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Carry out these conversions: (a) A 6.0-ft person weighs 168 lb. Express this person's height in meters and weight in kilograms. \((1 \mathrm{lb}=453.6 \mathrm{~g} ; 1 \mathrm{~m}=\) \(3.28 \mathrm{ft} .\) ) (b) The current speed limit in some states in the United States is 55 miles per hour. What is the speed limit in kilometers per hour? (c) The speed of light is \(3.0 \times 10^{10} \mathrm{~cm} / \mathrm{s} .\) How many miles does light travel in 1 hour? (d) Lead is a toxic substance. The "normal" lead content in human blood is about 0.40 part per million (that is, \(0.40 \mathrm{~g}\) of lead per million grams of blood). A value of 0.80 part per million (ppm) is considered to be dangerous. How many grams of lead are contained in \(6.0 \times 10^{3} \mathrm{~g}\) of blood (the amount in an average adult) if the lead content is \(0.62 \mathrm{ppm} ?\)

Short Answer

Expert verified
(a) 1.83 m, 76.06 kg. (b) 88.51 km/h. (c) 6.71 脳 10鈦 miles/hour. (d) 0.00372 g lead.

Step by step solution

01

Converting Height to Meters

To convert the height from feet to meters, use the conversion factor: \ \[ 1 ext{ m} = 3.28 ext{ ft} \]. Calculate the height: \[ ext{Height in meters} = \frac{6.0 ext{ ft}}{3.28 ext{ ft/m}} = 1.83 ext{ m} \]
02

Converting Weight to Kilograms

To convert the weight from pounds to kilograms, use the conversion factor: \[ 1 ext{ lb} = 453.6 ext{ g} \]. First, convert pounds to grams and then to kilograms: \[ ext{Weight in grams} = 168 ext{ lb} \times 453.6 ext{ g/lb} = 76060.8 ext{ g} \] \[ ext{Weight in kilograms} = \frac{76060.8 ext{ g}}{1000 ext{ g/kg}} = 76.06 ext{ kg} \]
03

Converting Speed to Kilometers per Hour

To convert miles per hour to kilometers per hour, use the conversion factor: \[ 1 ext{ mile} = 1.60934 ext{ km} \]. Calculate the speed limit: \[ 55 ext{ mph} \times 1.60934 ext{ km/mile} = 88.51 ext{ km/h} \]
04

Converting Light Speed to Miles per Hour

First, convert centimeters per second to meters per second: \[ 3.0 \times 10^{10} ext{ cm/s} = 3.0 \times 10^{8} ext{ m/s} \] Next, convert meters per second to miles per hour, using the conversion factors: \[ 1 ext{ mile} = 1609.34 ext{ m} \] \[ 1 ext{ hour} = 3600 ext{ seconds} \]. Calculate: \[ 3.0 \times 10^{8} \text{ m/s} \times \frac{1 \text{ mile}}{1609.34 \text{ m}} \times 3600 \text{ s/h} = 6.71 \times 10^8 \text{ miles/h} \]
05

Calculating Lead Content in Blood

To find the grams of lead in the blood, use the given ppm value: A ppm means \(0.62 \text{ g of lead per } 10^6 \text{ g of blood}\). Calculate the lead content: \[ \text{Lead in grams} = 6.0 \times 10^{3} \text{ g blood} \times \frac{0.62 \text{ g lead}}{10^6 \text{ g blood}} = 0.00372 \text{ g lead} \]

