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Unformatted text preview: — 1 — Problem. Battery We will insist on the importance of units in engineering applications. Dimensions indicated by numbers depend on the corresponding units: 1 meter = 100 centimeter, but 1 does not equal 100. The number and the unit are inseparable, at least in principle! Writing 1 meter rather than 1 is called ”carrying the unit.” As a general rule, units should be carried in all engineering computations. In working out equations, the units are treated as algebraic quantities. It is best to work out the equations in symbolic form. Each symbol is replaced by its number and unit only at the very end. In addition to being important for applications in the real world, keeping track of units is a powerful way to check that an answer is at least consistent with the expected outcome. Getting the units right does not guarantee that the answer is right, but getting them wrong is a clear indication of difficulty. The units we will use in this problem are Coulombs (the standard unit of charge, denoted C ), Joules (the standard unit of energy, 1 J = 1 kg · m 2 / s 2 ), Amperes (the standard unit of current, 1 A = 1 C / s ), and Volts (the standard unit of potential, 1 V = 1 J / C ). A car battery is charged with a constant current source of I = 20 Amperes. The object is to calculate the amount of energy in Joules stored in the battery after T f = 9 hours if the voltage buildup has the temporal form: V ( t ) = a p t/τ where a = 7 Volt, and where the constant parameter τ = 3 hours....
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This note was uploaded on 10/01/2008 for the course MATH 1910 taught by Professor Berman during the Fall '07 term at Cornell.
- Fall '07