ch01 solutions

ch01 solutions - CHAPTER 1 INTRODUCTION AND MATHEMATICAL...

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CHAPTER 1 INTRODUCTION AND MATHEMATICAL CONCEPTS CONCEPTUAL QUESTIONS ____________________________________________________________________________________________ 1. REASONING AND SOLUTION The quantity tan θ is dimensionless and has no units. The units of the ratio x/v are m (m / s) m s m s = F H G I K J = Thus, the units on the left side of the equation are not consistent with those on the right side, and the equation tan = x / v is not a possible relationship between the variables x , v , and . ____________________________________________________________________________________________ 2. SSM REASONING AND SOLUTION It is not always possible to add two numbers that have the same dimensions. In order to add any two physical quantities they must be expressed in the same units . Consider the two lengths: 1.00 m and 1.00 cm. Both quantities are lengths and, therefore, have the dimension [L]. Since the units are different, however, these two numbers cannot be added. ____________________________________________________________________________________________ 3. REASONING AND SOLUTION a. The SI unit for x is m. The SI units for the quantity vt are m s (s) = m m s (s) m F H G I K J = Therefore, the units on the left hand side of the equation are consistent with the units on the right hand side. b. As described in part a , the SI units for the quantities x and vt are both m. The SI units for the quantity 1 2 at 2 are m s (s ) m 2 2 F H G I K J = Therefore, the units on the left hand side of the equation are consistent with the units on the right hand side. c. The SI unit for v is m/s. The SI unit for the quantity at is m s (s) m s 2 F H G I K J =
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2 INTRODUCTION AND MATHEMATICAL CONCEPTS Therefore, the units on the left hand side of the equation are consistent with the units on the right hand side. d. As described in part c , the SI units of the quantities v and at are both m/s. The SI unit of the quantity 1 2 at 3 is m s (s ) m s 2 3 F H G I K J =⋅ Thus, the units on the left hand side are not consistent with the units on the right hand side. In fact, the right hand side is not a valid operation because it is not possible to add physical quantities that have different units. e. The SI unit for the quantity v 3 is m 3 /s 3 . The SI unit for the quantity 2 ax 2 is m s (m ) m s 2 2 3 2 F H G I K J = Therefore, the units on the left hand side of the equation are not consistent with the units on the right hand side. f. The SI unit for the quantity t is s. The SI unit for the quantity 2 x a is m (m / s ) m s m ss 2 2 2 = F H G I K J == Therefore, the units on the left hand side of the equation are consistent with the units on the right hand side. ____________________________________________________________________________________________ 4. REASONING AND SOLUTION a. The dimension of a physical quantity describes the physical nature of the quantity and the kind of unit that is used to express the quantity. It is possible for two quantities to have the same dimensions but different units. All lengths, for example, have the dimension [L]. However, a length may be expressed in any length unit, such as kilometers, meters, centimeters, millimeters, inches, feet or yards.
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This note was uploaded on 05/09/2008 for the course PHYS 23 taught by Professor Holland during the Spring '08 term at Pacific.

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ch01 solutions - CHAPTER 1 INTRODUCTION AND MATHEMATICAL...

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