravitational forces in class today.
 * Apr 16 || Review for test on Thursday - one written question: describe or explain several key events, discoveries, people or institutions, as they relate to the change from an Earth-centred to a Sun-centred solar system.



|| Impulse is the change in an object's momentum; if a force acts on an object for a period of time, and it changes the momentum of the object, we say that the change in momentum is equal to the impulse (for that object) Calculation of momentum p = m * v (both scalar and vector calculations, both one and two dimensions)Calculation of impulse Δp = f * Δt (which also gives us this relationship: f * Δt = m * Δv) Law of Conservation of Momentum - p(initial) = p(final) (again, both scalar and vector) There are several conservation laws, including energy and mass. ||  || For elastic collisions in one dimension it is helpful to treat one object as being at rest; we did this with relative motion in the past, so the concept is not completely new. If one object is moving 3 m/s [R] and the other 5 m/s [L], we can treat the first one as moving 8 m/s [R] and the second one at rest. Once we calculate the final speeds, we need to adjust for adding 5 m/s right to each one (by adding 5 m/s [L] to each one). Calculation for impulse Δp = f * Δt = m * Δv || Homework problems p 327 11, 12, 14, 19, 20, 25-28 || Problems on elastic and inelastic collisions || p 327 # 15-18, 29-34 || example - a 1 kg ball moving 3 m/s strikes a second 1 kg ball at rest. The first ball moves at 2.5 m/s at an angle of 35 degrees away from the initial direction of motion. Find the speed and direction of the second ball - and then verify the energy is conserved. 1.72 m/s at 55 degrees (in other direction). Energy = 4.5 J. || p 327 # 23, 36, 37 p 370 # 24, 25a || review of the vector nature of conservation of momentum. || Homework problems p 327 # 35, 39, 42 || We managed to get correct solutions for all FOUR problems - well done! Bird problem - this is a projectile and conservation of momentum problem. You need to: find the height of the bird, using the initial velocity of the arrow, find the initial horizontal speed of the bird + arrow, then solve for a horizontal projectile (14 m) Airplane + Barge problem - find the frictional force acting on the plane, find the distance and time to land on a regular runway, then use conservation of momentum to find the length of the barge (340m) Collision problem - use trig for conservation of momentum in two dimensions, you can either use the given speed (60 km/hr) or solve for the actual speed (90 km/hr) Physics cart problems - the first one is an elastic collision and the second is inelastic. you need to account for the x component of Fg, which slows down the cart (or carts). The answers are 0.92 m and 0.23 m || || Review of - Fundamental forces (strong, electromagnetic, weak, gravity), atomic theory (plum pudding and planetary model; plus recent discoveries), transfer of charge (contact vs induction; electron flow vs current flow), electrostatic series (listing of materials by their ability to take or give electrons) ||
 * Apr 17 || Euclid contest date - did review work for the whole time. ||  ||
 * Apr 18 || Test on planetary motion - one longer written question on the change from an Earth-centred to a Sun-centred solar system; one problem on vectors and the force of gravity; at least one question of each of Kepler's constant and Fg = Fc (satellites and orbits); I promised you a question like 17 or 25 from the homework. ||  ||
 * April 19 || Momentum is like inertia - a property of matter. It is the product of an object's mass and velocity; it follows conservation laws
 * April 22 || Review of calculations for elastic and inelastic collisions.
 * April 23 || Review of summative assignment # 2 - due date is May 1.
 * April 24 || Collisions in 2 dimensions:
 * April 25 || Two problems involving collisions - diagrams from problem handout. ||  ||
 * April 26 || take up problems from homework - P 327 # 30, 34
 * April 29 || Finish unit on Collisions - challenge problems and quiz to end the unit
 * April 30 || many students are gone this week for choir, business leadership, and track and field. Your work for this class is to finish the collisions quiz - answers are on the quiz. Test will be next week Tuesday or Wednesday. || Last quiz problem - the angle of the second ball is 63 degrees, not 53. ||
 * May 1 || New Unit - Electric Forces and Fields

