Unit 2B

Unit 2B

Extending Unit Analysis

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17. One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 6 cubic feet of water weigh in pounds? In tons? (Round to two decimal places.)

•  $\frac{6ft^3}{1}$  

•  $\frac{6\ ft^3}{1}\cdot\frac{7.48\ gallons}{1\ ft^3}$  

•  $\frac{6\ ft^3}{1}\cdot\frac{7.48\ gallons}{1\ ft^3}\cdot\frac{8.33\ lbs}{1\ gallon}$  

• = 373.85 lbs

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17. One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 6 cubic feet of water weigh in pounds? In tons? (Round to two decimal places.)

• 373.85 lbs

•  $\frac{373.85\ lbs}{1}\cdot\frac{1\ ton}{2,000\ lbs\ }$ 

•  = 0.19 tons

49. Your utility company charges 13¢ per kilowatt-hour of electricity. What is the daily cost of keeping a 100-watt light bulb lit for 12 hours each day?

• 100 watts = 0.1 kilowatt

• 0.1 kilowatt * 12 hours = 1.2 kw-hr

•  $\frac{1.2\ kw-hr}{1}\cdot\frac{\text{0.13 dollars}}{1\ kw-hr}\$  

• 0.156 or $0.16 for each day

49. Your utility company charges 13¢ per kilowatt-hour of electricity. What is the daily cost of keeping a 100-watt light bulb lit for 12 hours each day? How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light using only 25 watts of power?

• 100 watt costs $0.156 per day. How much does 25 watt cost?

•  $0.025\ kilowatts\ \cdot\ 12\ hours\ \cdot\ 0.13\ dollars\ per\ kw-hr$  = $0.039 per day

• $0.156 - $0.039 = $0.117 savings per day

•  $\frac{0.117\ dollars}{day}\cdot\frac{365\ days}{1\ year}\$ = 42.705 or $42.71 per year

51. A block of oak has a volume of 200 cubic centimeters and weighs 0.12 kilogram. What is its density? Will it float in water?

Convert to grams 0.12 kg = 120 grams.

Find density 120 grams/200 cm^3 = 0.6 g/cm^3

Multiple Choice

51. A block of oak has a volume of 200 cubic centimeters and weighs 0.12 kilogram. What is its density? Will it float in water?

(The density of water is

 $1\frac{gr}{cm^3}$ .) 

• Floater

• Sinker

73. Shower vs. Bath. Assume that when you take a bath, you fill the tub to the halfway point and the tub measures 6 feet by 3 feet by 2.5 feet. When you take a shower, you use a showerhead with a flow rate of 1.75 gallons per minute and you typically spend 10 minutes in the shower. There are 7.5 gallons in one cubic foot.

a. Do you use more water taking a shower or taking a bath?

b. How long would you need to shower in order to use as much water as you use taking a bath?

c. Assuming your shower is in a bath tub, propose a nonmathematical way to compare, in one experiment, the amounts of water you use taking a shower and a bath.

73. Shower vs. Bath. Assume that when you take a bath, you fill the tub to the halfway point and the tub measures 6 feet by 3 feet by 2.5 feet. When you take a shower, you use a showerhead with a flow rate of 1.75 gallons per minute and you typically spend 10 minutes in the shower. There are 7.5 gallons in one cubic foot.

How much water (in gallons) does a bath use?

 $Half\ tub\ :\ \frac{6\ feet\ \cdot3\ feet\ \cdot2.5\ feet\ }{2\ }$ = 22.5 cubic feet

 $22.5\ ft^3\cdot\frac{7.5\ gallons}{1\ ft^3}$   = 168.75 gallons

Multiple Choice

73. a. Do you use more water taking a shower or taking a bath?

• Bath

• Shower

Open Ended

73. c. Assuming your shower is in a bath tub, propose a nonmathematical way to compare, in one experiment, the amounts of water you use taking a shower and a bath.

