sph4u+HW

**SPH4U Homework - Spring, 2014**
=**Date**= || =**Class Topics and Summary**= || =**Handouts-and-Homework**= || - same as in functions class ; Lowest test will be dropped, but not before the midterm marks go home. Quiz and homework marks count toward your 100 points and this time YOU will be keeping track of the points. 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 much pizza was eaten yesterday in Canada? What assumptions and calculations can we make to get a reasonable answer? make 3-5 good assumptions and show your calculations.
 * =**Today's**=
 * Jan 28 || **How to earn your mark in this class:** Unit tests (6 or 7); 100 points for 15% of your mark

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. ||
 * Unit 1 outline - measurement and analysis **

[|100 points for 15%] [|100 points tracking]

Fermi: how many pizzas were eaten in Canada last night? || The question of how to know if zeros are significant is answered here: [|University of Guelph - Physics] 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 will choose a problem from the handout to present to the class next week; do this in pairs. One does the homework, one does the presentation. 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 standard power functions - cubic, quadratic, linear, root, rational (1/x and 1/x²) ||
 * Jan 29 || review of homework problems - what to do with zeros (how to determine if they are significant)

how air will a person breathe in 20 years?

p 12 # 1 p 25-26 # 1-3 for p 25 - the best answer will be a function, not a graph || - the top right data set has an error - instead of 90, it should read 9.0 Intro to relationships where the exponent is not a whole number - use logs to determine the power: 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 ||
 * Jan 30 || Take up relationships from p 25 and 30 - here is a sheet with lots of variety in functions

[|how to graph with log-log paper]

y=10/x² y = 20x² y=0.2x^½ || Today's work is to review all the new things we learned and to prepare for your Fermi question presentation next week. You can pick a problem and a partner to work with. You have a quiz to work on once you finish the day's work - it is due on Tuesday, so I can return it to you on Wednesday, for the TEST ON FRIDAY some answers from today's handout a) (1, 500) (3, 32.1) (5, 8.9) (7, 3.8) y = 500 / x 2.5 b) (2, 7.798) (3, 15.535) (4, 25.335) (5, 37.022) y = 2.4 x 1.7 c) (2, 70.31) (3, 247.01) (4, 602.84) (5, 1203.98) y = 8.2 x 3.1 ||
 * Jan 31 || Many students are gone today - volleyball, basketball, just cause it's Friday...



[|a primer on log graphs]

- due Tuesday || - physical measurement of slope on log-log graph gives the exponent in y = a x n - m = (log y 2 - log y 1 ) / (log x 2 - log x 1 ) (gives more exact answer) - give yourself two homework checks if you finished the worksheet Today's work - and the 8 data sets from last week. - quiz - I will collect them tomorrow and return them first thing on Thursday - Fermi problems - in pairs, choose a Fermi problem and prepare a solution to present to the class on Wed or Thurs - 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. 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: --- and ---. || p 16 # 1-3 finish the quiz finish 2 homework checks partner and fermi question for Wed || Facebook your Fermi question partner and decide how you will present your question. Here are the rules: - no powerpoint allowed. You may show a single image, if you wish. - 3 minute maximum - you must give between 3 and 5 assumptions that you consider to be valid - your classmates will perform the calculation and tell you the order of magnitude - at least one person will be asked to challenge an assumption of yours || here are a few review problems
 * Feb 3 || Review topics from Friday's class:
 * Feb 4 || Finish your quiz - have it ready at the beginning of class tomorrow

Ex 1.10 # 4, 7, 28, 29 || 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. ||  || hand in work that represents your best effort. Due date: Begin unit two - start with a review of motion - graphs of distance vs time and speed vs time - review of kinematic formulas and acceleration - algebraic motion problems - projectile motion 1.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 2. boat travels upstream 20 km (against the river current) and downstream 20 km (back to start) in FOUR hours. Can you find the speed of the boat - b - and the speed of the current - r? 3. Walking up the "down" escalator takes 20 sec; riding down the "down" escalator takes 12 sec. How much time does it take to walk down the "down" escalator? (60/13 seconds) || derive one more kinematic formula: d = vf t - ½ a t²
 * Feb 5 || Collect quizzes - to return tomorrow
 * Feb 6 || Fermi problem presentations - there are a few students who need to present next week. ||  ||
 * Feb 7 || Test on unit one - Fermi questions, precision, data and functions ||  ||
 * Feb 10 || Summative assignment for Unit 1 - the pendulum. Follow the requirements carefully and