|| d is the distance between the centres of the charged objects and K is Coulomb's constant (9x10⁹ N*m²/c²) And what is a coulomb? The charge on a single proton or electron is so small that it is far more convenient to talk about a substantial amount of charge passing a point per second (1 amp per second). And with this definition, 1 C of charge is 6.24×10¹⁸ electrons. || P 583 # 1-6 P 586 # 1-3 || Problem solving with electric fields || P 583 # 7 - balloon problem with vectors P. 612 # 13, 14, 15, 17 || - a field is the region around an object that affects other objects, based on charge, mass, polarity, etc. A field exists whether or not there is a "test" mass/charge near the object responsible for the field. We can think of a field as an alteration of space around an object; like we did in demonstrating the curvature of space around masses. The field lines point in the direction of movement of a positive test charge (or in the direction that a mass would move) - a force describes the way that two or more charged particles, magnetized objects, or masses interact; this depends on the amount of charge, magnetism, or mass on each object, the distance between the objects, and the value of the constant for that force. If there are more than two objects involved, we refer to vector methods established earlier in the course. The field strength is independent of the charged object placed in the field - think about the gravitational field around the Earth: the force is gravity is larger on massive objects, but it is exactly 9.8 N/kg. The same happens with the electric field around a charged object. The electric field around a +3C charge does not change just because a larger or smaller charge is brought near; the force increases or decreases, but the field is independent of the second charge. || P 591 # 1-5 problems on electric fields || Forces and fields using vector methods Discussion of the electric field between parallel plates - the field is: - uniform (same strength at all points); we can show this is true by using vectors - its direction is from positive to negative;p think 'symmetry' - the field strength is given by € = V/d (where € is the field strength, v is voltage difference between the plates, and d is separation distance of the plates) [|parallel plates] Why are parallel plates important in this unit? applications - picture tubes (CRT), pollution control (ESP) ||  || 1. near another charged particle 2. between parallel plates Discussion of the electric field between parallel plates - the field is: - uniform (same strength at all points); we can show this is true by using vectors - its direction is from positive to negative;p think 'symmetry' - the field strength is given by € = V/d (where € is the field strength, v is voltage difference between the plates, and d is separation distance of the plates) [|parallel plates] Why are parallel plates important in this unit? applications - picture tubes (CRT), pollution control (ESP) || P 612 # 16, 18, 22, 23, 28 || 1. with point charges, the PE increases as we bring the charges closer together and decreases as we bring the charges farther apart. We will use conservation of energy to solve these problems in a few days (PE + KE = constant). 2. with parallel plates, the force on the particle is constant, so we cannot use energy conservation (it's an open system); as a result, we need to use Newton's second law and kinematic formulas to solve these problems. ||  || Can we use both energy calculations AND force/kinematics calculations? Yes - where the electric force is constant (plates) we can use force/kinematics (open system); if the electric force changes with distance (points) we can use energy conservation (closed system)
 * May 2 || Calculation for electric force between two charged particles:Fe = K (q1*q2) / d² where q is the charge in coulombs,
 * May 3 || Summative # 2 due next class.
 * May 6 || Difference between the electric force on a charged particle and the electric field strength around a particle. In general, here's the difference between a field and a force:
 * May 7 || Review for Tomorrow's test on Momentum, Impulse, and Energy
 * May 8 || **test on momentum, impulse, and energy** ||  ||
 * May 9 || Comparison of the force on a charged particle in two different situations:
 * May 10 ||  ||   ||
 * May 13 || Intro to electric potential energy - regions of higher and lower PE. Calculation of PE
 * May 14 || Motion of charged particles in an electric field - handout based on yesterday's work.

