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Chapter_1_solutions - Chapter 1 Overview Chapter 1 Overview...

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Chapter 1 : Overview 1 Chapter 1: Overview In-Class Exercises 1.1. a 1.2. a) 4 b) 3 c) 5 d) 6 e) 2 1.3. e 1.4. a) 4 th b) 2 nd c) 3 rd d) 1 st Multiple-Choice 1.1. c 1.2. c 1.3. d 1.4. b 1.5. a 1.6. b 1.7. b 1.8. c 1.9. c 1.10. b Questions 1.11. (a) In Europe, gas consumption is in L/100 km. In the US, fuel efficiency is in miles/gallon. Let’s relate these two: 1 mile = 1.609 km, 1 gal = 3.785 L. Therefore, is the reciprocal of (b) Gas consumption is . Using from part (a), Therefore, a car that consumes of gasoline has a fuel efficiency of 19.3 miles/gal. (c) If the fuel efficiency of the car is 27.4 miles per gallon, then = Therefore, 27.4 miles/gal is equivalent to 8.59 L/100 km. (d) 1.12. A vector is described by a set of components in a given coordinate system, where the components are the projections of the vector onto each coordinate axis. Therefore, on a two-dimensional sheet of paper there are two coordinates and thus, the vector is described by two components. In the real three-dimensional world, there are three coordinates and a vector is described by three components. A four-dimensional world would be described by four coordinates, and a vector would be described by four components. 1.13. A vector contains information about the distance between two points (the magnitude of the vector). In contrast to a scalar, it also contains information direction. In many cases knowing a direction can be as important as knowing a magnitude. 1.14. In order to add vectors in magnitude-direction form, each vector is expressed in terms of component vectors which lie along the coordinate axes. The corresponding components of each vector are added to
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Bauer/Westfall: University Physics, 1E 2 obtain the components of the resultant vector. The resultant vector can then be expressed in magnitude- direction form by computing its magnitude and direction. 1.15. The advantage to using scientific notation is two-fold: Scientific notation is more compact (thus saving space and writing), and it also gives a more intuitive way of dealing with significant figures since you can only write the necessary significant figures and extraneous zeroes are kept in the exponent of the base. 1.16. The SI system of units is the preferred system of measurement due to its ease of use and clarity. The SI system is a metric system generally based on multiples of 10, and consisting of a set of standard measurement units to describe the physical world. In science, it is paramount to communicate results in the clearest and most widely understood manner. Since the SI system is internationally recognized, and its definitions are unambiguous, it is used by scientists around the world, including those in the United States. 1.17. It is possible to add three equal-length vectors and obtain a vector sum of zero. The vector components of the three vectors must all add to zero. Consider the following arrangement with : The horizontal components of and cancel out, so the sum is a vertical vector whose magnitude is . The vector sum is zero if Therefore it is possible for three equal-length vectors to sum to zero.
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