|| 1.start with one of the basic formulas and substitute to eliminate variables 3.solve 3 equations with 3 unknowns 2.we arrived at the formula T(up) = 2(r/d) + 2, which tells us that the time upstream is both -a ratio between the two speeds -and that there are many solutions -you are asked to solve for a ratio of 1/4 or 1/6 and calculate the speeds and verify the total time. || p 52 #1,2,3, p 54 a-d || 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. Most importantly - any time you can determine the distance function, you can use calculus to find the speed and acceleration Equally important - if you are given a graph, either use tangents or area to find the required quantity (dist/speed/accel) If you can turn a graph into a function, you will save lots of time, since you know calculus || p 56 a-e p 59,60 # 1-4
 * Feb 11 || We reviewed questions 1,2, and 3 from the homework in detail
 * Feb 12 || With graphing problems, you are often asked to find the distance when given a velocity-time graph;

p 73 # 1-4 || 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) || - handout
 * Feb 13 || Graphs of distance vs time and speed vs time

Homework problem: car speeds up from 15 m/s to 30 m/s in 5 seconds the car maintains that speed for 8 sec then it decelerates in 75 m 1.sketch - dist vs time, speed vs time locate endpoint of each section 2.calculate - total distance traveled, average speed for car (2 ways each?) 3.find the piecewise function that models -the speed of the car -the distance the car travels || - finding the relationship between length and the period of a pendulum Review of Thursday's homework problem. Review of graphs for speed vs time and distance vs time. 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. || 79 # 7, 8, 13, 17, 19, 20 (sketch d-t and v-t graphs) 22 a,e, 24 b,e, 25 || I will only mark assignments that are printed and handed in. This is your reminder to stay on top of things until midterm marks go out in April. Review of kinematics and calculations - today we work in one-dimension; then we look at the special case of projectiles - in which the motion is both horizontal and vertical. 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) Another calculus problem: the speed of an object is given by v(t) = 2/3 t² t<=6 sec v(t) = 24 - 3(t-6) 6<=t<=14 sec sketch the graph of v vs t, find the total distance traveled, and find the d(t) piecewise function || - due Friday
 * Feb 18 || Last questions on summative assignment
 * Feb 19 || Summative Assignment due - by end of the day -

projectile problems start today, finish Friday p 79 # 28, 29, 30, 32, 33, 36, 39, 40, 45, 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. Case 2 - 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 [] ||
 * Feb 20 || Intro to projectiles - the curved path of an object under the influence of gravity.



do six of the problems, ideally one or more of each case. || 1.You have two problems on projectiles - from yesterday's second handout - 2nd question, use 160m. check your first solution before starting the second 2.You have homework problems that involve graphs of motion - Feb 18 work 3.You have homework problems that involve kinematic formulas - Feb 19 work 4.And you have a quiz that is due on Monday We have a test next week Friday, so stay current with the daily work! ||  || what changes in our equations? Is this an easier case than yesterday's case? Case # 3b - 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 || || Take up problems from question sheet. What about projectile problems in which the start and end heights are equal? Range formula R = dx = (v² sin 2Ø)/g - can you derive this from the dx and dy formulas? ||  || Last test topic - algebraic motion problems. Quiz 3 - you can check your answers with the link on this web page will take up problems tomorrow - 2 pts if done before class || || in block D or E, you can likely start early or write late - ask! ||  || - this is a major part of any first-year physics course at university. We look at the following situations: - 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 pulley, or an object on a table that is connected to a falling object 4 Examples: - 2 kg mass pulled by a hanging 1 kg mass (a = 3.27 m/s²) - 2 kg mass on 30 degree slope (a = 4.9 m/s²) - Atwood machine with 1 kg and 3 kg masses (a = 4.9 m/s²) - 3 kg mass on table pulled in opposite directions by hanging 1 kg and 2 kg masses (a = 1.63 m/s²) ||
 * Feb 21 || Work period for kinematics problems and for projectile calculations
 * Feb 24 || Projectile motion - Case # 3a - what if the projectile is fired horizontally?
 * Feb 25 || Hand back first quiz. Additional questions on projectiles.
 * Feb 26 || Check homework for projectile problems - few more on homework sheets
 * Feb 27 || take up problems from this unit - including quiz - write tomorrow - for students with spare
 * Feb 28 || Test - whole class - graphs of motion, algebraic problems, kinematics, projectiles ||  ||
 * Mar 3 || Begin new unit on Newton's Laws, Forces, and Systems of Masses