Application of electrostatics and electric fields: - industrial scrubbers, copiers, medical diagnostics - to the explosives detection industry [|background] and video of the [|ADE-651] hints for today's homework
 * 1) 40 - find the sum of the KE of each particle; equate this with the PE between the particles at min separation: d = 1.55 x 10-¹⁴ m
 * 2) 41 - find € = 3 x 10⁴ N/C, Fe = 4.8 x 10-¹⁵ N, a = 5.27x10¹⁵ m/s²; then find out how much time the electron takes to travel the length of the plates = 1.25 x 10-⁹ sec; and we get an answer of .0041 m deflection || [[file:motionChargedParticles.pdf|motion of charged particles]]

P 612 # 40, 41 || Introductory lecture on Modern Physics - a survey of some of the key moments in the last 150 (or so) years of physics: Thomas Young (double slit experiment), Michelson Morley (detecting Ether), the Photoelectric Effect, Special Relativity. And the crucial question in physics: why the universe appears to behave differently on the macro level (planets and galaxies) than it does on the microscopic level (atoms and sub-atomic particles). The search for a unified theory - gravity and quantum mechanics. ||  || diffraction is the spreading out of waves as they pass through a narrow opening (opening size = wavelength) Thomas Young's double slit experiment showed that light behaves as a wave, since a distinct interference pattern was seen - and you will observe this in class as well. Young used a single light source and very narrow slits that were close together - previous attempts to verify the wave nature of light failed because of these problems. And we learned to calculate the wavelength of light based on the diffraction pattern geometry: the spacing between the double slits, the distance to the "screen" on which the pattern is noticed, and the number of light and dark fringes counted on the pattern. ||  || More problems with diffraction and wavelength of light Demo of Young's double slit experiment - in class demo and interactive site[] Calculation of wavelength from Young's experiment: lambda = (delta)x * d/L (see handout) || || [] Michelson-Morley experiment - description of the experiment and the expected results. The failure of this experiment to detect ETHER was one of the key contributions to quantum theory. Video clip of the [|Michelson-Morley experiment] - you can also watch parts 2 and 3 at your leisure Michelson-Morley Experiment - on a test or exam, you should be able to: - describe the evidence for the wave model of light - identify the one problem with this theory - describe Ether - what is it, describe its properties - describe the experiment to detect Ether - identify and explain the "null result" of this experiment - explain how this experiment paved the way for 20th century discoveries ||  || Review of concepts and calculations for test ||  || - E shone light of different colours on a metal plate and noticed that electrons moved through the resulting circuit only when the wavelength of light was short (= high energy) - E theorized that if the wavelength was too high, the electron would not have the required energy to leave the atom; only with short wavelength light would the electrons leave the atom (= ionization) Photoelectric Effect - is light a particle or a wave? This experiment, attributed to Einstein, confirms the particle nature of light = photons. Discussion of ionization energy, work function, and the relationship between color (wavelength) of light and energy. The work function is the energy (in joules or eV) to ionize an atom - how much energy will release an electron from the atom? Formulas to use: E(photon) = h*f (h = 6.63 x 10-³⁴ J*s), E(photon) = h*c/λ, c = f*λ 1 electron volt (eV) = 1.6 x 10-¹⁹ J || Work Function for Metals
 * May 15 || Discussion of Millikan's oil drop experiment to determine the charge on the electron - handout and [|demo] || [[file:millikan.pdf|Millikan's oil drop]] ||
 * May 16 || Finish homework problems on electric forces unit. The key problem in this unit is to describe and calculate the motion of a charged particle in an electric field; either an electric field around another charged particle or an electric field between parallel plates. ||  ||
 * May 17 || Remember that you need to be able to describe an application of electrostatics or electric fields. This will be a test question and will require some detail in your answer. Your application is to be one of the following: industrial scrubber technology OR copier, laser printer, fax technology.
 * May 21 || Thomas Young - Review of refraction and diffraction (from grade 11) refraction is the bending of waves as they pass from one material to another; for light, we refer to the differences in "optical density"
 * May 22 || Take up questions from p 529 - remember to divide the distance from the centre to the specific fringe by the number of fringes. Demonstration of the experiment - we used a laser, which Young did not have access to (almost 200 yrs ago).
 * May 23 || Review of Young's experiment - here's a good resource:
 * May 27 || Review of Michelson Morley experiment
 * May 28 || Test on Electric Forces and Fields ||  ||
 * May 29 || Intro to Quantum Physics and the Photoelectric Effect

