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Chapter 1: Problem 30

The average density of Earth is \(5.52 \mathrm{~g} / \mathrm{cm}^{3}\). What is its density in (a) \(\mathrm{kg} / \mathrm{m}^{3} ;\) (b) \(\mathrm{lb} / \mathrm{ft}^{3}\) ?

Short Answer

Expert verified
The density of Earth is 5520 办驳/尘鲁 and 344.61 濒产/蹿迟鲁.

Step by step solution

01

- Understand the Given Data

The given average density of Earth is 5.52 驳/肠尘鲁. This needs to be converted into two different units: 办驳/尘鲁 and 濒产/蹿迟鲁.
02

- Convert 驳/肠尘鲁 to 办驳/尘鲁

First, we convert 5.52 驳/肠尘鲁 to 办驳/尘鲁. We know that 1 驳/肠尘鲁 = 1000 办驳/尘鲁. Therefore, we multiply the given density by 1000:odensity = 5.52 驳/肠尘鲁 脳 1000 (办驳/尘鲁 per 驳/肠尘鲁) = 5520 办驳/尘鲁.
03

- Convert 驳/肠尘鲁 to 濒产/蹿迟鲁

Next, we convert 5.52 驳/肠尘鲁 to 濒产/蹿迟鲁. Using the conversion 1 驳/肠尘鲁 = 62.428 濒产/蹿迟鲁, we multiply the given density by 62.428:density = 5.52 驳/肠尘鲁 脳 62.428 (濒产/蹿迟鲁 per 驳/肠尘鲁) 鈮� 344.61 濒产/蹿迟鲁.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

unit conversion
In science and engineering, unit conversion is essential because it allows us to express measurements in different units. These conversions are necessary when working with various engineering applications and scientific data.
Unit conversion involves knowing the relationship between different units and applying this relationship through multiplication or division.
  • In our problem, we are converting the Earth's density from 驳/肠尘鲁 to 办驳/尘鲁 and 濒产/蹿迟鲁.
  • 1 驳/肠尘鲁 can be converted to 办驳/尘鲁 by recognizing that there are 1000 g in a kg and 1,000,000 cm鲁 in a m鲁. So, 1 驳/肠尘鲁 equals 1000 办驳/尘鲁.
  • For converting 驳/肠尘鲁 to 濒产/蹿迟鲁, we use the conversion factor 1 驳/肠尘鲁 = 62.428 濒产/蹿迟鲁.
Understanding these relationships and conversion factors is critical in making accurate and meaningful conversions.
density calculation
Density is a fundamental concept in physics and engineering, describing how much mass is contained in a given volume. It is generally expressed as mass per unit volume: \(\rho = \frac{m}{V}\), where \(\rho\) is density, \(m\) is mass, and \(V\) is volume.
In our exercise, we use the given density of the Earth in 驳/肠尘鲁 and convert it to different units of measurement.
  • A crucial step is understanding the conversion factors between these units.
  • First, we converted the density from 驳/肠尘鲁 to 办驳/尘鲁: 5.52 驳/肠尘鲁 脳 1000 办驳/尘鲁 per 驳/肠尘鲁 = 5520 办驳/尘鲁.
  • Next, we converted the density into 濒产/蹿迟鲁 using the factor 1 驳/肠尘鲁 = 62.428 濒产/蹿迟鲁: 5.52 驳/肠尘鲁 脳 62.428 濒产/蹿迟鲁 per 驳/肠尘鲁 鈮� 344.61 濒产/蹿迟鲁.
These density conversions help in comparing and using the density value in multiple settings and units.
measurement units
Measurement units are standardized quantities used to specify the size, length, or amount of something. Understanding different measurement units and their conversions is essential in science and daily life.
Commonly used density units in our problem include:
  • 驳/肠尘鲁 (grams per cubic centimeter) - used for small objects and in scientific settings.
  • 办驳/尘鲁 (kilograms per cubic meter) - more common in engineering and for larger scales.
  • 濒产/蹿迟鲁 (pounds per cubic foot) - often used in the U.S. customary system for practical applications.
Knowing how to convert between these units helps in avoiding errors in measurement and ensuring consistent results across various applications.

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Most popular questions from this chapter

Which procedure(s) decrease(s) the random error of a measurement: (1) taking the average of more measurements; (2) calibrating the instrument; (3) taking fewer measurements? Explain.

Carry out the following calculations, making sure that your answer has the correct number of significant figures: (a) \(\frac{2.795 \mathrm{~m} \times 3.10 \mathrm{~m}}{6.48 \mathrm{~m}}\) (b) \(V=\frac{4}{3} \pi r^{3},\) where \(r=17.282 \mathrm{~mm}\) (c) \(1.110 \mathrm{~cm}+17.3 \mathrm{~cm}+108.2 \mathrm{~cm}+316 \mathrm{~cm}\)

Carry out the following calculations, making sure that your answer has the correct number of significant figures: (a) \(\frac{2.420 \mathrm{~g}+15.6 \mathrm{~g}}{4.8 \mathrm{~g}}\) (b) \(\frac{7.87 \mathrm{~mL}}{16.1 \mathrm{~mL}-8.44 \mathrm{~mL}}\) (c) \(V=\pi r^{2} h,\) where \(r=6.23 \mathrm{~cm}\) and \(h=4.630 \mathrm{~cm}\)

Underline the significant zeros in the following numbers: (d) \(4.0100 \times 10^{4}\) (a) \(0.41 ;\) (b) \(0.041 ;\) (c) 0.0410

The area of a telescope lens is \(7903 \mathrm{~mm}^{2}\). (a) What is the area in square feet \(\left(\mathrm{ft}^{2}\right) ?\) (b) If it takes a technician \(45 \mathrm{~s}\) to polish \(135 \mathrm{~mm}^{2},\) how long does it take her to polish the entire lens?
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