College Physics
10th Edition
ISBN: 9781285737027
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Textbook Question
Chapter 1, Problem 13CQ
Answer each question yes or no. Must two quantities have the same dimensions (a) if you are adding them? (b) If you are multiplying them? (c) If you are subtracting them? (d) If you are dividing them? (e) If you are equating them?
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Chapter 1 Solutions
College Physics
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One student uses a meterstick to measure the thickness of a textbook and obtains 4.3 cm 0.1 cm. Other students measure the thickness with vernier calipers and obtain four different measurements: (a) 4.32 cm 0.01 cm. (b) 4.31 cm 0.01 cm, (c) 4.24 cm 0.01 cm, and (d) 4.43 cm 0.01 cm. Which of these four measurements, if any, agree with that obtained by the first student?
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Consider the physical quantities m,s,v,a, and t with dimensions [m]=M,[s]=L,[v]=LT1 and [a]=LT2 . Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: (a)F=ma;(b)K=0.5mv2;(c)p=mv;(d)W=mas;(e)L=mvr
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In general, when a derived unit becomes complicated (involves too many standard units), what is done?
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Answer each question yes or no. Must two quantities have the same dimensions (a) if you are adding them? (b) If you are multiplying them? (c) If you are subtracting them? (d) If you are dividing them? (e) If you are equating them?
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The Hoover Dam Bridge connecting Arizona and Nevada opened in October 2010 ( Fig. 1.18). It is the highest and longest arched concrete bridge in the Western Hemisphere, rising 890 ft above the Colorado River and extending 1900 ft in length. What are these dimensions in meters? Figure 1.18 High and Wide An aerial view of the new four-lane Hoover Dam Bridge between Arizona and Nevada with the Colorado River beneath (as seen from behind the dam). See Exercise 16.
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Use the rules for significant figures to find the answer to the addition problem 21.4 + 15 + 17.17 + 4.003. (See Section 1.4).
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The purpose of this problem is to show the entire concept of dimensional consistency can be summarized but the old saying “You can’t add apples and oranges.” It you have studied power series expansions in a calculus course, you know the standard mathematical funstions such as trigonometric functions, logarithms, and exponential function can be expressed as infinite sums of the form where the an are dimensionless constants for all n = 0, 1, 2, … and x is the argument of the function. (If you have not studied power series in calculus yet, just trust us.) Use this fact to explain why the requirement that all terms in an equation have the same dimensions is sufficient as a definition of dimensional consistency. That is, it actually implies the arguments of standard mathematical funstions must be dimensional consistency. That is, it actually implies the arguments of standard mathematical functions must be dimensionless, so it is not really necessary to make this latter condition a separate requirement of the definition of dimensional consistency as we have done in this section.
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How many significant figures does each number have? If the number is exact or if the number of significant figures is ambiguous, explain. a. 12 in the formula r12d, where r is radius and d is diameter b. 105 c. 150 d. 1.50 102 e. 1.5 102 f. 0.15 103
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