80. Metric Area. When the metric system was first proposed, the unit of area was the are with  $1\ are\ =\ 100m^2$  .
Today, the accepted metric unit of area is the hectare (ha), where 1 ha=100 are. This unit is used around the world in forestry and agriculture.

a. Using a power of 10, how many square meters are there in 1 hectare?
b. Express  $1\ km^2$   in hectares.
c. Find the conversion factor between hectares and acres.
d. Using the currency conversions in Table 2.1, which is the more expensive price for land, $5000/acre or 10,000 euro/ha?

How many square meters are there in 1 hectare?   $1\ are\ =\ 100\ m^2$ .
(1 ha = 100 are)

•  $\frac{1\ ha}{1}\cdot\frac{100\ are}{1\ ha}\cdot\frac{100\ square\ meters}{1\ are}$  

• = 10,000 square meters 

80. b. Express $1\ km^2$ in hectare.

• 1km * 1km

•  $\frac{1\ km\cdot\ 1km}{1}\cdot\frac{1,000\ m}{1\ km}\cdot\frac{1,000\ m}{1\ km}$  

•  $\frac{1km\ \cdot\ 1km}{1}\cdot\frac{1,\ 000\ m}{1\ km}\cdot\frac{1,000\ m}{1km}\cdot\frac{1\ hectare}{10,000\ m\cdot m}$  

80. c. Find the conversion factor between hectares and acres.

1 hectare = 2.47105 acres (Use Google)

Fill in the Blanks

Multiple Choice

Which is more expensive?

• 10,000 euro/hectare

• $5,000/acre

87–88: Solar Energy. Use these facts in the following exercises: Solar (photovoltaic) cells convert sunlight directly into electricity. If solar cells were 100% efficient, they would generate about 1000 watts of power per square meter of surface area when exposed to direct sunlight. With lower efficiency, they generate proportionally less power. For example, 10% efficient cells generate 100 watts of power in direct sunlight.

• 87. Suppose a 1-square-meter panel of solar cells has an efficiency of 20% and receives the equivalent of 6 hours of direct sunlight per day. How much energy, in joules, can it produce each day? What average power, in watts, does the panel produce?

• 88. Suppose you want to supply 1 kilowatt of power to a house (the average household power requirement) by putting solar panels on its roof. If you use the solar cells described in Exercise 87, how many square meters of solar panels would you need? Assume that you can make use of the average power from the solar cells (by, for example, storing the energy in batteries until it is needed).

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89. Wind Power: One Turbine. Modern wind energy “farms” use large wind turbines to generate electricity from the wind. At a typical installation, a single modern turbine can produce an average power of about 2.5 megawatts. (This average takes wind variations into account.) How much energy, in kilowatt-hours, can such a turbine generate in a year?

• megawatts ( $10^6\ watts$  ) to kilowatts ( $10^3\ watts$  )      $\frac{2.5\ megawatts}{1}\cdot\frac{10^6watts}{1\ megawatt}\cdot\frac{1\ kilowatt}{10^3watts}$  

• One year to hours              $1\ year\ \cdot\frac{365\ days}{1\ year}\cdot\frac{24\ hours}{1\ days}$  

• kw-hr is killowatts multiplied by hours, therefore 2500 kilowatts * 8760 hours = 21,900,000 kw-hr

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98. Drug Dosage. The label on a particular drug recommends 75–150 mg of the drug per kilogram of body weight per day. A doctor prescribes 200 mg of the drug every 8 hours for a 20-pound child. Is the prescription within the guidelines?

First figure out: How much medicine did the doctor prescribe in mg per kg?

• How much med? 3 doses of 200 mg is 600 mg total.

• Convert the 20 pound child to kilograms.            $20\ lb\cdot\frac{1\ kg}{2.205\ lb}$  = 9.07 kg

• mg of drug to kg of body?  $\frac{600\ mg\ of\ drug}{9.07\ kg\ child\ weight}$      =    66.15 mg per kg

Multiple Choice

98. Drug Dosage. The label on a particular drug recommends 75–150 mg of the drug per kilogram of body weight per day. A doctor prescribes 200 mg of the drug every 8 hours for a 20-pound child. Is the prescription within the guidelines?

• Below the guidelines. There may not be enough dosage to treat the patient.

• Within the guidelines. The patient is adequately medicated.

• Above the guidelines. This is potentially an overdose.