Question

solving problems iii
solve each of the problems using the factor - unit analysis method.

1. how many days are in 726000 jiffies (a jiffy is one - hundredth of a second)?
2. how many cups are in 637.8 quarts? (hint: 8 oz = 1 cup, 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon)
3. 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)?
4. 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)

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?

Explanation:

Step1: Convert jiffies to seconds

We know 1 jiffy = 0.01 s. So for 726000 jiffies, the number of seconds is $726000\times0.01 = 7260$ s.

Step2: Convert seconds to minutes

Since 1 min = 60 s, the number of minutes is $\frac{7260}{60}=121$ min.

Step3: Convert minutes to hours

As 1 h = 60 min, the number of hours is $\frac{121}{60}\approx2.0167$ h.

Step4: Convert hours to days

Given 1 day = 24 h, the number of days is $\frac{2.0167}{24}\approx0.084$ days.

Step1: Convert quarts to gallons

Since 4 quarts = 1 gallon, for 637.8 quarts, the number of gallons is $\frac{637.8}{4}=159.45$ gallons.

Step2: Convert gallons to pints

As 1 gallon = 8 pints, the number of pints is $159.45\times8 = 1275.6$ pints.

Step3: Convert pints to cups

Given 1 pint = 2 cups, the number of cups is $1275.6\times2=2551.2$ cups.

Step1: Convert miles to kilometers

We know 1 mile = 1.6 km, so 55.0 miles = $55.0\times1.6 = 88$ km.

Step2: Convert kilometers to meters

Since 1 km = 1000 m, 88 km = $88\times1000=88000$ m.

Step3: Convert hours to seconds

As 1 h = 3600 s.

Step4: Calculate meters per second

The speed in m/s is $\frac{88000}{3600}\approx24.44$ m/s.

Step1: Convert grams to ounces

Given 28.4 g = 1 oz, so 13.6 g = $\frac{13.6}{28.4}\approx0.48$ oz.

Step2: Convert cubic - centimeters to cubic - inches

Since 2.54 cm = 1 in, 1 $cm^{3}=(\frac{1}{2.54})^{3}\text{ in}^{3}\approx0.061\text{ in}^{3}$.

Step3: Convert cubic - inches to cubic - feet

As 1 ft = 12 in, 1 $ft^{3}=12^{3}=1728\text{ in}^{3}$, so 1 $\text{in}^{3}=\frac{1}{1728}\text{ ft}^{3}$.

Step4: Convert ounces to pounds

Since 16 oz = 1 lb.
The density in lb/$ft^{3}$:
\[

$$\begin{align*} &\frac{0.48\text{ oz}}{0.061\text{ in}^{3}}\times\frac{1\text{ lb}}{16\text{ oz}}\times\frac{1728\text{ in}^{3}}{1\text{ ft}^{3}}\\ =&\frac{0.48\times1728}{0.061\times16}\text{ lb/ft}^{3}\\ =&847.87\text{ lb/ft}^{3}\approx848\text{ lb/ft}^{3} \end{align*}$$

\]

Answer:

0.084 days