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ch01-units-and-vectors(2) - MasteringPhysics 1:09 AM Print...

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10/13/08 1:09 AM MasteringPhysics Page 1 of 10 http://session.masteringphysics.com/myct?productID=22377 [ Print View ] Introductory mechanics Chapter 01 - Units, Physical Quantities, And Vectors Due at 11:59pm on Tuesday, September 9, 2008 View Grading Details Scientific Notation A number written in scientific notation has the form , where and is an integer. Part A Consider the expression . Determine the values of and when the value of this expression is written in scientific notation. Hint A.1 A walk-through Hint not displayed Enter and , separated by commas. ANSWER: , = 5,-2 Vector Components--Review Learning Goal: To introduce you to vectors and the use of sine and cosine for a triangle when resolving components. Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector quantities, resolving vectors into components is the most important skill required in a mechanics course. The figure shows the components of , and , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system's orientation, the key being the angle between the vector and the coordinate axes, often designated . Part A The figure shows the standard way of measuring the angle. is measured to the vector from the x axis, and counterclockwise is positive. Express and in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER: , = In principle, you can determine the components of any vector with these expressions. If lies in one of the other quadrants of the plane, will be an angle larger than 90 degrees (or in radians) and and will have the appropriate signs and values. [ Print ]
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10/13/08 1:09 AM MasteringPhysics Page 2 of 10 http://session.masteringphysics.com/myct?productID=22377 Unfortunately this way of representing , though mathematically correct, leads to equations that must be simplified using trig identities such as and . These must be used to reduce all trig functions present in your equations to either or . Unless you perform this followup step flawlessly, you will fail to recoginze that , and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to express all components in terms of either or , with between 0 and 90 degrees (or 0 and in radians), and determine the signs of the trig functions by knowing in which quadrant the vector lies.
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