# Comprehension check 7 10 a boat is traveling at 20

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Chapter 7 / Exercise 12
Physics for Scientists and Engineers
Jewett/Serway Expert Verified
Comprehension Check 7-10A boat is traveling at 20 knots. Convert this speed to units of meters per second [m/s]. Conversion factor: 1 knot = 1 nautical mile per hour; 1 nautical mile = 6076 feet [ft].7.6 Derived Dimensions and UnitsLearning Objectives1.Identify a quantity as a fundamental or derived dimension and express the fundamental dimensions of the quantity using fractional or exponential notation2.Given the units of a quantity, determine the fundamental dimensions3.Given the fundamental dimensions of a quantity, determine the base SI unitsWith only the seven base dimensions in the metric system, all measurable things in the known universe can be expressed by various combinations of these concepts, called derived dimensions. As simple examples, area is length squared, volume is length cubed, and velocity is length divided by time.As we explore more complex parameters, the dimensions become more complex. For example, the concept of force is derived from Newton’s second law, which states that force is equal to mass times acceleration. Force is then used to define more complex dimensions such as pressure,which is force acting over an area, or work, which is force acting over a distance. As we introduce new concepts in later chapters, we introduce the dimensions and units for each parameter.Sometimes, the derived dimensions become quite complicated. For example, electrical resistanceis mass times length squared divided by both time cubed and current squared. Particularly in the more complicated cases like this, a derived unitis defined to avoid having to say things like “The resistance is 15 kilogram-meter squared divided by second cubed ampere squared.” It is much easier to say “The resistance is 15 ohms,” where the derived unit “ohm” equals one (kgm2)/(s3A2).Within this text, dimensions are presented in exponential notation rather than fractional notation for written clarity.
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Chapter 7 / Exercise 12
Physics for Scientists and Engineers
Jewett/Serway Expert Verified
One way to determine the dimensions of a quantity, such as volume, is to examine the common units used to express the quantity. While volume can be expressed in gallons, it can also be expressed as cubic feet or cubic meters. The units of cubic meters express volume in a manner easily transferred to dimensions. Remember, the boxes on the inside front cover of the textbook show units that have equivalent dimensions. The units of gallons and of cubic feet and of cubic meters are dimensionally equal to length cubed.Volume a: 1 L=0.264 gala: 1 L=0.0353 fta: 1 L=33.8 fl oza: 1 m3=1000 La: 1 mL=1 cm
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3Example 7-11Determine the fundamental dimensions of the following quantities.Currently, there are officially 22 named derived units in the SI system. All are named after famous scientists or engineers who are deceased. Five of the most common derived units can be found in Table7-5and on the back cover of the textbook. It is worth noting that numerous
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