Today's work consists of two questions: 1. Find the colour of light that would remove an electron from a cesium atom 2. If the actual light had a wavelength of 400 nm, what would the speed of the ejected electron be? || []
 * May 30 || Review of Photoelectric effect - []

I want you to become familiar with all the calculations involved in this unit - work function, photon energy, kinetic energy of electron, conversion between frequency and wavelength of photon. review of light and quantum theory - [] || Problems: p 705 # 2,3,4,5 p 728 # 15,20,22,24 ||
 * May 31 || Energy levels in atoms

Explanation of what happens when a photon strikes an atom. One of the following: - there is not enough energy in the photon to raise an electron to one of the excited states, so the energy is passed from the atom - there is enough energy to raise an electron to one of the excited levels; the electron drops to ground state and releases a photon with that amount of energy; any other energy is released immediately - there is enough energy to remove the electron from the atom (work function or ionization); any additional energy becomes kinetic energy in the free electron

Calculations to perform: - determine if a specific wavelength of light can excite or remove an electron - determine the min wavelength of light that can excite or remove an electron - determine the transitions to ground state that are visible (300 - 700 nm) - if an electron is ionized, determine the KE of that electron

For the energy levels of Hydrogen and Mercury: - find the minimum wavelength that excites an electron to the 1st, 2nd excited energy level - find min wavelength that will ionize the electron and give an ionized electron a speed of 3 x 10⁵ m/s - for each element, find 3 transitions that result in visible light ||

Homework - energy level problems for Hydrogen and Mercury. We will finish this on Monday || 1. What happens in an atom with energy levels of G = 0 eV, 1st = 3.4 eV, 2nd = 4.5 eV, 3rd = 7.2 eV, and ionization = 8.0 eV? - find the wavelength of light that raises an electron from G to 1st excited level? - an electron decays from the second to the first energy level. Find the wavelength of light emitted - determine the transitions that result in visible light (300 - 700 nm). It may be easier to find the energy levels of both ends of the spectrum and then look for gaps within that range - find the wavelength of light that ionizes an electron in this atom. Applications of light - interference of light waves - even though we consider light to be a particle, its wave properties allow us to investigate two interesting technologies: holograms and CD/DVD data storage. - since light is a wave (Thomas Young) we can use wave properties of light to store information binary information (zeros and ones) stored as destructive/constructive interference patterns when a reference beam from a laser is compared to a "pit" or "no pit" on a cd or dvd surface. holograms store the interference pattern between a reference beam and the reflected light from an object; and the original image can be seen when the same light is shone through the hologram. || includes first sheet of exam with formulas || - high voltage power supply passes through gas in a sealed tube (helium, hydrogen, neon, oxygen). - as the atom is bombarded with high energy electrons, the electrons in the atom get excited, and then drop to a lower energy level - these changes, from one excited state to another, or from one excited state to ground level, represent specific amounts of energy, which are released as light. - so, when you see the emission spectrum from a particular substance, you can tell a lot about the atomic structure of that atom (or at least about the energy levels). Calculation: Find the simplest atomic energy level structure to account for these four lines: red-630 mn, green-525 nm, turquoise-485 nm, blue-460 nm ||  || Application of energy levels to the operation of a helium-neon laser - key concepts to know: what is a metastable state, how a population inversion occurs, time for excited states (specifically the difference in times - He is 10-⁸ sec and Ne is 10-⁴ sec ), why He and Ne work well together (both are noble gases, but there is more...) For the exam, you will need to explain how the either lasers or the auroras: 1. Lasers produce coherent light: one colour, in phase, very little dispersion, making reference to the above concepts. The specific questions to answer are: -what is a metastable state and which element has it? -how does a population inversion take place? -what do we mean by stimulated emission? -what is coherent light? 2. Northern Lights - what elements do we find in the upper atmosphere? - why do high energy particles from the sun concentrate at the poles? - how do quantum energy levels explain the process? || [|NASA explanation] of the Northern Lights
 * June 3 || Review of quantum calculations for photon absorption and emission - light taken in by an atom to excite an electron and light given off by an atom when an electron transitions to a lower energy level.
 * June 4 || Demo of emission spectra from gas discharge tubes - as an application of quantum physics. You have probably seen this in chemistry class last year. Here's a brief overview:
 * June 5 || Applications of energy levels - Auroras - high energy particles from the sun (solar wind) react with the Earth's magnetic field (stronger near the poles). The light we see is produced by quantum jumps in Nitrogen and Oxygen in the atmosphere.