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Key Concepts

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

Length Conversion
Understanding length conversion is essential, especially when dealing with measurements in different units like feet and meters. In this context, converting height from feet to meters requires an understanding of the conversion factor: \[ 1 \text{ m} = 3.28 \text{ ft} \]. This tells us that for every meter, there are approximately 3.28 feet. To convert a height measured in feet to meters, you divide the number of feet by 3.28.
For example, a person who is 6.0 ft tall would have their height calculated in meters as follows:
  • Divide 6 feet by 3.28 to get approximately 1.83 meters.
This process helps in understanding metrics that are universally accepted, like meters, especially in scientific contexts or when traveling internationally.
Weight Conversion
When converting weight from pounds to kilograms, it's important to know that 1 pound is equivalent to 453.6 grams. This conversion factors allows you to shift between standard units used in different regions of the world.
To perform a conversion from pounds to kilograms, you first convert pounds to grams, then grams to kilograms.
  • Multiply the weight in pounds (e.g., 168 lb) by 453.6 to get grams.
  • Then, convert grams to kilograms by dividing by 1,000.
  • For the exercise, this gives you:
    • 168 lb * 453.6 g/lb = 76060.8 g
    • 76060.8 g / 1000 = 76.06 kg
This method helps you understand the relationship between different weight measures and facilitates ease in conversions.
Speed Conversion
Speed conversion is necessary when translating speeds familiar in one country to another's conventions. As a case study, let's take the United States speed limit of 55 miles per hour (mph) and convert it to kilometers per hour (km/h) using the conversion \[ 1 \text{ mile} = 1.60934 \text{ km} \].
The conversion process involves simply multiplying the speed in miles per hour by the kilometers conversion factor.
  • For a speed of 55 mph, the conversion to km/h would be:
    • 55 mph * 1.60934 km/mile = 88.51 km/h
This helps in understanding road signs when traveling internationally or collaborating in global projects where metric units are used.
Density Calculation
Density calculations, such as determining the concentration of substances in a mixture, play critical roles in fields like chemistry and biology. In the given problem, we're calculating the amount of lead in blood using parts per million (ppm), where 0.62 ppm means 0.62 grams of lead per one million grams of blood.
To calculate the grams of lead in a specific amount of blood:
  • Multiply the total grams of blood by the fraction of lead in ppm.
  • For 6,000 grams of blood with a lead concentration of 0.62 ppm:
    • \[ 6.0 \times 10^{3} \text{ g of blood} \times \frac{0.62 \text{ g lead}}{10^6 \text{ g blood}} = 0.00372 \text{ g lead} \]
Understanding and performing such calculations ensures you can ascertain the concentration of components in various mixtures or solutions.

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Most popular questions from this chapter

A cylindrical glass tube \(12.7 \mathrm{~cm}\) in length is filled with mercury. The mass of mercury needed to fill the tube is found to be \(105.5 \mathrm{~g}\). Calculate the inner diameter of the tube. (The density of mercury \(=\) \(13.6 \mathrm{~g} / \mathrm{mL} .)\)

Express these numbers in scientific notation: (a) 0.000000027 , (b) \(356,\) (c) 0.096 .

Dinosaurs dominated life on Earth for millions of years and then disappeared very suddenly. In the experimentation and data-collecting stage, paleontologists studied fossils and skeletons found in rocks in various layers of Earth's crust. Their findings enabled them to map out which species existed on Earth during specific geologic periods. They also revealed no dinosaur skeletons in rocks formed immediately after the Cretaceous period, which dates back some 65 million years. It is therefore assumed that the dinosaurs became extinct about 65 million years ago. Among the many hypotheses put forward to account for their disappearance were disruptions of the food chain and a dramatic change in climate caused by violent volcanic eruptions. However, there was no convincing evidence for any one hypothesis until 1977\. It was then that a group of paleontologists working in Italy obtained some very puzzling data at a site near Gubbio. The chemical analysis of a layer of clay deposited above sediments formed during the Cretaceous period (and therefore a layer that records events occurring after the Cretaceous period) showed a surprisingly high content of the element iridium. Iridium is very rare in Earth's crust but is comparatively abundant in asteroids. This investigation led to the hypothesis that the extinction of dinosaurs occurred as follows. To account for the quantity of iridium found, scientists suggested that a large asteroid several miles in diameter hit Earth about the time the dinosaurs disappeared. The impact of the asteroid on Earth's surface must have been so tremendous that it literally vaporized a large quantity of surrounding rocks, soils, and other objects. The resulting dust and debris floated through the air and blocked the sunlight for months or perhaps years. Without ample sunlight most plants could not grow, and the fossil record confirms that many types of plants did indeed die out at this time. Consequently, of course, many plant-eating animals gradually perished, and then, in turn, meat-eating animals began to starve. Limitation of food sources obviously affects large animals needing great amounts of food more quickly and more severely than small animals. Therefore, the huge dinosaurs vanished because of lack of food. (a) How does the study of dinosaur extinction illustrate the scientific method? (b) Suggest two ways to test the hypothesis. (c) In your opinion, is it justifiable to refer to the asteroid explanation as the theory of dinosaur extinction? (d) Available evidence suggests that about 20 percent of the asteroid's mass turned to dust and spread uniformly over Earth after eventually settling out of the upper atmosphere. This dust amounted to about \(0.02 \mathrm{~g} / \mathrm{cm}^{2}\) of Earth's surface. The asteroid very likely had a density of about \(2 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate the mass (in kilograms and tons) of the asteroid and its radius in meters, assuming that it was a sphere. (The area of Earth is \(5.1 \times 10^{14} \mathrm{~m}^{2} ; 1 \mathrm{lb}=453.6 \mathrm{~g} .\) ) (Source: Consider a Spherical Cow-A Course in Environmental Problem Solving by J. Harte, University Science Books, Mill Valley, CA, 1988 . Used with permission.

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