do several problems from p 138 amd 145 || 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 || for Accel and Tension
 * Mar 4 || We will take up some of the introductory problems from p 138 and 145



to ABC problems

do two problems from part A and one problem from part B  for tomorrow. If you are gone Thursday do one more of each || 3-page handout on pulleys, horizontal systems, and inclined planes - acceleratingSystems.pdf 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 Do the two problems on the bottom of the first page of the handout. || more problems from ABC || Your focus is the ABC problems from the handout The answers are posted online - and printed out for you. ||  || Accelerating systems - Kahn Academy - listen for ideas that have been taught in class [] 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.
 * Mar 5 || What happens to our calculations of force, acceleration and tension when we include friction?
 * Mar 6 || Mr Guetter is not here today but you still have work to do.
 * || == **Spring Break - Europe Trip - Relax** == ||  ||
 * Mar 17 || ** Whirlwind review of accelerating systems - forces, acceleration, tension, friction **

Two new problems for today; 1. 30 degree ramp with 1 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) || Start with three problems that review last week's work

- 2 kg object on 20 degree slope. Find u so the system is at rest - 2 kg on 45 degree slope 4 kg hanging down. Find u so the system is at rest - 2 kg object on 30 degree slope. u = 0.25. Find hanging mass (m) so the system is at rest || New problems related to kinematics Two more problems - in which the mass does not affect the outcome: 3. Bartender slides a glass along the countertop with Vi = 2.5 m/s²; if µ = 0.10, find the distance the glass slides before coming to a stop. (d = 3.19 m) 4. A toboggan starts from rest at the top of a 20 degree slope. If µ = 0.25, find the speed after the toboggan has traveled 30 m down the slope. (vf = m/s) || Finish ABC problems Work on P 151 and 197 problems || with only friction acting on it: µ = v²/2dg d = v²/2µg ||
 * Mar 18 || Take up problems from handout (ABC problems) - just give starting points, not complete solutions.
 * Mar 19 || General solution for the coefficient of friction problems in which an object slows to a stop,

|| Mar 21 || Mr Guetter is away at a robotics competition. You have two days in which to review (perhaps learn) the main ideas in this unit: - 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 test. ||
 * Mar 20



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 || Set up and solve the mouse and cheese problem (m=0.173 kg) Summative #2 - take ONE of the two projectile problems and make changes to THREE initial values in the problem (change by at least 10%, but use nice, round numbers to keep things simple) 1. solve the new problem - no need to use computer; paper and pencil is fine, as long as I can read it (5 pts) 2. explain, using FBD and words, how you got the answer. (5 pts) Include a diagram, but no computer skills are needed. ||  || but the goal is to apply circular motion to the solar system: planetary motion. 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 ||
 * Mar 24 || Review of quiz, of homework problems, of two forces/projectiles problems.
 * Mar 25 || Introduction to circular motion - we start with the motion of cars on a race track,

Answers to car problems: 2a. µ = 0.92 2c. v = 34.3 m/s 3. With 20 degree bank: µ = 0.61 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 || || 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.
 * Mar 26 || Test today - whole class. If you are leaving early for sports, drama, work...please arrange to start earlier. ||  ||
 * Mar 27 || Introduction to planetary motion - as an extension of circular motion.
 * Mar 28/29 || Take up weightless point between the Earth and the moon.

