Assignment 2 Outline

Comp 1012 winter 2014 assignment 2 page 2 of 9

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Unformatted text preview: ivescience.com/18749- human- brain- cell- number.html], about when will a computer chip have as many transistors as a brain has neurons, if Moore’s Law continues to hold?1 Start with the number of transistors on the Haswell processor in 2013. 1 Brain neurons and computer transistors are not strictly comparable, since a transistor has only three connections, and a neuron can have thousands, but this type of comparison shows the machines are catching up. COMP 1012 Winter 2014 Assignment 2 Page 2 of 9 Question 2—Chain Fence [9 marks] Description A chain or rope suspended at two points hangs in a curve called a catenary; such a chain is sometimes used as a fence, as in Figure 1(a). In this question you will determine the shape when a chain of a given length is suspended between two supports about 2 metres apart, as in Figure 1(b). You will determine what the total force is on a support for various lengths of chain (long chains are heavy and have a significant downward force; shorter chains are taut and pull the supports toward one another). Finally you will find the approximate length of chain that has the minimum total force on each support. Figure 1: Chain Fence. (a) Photo. (b) Diagram for d = 0.98m, h = 1.1m, various chain lengths. Theory Shape of the Catenary The catenary is in the shape of the cosh function.2 If the origin (that is, x = 0) is in the middle between two support posts at ±d, the position of a point (x, y) on the hanging chain is given by the following equation between x and y. (1) = + cosh cosh Here h is the height of the points of support [m], the support posts are located at x = ±d [m], and a is a parameter [m] that determines how low the chain sags, and how long it is. Finding the Length of the Chain for a given...
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