And [|another explanation], with specific information on Oxygen and Nitrogen || - state the two postulates of Einstein's special theory of relativity - explain the difference between an inertial and a non-inertial reference frame - what does relativity predict about mass, length and time as the speed of an object increases?
 * June 6-10 || Review of quantum energy levels in atoms. Introduction to Einstein's Special Theory of Relativity

Review of the postulates of relativity - []

Lorentz transformation - the factor by which mass increases, length decreases, or time shortens as your speed increases. Notice that these changes are not evident at "normal" speeds; only as we approach the speed of light.

Handout of relativity problems - time will be the hardest calculation since the length of a second actually increases, but the amount of time that passes, decreases.

We will distinguish between "rest" measurements - done when you are in the same frame of reference as an object - and "relativistic" measurements - done when we are at rest in relation to a (moving) object. the Lorentz Transformation allows us to calculate the changes to fundamental quantities as the speed of an object increases, relative to the observer. Specifically Lz =√ 1 - v²/c² If our rest(o) measurements are taken in the same frame of reference as the object and our relativistic(r) measurements are taken with the object in motion, relative to our position, the following relationships are true: 1. Mass increases as the speed of an object increases: Mr = Mo / √ 1 - v²/c² 2. Length decreases as the speed of an object increases: Lr = Lo * √ 1 - v²/c² 3. The length of a unit of time increases : Tr = To / √ 1 - v²/c² (but the amount of time decreases) Results - which have been experimentally verified - you age less if you travel fast - time passes by more slowly if you travel fast - an observer would notice that a second takes longer when the object is moving fast || || and here is your final exam summary question:
 * June || Here are copies of the unit tests - available until June 15

Earlier this year, you read an article by Neil Turok, the Director of the Perimeter Institute. Here is an excerpt, in which he talks about inspiration, beauty, and simplicity in the universe.

There’s an inspirational aspect of science and of understanding our place in the universe that enriches society and art and music and literature and everything else. Ever since the ancient Greeks, science has well appreciated that a free exchange of ideas, in which we are constantly trying out new theories, is the best way to make progress. Again and again, our efforts have revealed the fundamental beauty and simplicity in the universe. Neil Turok - 2012

a. what is inspiring about physics - either on the cosmic (planetary) scale, or on the atomic level? b. how have you come to appreciate that “trying out new theories is the best way to make progress?” Use specific ideas from our study of modern physics or planetary motion to describe this “progress”. Murray Gell-Mann talks about the layers of an onion - how each one is similar to the previous, yet beautifully different. c. Is there a fundamental beauty, elegance, or simplicity in the universe? Why or why not? || unit tests

[|Article by Turok] [|TED talk by Gell-Mann] ||