Introduction to Kepler's Three Laws of planetary motion. 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.

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. For homework, verify Kepler's Third Law for the Earth-centred system - you have three satellites to work with. || Problem 14 from handout

New homework problem #10 do two 2-moon systems and # 11, 12, 22a, 23 || Tomorrow and Thursday I will spend time going through your points accumulated so far. You should make sure that you have your quizzes and summatives, and that if you have given yourself lots of homework checks, that you are able to show me any random problem that I ask for. 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. || Review of calculations so far. Take up problems from homework Assign problem 25 || distances and/or angles. Give your answer in terms of G. Do not multiply G out. || Problems 16, 18 plus three masses in a 1, 2, root 3 triangle || 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
 * April 1 || Your summative assignment is due tomorrow, but you will have until Thursday to hand it in without penalty.
 * No test this week - it's called an April Fool's Joke**
 * April 2 || Force of gravity and vector calculations - find the Fg on a mass due to two or more masses at specific
 * April 3 || Few classes on the history of astronomy and the change from an earth-centred to a sun-centred solar system.
 * April 4 || Review of the change from a geocentric to heliocentric model of the solar system:

For today's class, you have three things to work on: 1. the quiz - handed out in class already - due Monday 2. your midterm mark - if you are not content with the average of your first three tests, you will complete your Points Sheet and be prepared to show me evidence of your dedication to homework, quizzes, and summatives. I will consider discounting your lowest test at this point (make it seem less important). 3. based on my presentation yesterday, be prepared to answer several of these questions on next week's test. You may have to find a bit of information in your history notes or online, but I know that you can do it: - how was the geocentric solar system based on Greek (Plato's) ideas? - explain the role of the church in promoting the geocentric worldview - did the church have a positive contribution to astronomy, or was it all bad? - why did the geocentric model run into problems? list a few specific examples - what is the significance of the invention of the telescope? - what is the significance of Occam's Razor in the switch from a Geo-centric to a Helio-centric model of the solar system || || Last call for summative assignment # 2 Test this week Thurs/Fri - many conflicts with athletics, drama, ... Based on the results of this test, I can drop your lowest test for the midterm mark - I will need to adjust your report card mark before it gets submitted. This week I would like to see your record of marks earned for your 100 points - I want to make sure that you are doing your part. Final questions for planetary motion - test includes a written component, but mostly problems. ||  || Two problems: 1. a 500g grenade explodes; a 100g piece flies N at 12.5 m/s, a 200 g piece flies E at 15 m/s which way does the remaining 200g piece fly, and at what speed? 2. a 3 kg ball rolls E at 2 m/s; a 2 kg ball rolls W at 1 m/s. Can you calculate the final speed and direction of each ball? you will need to use calculations of energy: E = ½mv² and momentum: p = mv ||
 * April 7 || Collect quizzes and return tomorrow
 * April 8 || introduction to momentum and energy



