Question

challenge question
a square of aluminum foil has a mass of 1.85 grams. it has dimensions of 10.00 centimeters on a side. if the density of aluminum is 2.7 g/cm³, what is the thickness of the foil?

1. if your average speed is 55.0 miles per hour, how many meters per second are you traveling (1.6 kilometers = 1 mile, 1 kilometer = 1000 meters)?
2. mercury has a density of 13.6 g/cm³. how many pounds per cubic foot is that? (28.4 grams = 1 ounce, 2.54 cm = 1 inch)

Explanation:

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Step1: Convert miles per hour to kilometers per hour

Since 1 mile = 1.6 kilometers, if the speed is 55.0 miles per hour, then in kilometers per hour, we multiply the speed in miles per - hour by the conversion factor.
$55.0\ miles/hour\times1.6\ km/mile = 88.0\ km/hour$

Step2: Convert kilometers per hour to meters per hour

Since 1 kilometer = 1000 meters, we multiply the speed in kilometers per hour by 1000.
$88.0\ km/hour\times1000\ m/km=88000\ m/hour$

Step3: Convert meters per hour to meters per second

Since 1 hour = 3600 seconds, we divide the speed in meters per hour by 3600.
$\frac{88000\ m}{1\ hour}\times\frac{1\ hour}{3600\ s}\approx24.4\ m/s$

Step1: Convert cubic feet to cubic inches

Since 1 foot = 12 inches, 1 cubic foot = $(12\ in)^3=1728\ in^3$. And since 1 inch = 2.54 cm, 1 cubic inch=$(2.54\ cm)^3 = 16.387064\ cm^3$. So 1 cubic foot=$1728\times16.387064\ cm^3\approx28316.85\ cm^3$.

Step2: Convert grams to pounds

Since 1 ounce = 28.4 grams and 1 pound = 16 ounces, 1 pound=$16\times28.4\ g = 454.4\ g$.

Step3: Calculate the density in pounds per cubic foot

The density of mercury is 13.6 g/cm³. First, convert the mass in grams per cubic - centimeter to pounds per cubic - centimeter. $\frac{13.6\ g}{1\ cm^3}\times\frac{1\ pound}{454.4\ g}\approx0.0299\ pounds/cm^3$. Then convert from pounds per cubic - centimeter to pounds per cubic foot. $\frac{0.0299\ pounds}{1\ cm^3}\times28316.85\ cm^3/ft^3\approx847\ pounds/ft^3$

Step1: Calculate the area of the square foil

The side of the square foil is $s = 10.00\ cm$, so the area $A=s^2=(10.00\ cm)^2 = 100\ cm^2$.

Step2: Use the density formula $d=\frac{m}{V}$ to find the volume

Given $d = 2.7\ g/cm^3$ and $m = 1.85\ g$. Rearranging the density formula $V=\frac{m}{d}$, we get $V=\frac{1.85\ g}{2.7\ g/cm^3}\approx0.685\ cm^3$.

Step3: Calculate the thickness $h$ of the foil

Since $V = A\times h$, then $h=\frac{V}{A}$. Substituting $V = 0.685\ cm^3$ and $A = 100\ cm^2$ into the formula, we get $h=\frac{0.685\ cm^3}{100\ cm^2}=0.00685\ cm = 0.0685\ mm$

Answer:

$24.4\ m/s$

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