Weekly homework

The current week is identified below by the pointer which advances at 4pm each Wednesday. Until then, the topics and problems mentioned below the pointer are only an approximate plan that may change, reflecting what happens in class. Readings (particular sections of the textbook) are not explicitly assigned; use the problems assigned as the guide as to what sections are being covered this week.

All homework is available to you through masteringphysics.com, an online tool. Use your Brock ID/email and the code included with the hardcopy of the textbook to register for either "FW2011D2PHYS1P23" or "FW2011D2PHYS1P93", as appropriate. If you do not enter your ID correctly, you will not get the credit for the homework - we have no way of fixing that.

Week 0. Introduction to Mastering Physics

Learning objectives: learn the MasteringPhysics interface: entering your answers in the form MP recognizes correctly; interpreting MP's responses; making use of Hints; the best ways to deal with MP.

Week 1. Bulk properties of matter.

Learning objectives: establish comfort with elementary algebraic manipulations (moving a factor from one side of an equation to another; expressing any unknown in terms of other knowns; recognizing the nature of the dependence on a particular factor and, therefore, on how the answer scales with changes in this factor); understand how the material's property - e.g., Young's modulus- translates into a particular response in a given piece of this material under a given force; how density changes - or not - as the dimensions of an object are scaled, etc.

Week 2. Hydrostatics

Learning objectives: recognize and relate bulk properties (density, pressure) to external characteristics of bodies (size, shape, external forces); hydraulics as an expression of conservation of mass; gravitational origin of buoyancy.

Week 3. Hydrodynamics. Viscosity. Reynolds' number.

Learning objectives: achieve comfort with the two important relations of hydrodynamics, the continuity equation (conservation of mass) and the Bernoulli's equation (conservation of energy). Reinforce the skill of translating a word problem into mathematical language, manipulating and solving the equations that arise, and translating the results back into words that describe the effect in question. Observe an unusually strong (r⁴) dependence of flow rate on the size of the pipe carrying the viscous fluid. Become aware of the role the Reynolds' number plays in relating physical phenomena vastly different in scope.

Week 4. Heat and temperature. Thermal expansion.

• From last week's material: Read Life at low Reynolds' number, by E.M.Purcell

Learning objectives: establish intuitive and calculational skills in the analysis of simple thermal problems: thermal expansion in 1D, 2D, and 3D; relationship between absorbtion of heat and a change in temperature; zeroth law of thermodynamics.

Week 5. Calorimetry. Phase changes. Heat transfer.

• Midterm: Thursday, Oct. 13, in class

  All of the material covered in weeks 1 through 5 is fair game. Formula sheets will be provided, do not bring any paper into the class, only pens and calculators. No dictionaries or electronic translators. To prepare for the midterm, you may want to review last year's midterm A and midterm B.

Learning objectives: accounting for a variety of calorimetric events as heat is added, taken away, or exchanged between bodies. Calorimetric calculations, especially when accompanied by a phase change, can get tricky. Identifying the mechanisms of heat transfer and deciding which is the dominant one.

Week 6. The ideal gas.

Learning objectives: pV and similar diagrams are a powerful tool summarizing the behaviour of the ideal gas under a variety of conditions, need to learn how to read them; "temperature is a measure of thermal energy" is a statement/definition that has immediate calculational consequences in terms of the kinetic properties of atoms/molecules.

Week 7. Laws of thermodynamics. Kinetic theory, heat engines, entropy.

• Read and understand this description of how a Stirling engine operates.

Learning objectives: to reconcile the top-down, thermal physics view with the bottom-up, kinetic theory and statistical mechanics view; to recognize how fundamental conservation laws are reflected in the more calculationally useful quantities like thermal engine efficiency; to learn how combining different types of thermodynamic processes allows one to construct cyclical thermal engines.

This week's challenge: build a simple Stirling engine, similar to the "soda-can Stirling engine".

Week 8. Simple Harmonic Oscillator. Waves and sound.

Learning objectives: relate the physical intuition into the SHO motion to its mathematical description; recognize and use descriptors of SHO such as amplitude, frequency, period, etc; interpret and make use the kinematic equations describing SHO and the applications of energy conservation; become comfortable with scaling arguments (ratios) in the qualitative analysis of oscillations; visualizing the traveling waves; relating wave equation to both the snapshots of the displacement at a certain moment in time, and to time traces of displacement at a certain position in space;

Week 9. Waves and sound, continued.

• Prove that the sum of two identical waves traveling in opposite direction generate a standing wave.
• Use the applet shown in class to develop intuition of what happens when you add two waves.

Learning objectives: how wave addition leads to standing waves (in space, string or wind instruments), or beats (in time, two tuning forks); and in reverse, how to extract mathematical representation of the wave (wavelength, period, etc.) from the graphical representations of the wave; relating the energy emitted at the source to the energy delivered to a location some distance away; logarithmic representation of intensity through the corresponding intensity level; conversions between the two ways of representing wave intensity, under the conditions of multiple waves adding up.

Week 10. The Doppler effect. Light as an EM wave: the spectrum of EM waves, polarization.

Learning objectives: Detecting the motion of the source, the observer, or both simultaneously through the shifts of perceived frequency, relative to the emitted one. Basic characteristics of electro-magnetic (e.m.) waves. Polarization is a wave phenomenon, crossing of polarizers, Malus' law, average $$\overline{\cos^2 x} = 1/2$$.

Week 11. Light interference and diffraction. Light in media.

• Print out (single-sided, to leave room for your own notes) and bring to class the notes on ray optics.

Learning objectives: just like polarization, interference and diffraction are wave phenomena, must learn to describe them both qualitatively (bright and dark fringes) and quantitatively (Young's two-slit interference pattern).

Week 12. Reflection and refraction of light. Snell's Law. Spherical lenses and mirrors.

• As appropriate, make use of the applets shown in class: ,

Learning objectives: making careful (ruler and sharp pencil, to scale) drawings of rays help solve many reflection and refraction problems; plain mirror produces an image that is located symmetrically to the object, but on the other side of the plane of the mirror, and the rays appear to come to the oberver as if from that point; refractive index is a measure of the speed of light in the medium, and a boundary between materials of two different refractive indices is where the rays undergo reflection and refraction; Snell's law and elementary geometrical considerations (definitions oif sin/cos/tan, properties of similar triangles, etc.) combine to give excellent numerical tools in ray tracing problems; for small angles, sin(x) and tan(x) can be approximated by x (in radians) itself. For spherical lenses and mirrors, too, sharp-pencil to-scale drawings are more than half the work, with the algebraic relationship (1/d_o+1/d_i=1/f) simply providing a numerical refinement of the graphical solution; while the algebra is simple, keeping straight the sign conventions for various distances is not; keep in mind that mirrors reflect while lenses transmit light to the other side, so the attribution of "real"/"virtual" (+ve/-ve) is different for lenses and mirrors; always check the numerical answer against your careful drawing.

Week 13. The Scientific Method.

The Final Exam

To prepare for the final exam, you may want to review the 2010 final in PHYS 1P23/93 and this year's weekly tutorial problems and midterm(s).

In 2009-10 there was a major revision of the content of our Y1 courses, so exams prior to 2010 may not be appropriate. They have been removed from the library reserve.