|| v1f = 3/5 m/s and v2f = 18/5 m/s however, we added 1 m/s [R] to each ball, so now we need to subtract 1 m/s [R] from each which gives v1f = -2/5 m/s and v2f = 13/5 m/s How do we know these are correct? We can calculate the original total KE and the final total KE If they are equal, we know the answers are correct - at least in ELASTIC collisions. || Homework - you should be able to do the following collision problems p 370 # 23-26 || Take up one problem on collision problems - p 370 We will look at parts b&c of these next week New - conservation of momentum problems. The assumption (always) is that Pi = Pf, initial momentum and final momentum are equal When the motion is along a straight line, we use + and - to indicate direction (right vs left) When the motion is in two dimensions, we need to use the Pythagorean Theorem to solve for momentum || p 327 # 23-26, 30 || 1. One dimensional collisions - 2 balls bounce off each other - both KE and p are conserved - 2 balls hit and stick together - only p is conserved 2. Two dimensional collisions - 2 objects strike each other and head off at some angle relative to the original path - not covered yet - 2 objects collide and head off at different angles relative to each other NEW for today - impulse - a force that changes the momentum of an object need to know the change in momentum, the force applied, and the time over which the force is applied as long as we know two of these three, we can calculate the third || p 327 # 12-18 || while part is conservation of energy and momentum (elastic collision) 2. collisions in two dimensions - page 3 of problem handout - ball 1 initial speed is 1.65 m/s and ball 2 speed is zero - both balls move at angles relative to the original path after the collision verify that both the momentum and the KE are conserved New problem - same situation - V1i = 3 m/s N and V2i = 0 after the collision, V1f = 2.5 m/s @ 30 degrees from horizontal and V2f has a speed of 1.5 m/s calculate the angle that ball 2 travels at (relative to North is best) ||  || Sometimes you are given too much information in a problem. Work through one of the two challenge problems AND the quiz. || problem 6 - angle is 63 degrees, not 53 || You should be able to solve any problem that deals with impulse, momentum, and collisions Quiz to be checked tomorrow - have it done Test date next week ...... Marks have been updated in maplewood based on your most recent test || p 327 11, 12, 14, 19, 20, 25-28 p 327 # 15-18, 29-34 p 327 # 23, 36, 37 p 370 # 24, 25a
 * April 9 || Show the solution to problem #2 - assuming ball 2 is initially at rest (and adding its speed to ball 1)
 * April 10-11 || Test on planetary motion - lots of students gone for sports and drama
 * April 14 || Review of energy and momentum calculations so far - notes and equations for:
 * April 15 || 1. polar bear question - #33 - part one is conservation of momentum (inelastic collision)
 * April 16 || Problem solving with collisions - solve yesterday's problem for both the speed and the direction of the second ball.
 * April 17-21 || Easter Break ||  ||
 * April 22 || Problem solving - last full day on Collisions and Energy

p 327 # 35, 39, 42 || 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) ||  || 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 23 || Collect, check, and hand back quizzes
 * Apr 24 || Begin New Unit - Electric Forces and Fields - Review of:

|| We will take up any last-minute questions for Tuesday's test when we return on Monday. Calculation for electric force between two charged particles:Fe = K (q1*q2) / d² where q is the charge in coulombs, 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. || work period || Take up questions from electric forces - explain how a balloon sticking to a wall involves all three methods of transfer of charge. Introduce problem # 7 from p 583 - 2 charged spheres connected by string Hand back summative #2 and introduce summatives 3 and 4 || [|summative # 3 - collisions] || We will meet in the commons so that you can start a bit early or end a bit later. ||  || 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: - 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. || 2 different formulas for the magnitude of the electric field around an object
 * Apr 25 || Mr Guetter is gone today - and so are a number of you. Today's assignment is posted in the homework column.
 * Apr 28 || Last review for tomorrow's test
 * April 29 || Test on Collisions - impulse, momentum and energy - whole class.
 * Apr 30 || Review of electric forces and introduction to electric fields

take up p 583 # 7 new: p 591 # 1-5 p 612 # 13,14,15,17 || It is one of the [|top ten physics discoveries] of all time. and a [|demo of the experiment] || - a written assignment or presentation to the class - your choice
 * May 1 || Discussion of Millikan's oil drop experiment to determine the charge on the electron - handout and [|demo]

