PSL201Y1 Chapter 5: chapter 5

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23 Oct 2011

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Chapter five sensation read monsters from the forest on pg. Our senses are the way we experience the world. Everything we learn is detected by sense organs and transmitted to our brains by sensory nerves. Without sensory input our brains would be useless, would learn nothing, no thoughts, no experiences. Sense organs & sensory nerves evolved to provide us with useful information about external world: evolving depends on specific modality of info, characteristics of info and state of brain when it receives the info. Differences between sources of info in the environment, have important results for the way in which sensory systems process that information. Example: difference between the world as we see it and hear it: visual scene received by our eyes changes fast because we move our body, our head, and our eyes. Senses contribute to the richness of our experience changes are more gradual than the visual system. Audition is extremely important for social behaviour.

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Situations arise in engineering when we want to control the flow rate of a solution. This solution could be pumped into a holding tank, distillation column, heat exchanger, reactor, etc. This means that the flow rate becomes a function of time. When we turn on a pump, the flow rate is (for the most part) constant. The problem is that we may want the flow rate to be very fast at first, and then very slow towards the end of the process. This is especially true in certain chemical reactors where the concentration of reactants is always important. Control systems that could handle this type of situation are very expensive. Pumps (relatively speaking) are cheap. So, having a bank of pumps will usually solve the problem. The pumps are simply turned on or off to regulate the flow. Mathematically, this amounts to taking the volumetric flow rate function and finding a piecewise-linear approximation. Suppose that, because of the application we are running, we need a flow rate given by the function ,where t is in hours and v(t) is in 100 cubic feet per hour (e.g., v(0)=1 which means that at time t=0, we need a flow rate of 1*100=100 cubic feet per hour). Find a linear approximation and a piecewise-linear approximation using first two lines and then three lines. Think about what using more lines would do to the approximation. You will need to find suitable values of t to be able to find your approximation. As a further exercise, try to find values of t for your approximation that keeps the error (i.e., the difference between the approximation and the real function v(t) ) less than 0.1.Hint: to help with this, ask yourself this question: where would more lines be useful - where the function changes a lot or where the function changes a little?]

DUE DATE: 12 00 noon Monday. Dec 6. 2010. The problems on this assignment are quite word because strong direction is being given to Students in how to proceed. Two problems will be selected at random for marking. Percentage polarization. It is useful to characterize partially polarized light in terms of its "percentage polarization". A light beam of constant intensity Io. is allowed to fall at normal incidence on an "ideal linear polarizer" (a linear polarizer is "ideal" if it panes all light polarized parallel to the polarizer's axis, and stops all light polarized perpendicular to that axis.) As the ideal polarizer is rotated continuously (see Figure 8.1; about an axis perpendicular to its plane, the transmitted intensity I passes through successive maximum and minimum values (denoted by I max and I min). The percentage polarization of the incident light is denned to be Find the percentage polarization measured in this way for the following light beams: "Unpolarized natural light" tor which I max = I min = Io/2. A beam of light. Initially unpolarixed. that has been passed through an ideal linear polarizer before being measured for percentage polarization. A beam of light, initially unpolarizcd, that has been passed through a non-ideal polarizer that (in terms of light intensity) transmits 70% of light polarized parallel to its polarizing axis and 20% of light polarized perpendicular to its polarizing axis. Circularly polarized light. (Circular polarization means that at any given fixed observation point In the beam, the E-vector has constant magnitude but rotates at the frequency of the electric field oscillations so that the tip of the vector describes a circle in the zy plane (perpendicular to the light ray at the point in question). Elliptically polarized light for which the tip of the E-vector moves on an ellipse in the x y plane, defined by where Ax and Ay are the amplitudes of the oscillating Ex and E y components of the electric field vector, and is the phase difference between those oscillations. NOTE: Do your calculation for the special case Ax = 2Ay and e =pi / 2. [(8.2) taxes a particularly simple form when e = pi / 2.]

PSL201Y1 Chapter 5: chapter 5

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