|| 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; - 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) Why are parallel plates important in this unit? applications - picture tubes (CRT), pollution control (ESP) || p 586 # 1,2 p 591 # 6 p 612 # 15,17,18 - already assigned the first two || with data from the sample problem. Once you have a solution, ask to check your answer. I would share it but I don't know how to prevent you from deleting all my formulas. Calculations of Force and Field strength with point charges and with parallel plates || Application problems for parallel plates p 612 # 28-31, 36,38 for # 36, use d = 25 cm between plates || 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) || part 2 - voltage is 100V P 612 35, 41 || Test next Thursday - May 15 - on Electric Forces and Fields || note: the proton-electron problem should have a distance of 0.12 m, not 5.1 m || - industrial scrubbers, copiers, medical diagnostics - to the explosives detection industry [|background] and video of the [|ADE-651] - update - the inventor of the ADE-651 is in prison - April 2013 hints for today's homework the length of the plates = 1.25 x 10-⁹ sec; and we get an answer of .0041 m deflection ||  || 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. || || for light, we refer to the differences in "optical density" 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. || Problems from p 529 || Demonstration of the experiment - we used a laser, which Young did not have access to (almost 200 yrs ago). 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) Review of Young's experiment - here's a good resource: [] 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 || HW problems from p 612 || - 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 Applications of "light as a wave" - CD/DVD storage - use light to encode and read zeros and ones - Holograms - take a picture of the interference of light rather than just the light from the object ||  || - 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 5 || Comparison of the force on a charged particle in two different situations:
 * May 6 || I've completed an answer [|checking spreadsheet for summative #3] - I have filled in the first row
 * May 7 || Intro to electric potential energy - regions of higher and lower PE. Calculation of PE
 * May 8 || Motion of charged particles in an electric field - handout based on yesterday's work.
 * May 9 || Review of motion of charged particles and two quizzes - you must do at least one to earn points
 * May 12 || Application of electrostatics and electric fields:
 * 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
 * May 13 || Introductory lecture on Modern Physics - a survey of some of the key moments in the last 150 (or so) years of physics:
 * May 14 || Thomas Young - Review of refraction and diffraction (from grade 11) refraction is the bending of waves as they pass from one material to another;
 * May 15 || **Test - electric forces and fields - whole class** ||  ||
 * May 16 || Take up questions from p 529 - remember to divide the distance from the centre to the specific fringe by the number of fringes.
 * May 20 || Michelson-Morley Experiment - on a test or exam, you should be able to:
 * May 21 || Intro to Quantum Physics and the Photoelectric Effect

p 705 # 1-5 p 728 # 15,20,21 || 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? || p 728 # 22-25 ||
 * May 23 || Today's work consists of two questions:
 * May 26 || 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 tomorrow || 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.
 * May 27 || 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.

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: - 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). || || Relationship between the calculations done in double-slit problems and the calculations for emission spectra - same formula for both 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 Applications of atomic energy levels - good topics for summative # 4 - lasers, //aurora borealis//,
 * May 28 || Review of energy levels in atoms.

Introduction to Einstein's Special Theory of Relativity - state the two postulates of Einstein's special theory of relativity - explain the difference between an inertial and a non-inertial reference frame - normally we add velocities, like vectors; how does this change in relativity? - what does relativity predict about mass, length and time as the speed of an object increases?

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 || || The Secrets of the Universe - Neil Turok - these will be the basis for a final exam question
 * May 29 || Truth and Beauty in Physics - Murray Gell-Mann

"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? || [|Article by Turok] [|TED talk by Gell-Mann] || Handout with derivation of the Paradoxes that arise because of Relativity - the pole and the barn; the traveling twins Problem solving with relativity - Lorentz Transformations, mass-energy equivalence || Relativity handout - problems 13-26 remember that time slows down but the length of a second increases. || Much of the work we have done is conceptual, which requires explanation, rather than calculation - double slit, Michelson-Morley, photoelectric effect Of course, there will be calculations on Young's experiment, work function of atom, quantum calculations, and relativity ||  || a 100 kg object moves E at 20 m/s and has a collision with a 200 kg object moving N at 25 m/s the objects take separate paths after the collision the 100 kg object's velocity is 23 m/s at 15 degrees (from N) determine the velocity of the 200 kg object - you will use conservation of momentum for this do a calculation to determine whether or not KE is conserved - it is NOT ||  ||
 * May 30 || Review of the postulates of relativity - []
 * June 2 || Review for test on modern physics - light, quantum physics, relativity
 * June 3 || Unit test on modern physics - 20 multiple choice questions, 3 or 4 problems (double slit, photoelectric effect, quantum energy levels, relativity) ||  ||
 * June 4 || course review and summative #4 presentations ||  ||
 * June 5 || course review and summative #4 presentations ||  ||
 * June 6 || Exam Problem: collisions
 * June 9 || Final exam for this class - Monday June 9, 12:15 - 2:45 pm. ||  ||
 * June 10 || No class today ||  ||