Webassign 3 -- Dimensional Analysis

1. Perform the following conversions.

• a) 5.03 days to s 
• (5.03 days / 1) * (24 hr / 1 day) * (60 min / 1 hr) * (60 sec / 1 min) = 435000 sec (to 3 significant figures)
• b) 0.0545 mi to m 
• (0.0545 mi / 1) * (5280 ft / 1 mi) * (12 in / 1 ft) * (2.54 cm / 1 in) * (1 m / 100 cm) = 87.7 m (to 3 significant figures)
• c) $1.79/gal to dollars per liter 
• ($1.79 / gal) * (1 gal / 3.785 L) = $0.473 / L (to 3 significant figures)
• d) 0.511 in./ms to km/hr 
• (0.511 in / 1 ms) * (2.54 cm / 1 in) * (1 m / 100 cm) * (1 km / 1000 m) * (1000 ms / 1 sec) * (60 sec / 1 min) * (60 min / 1 hr) = 46.7 km / hr (to 3 significant figures)
• e) 22.44 gal/min to L/s 
• (22.44 gal / 1 min) * (3.785 L / 1 gal) * (1 min / 60 sec) = 1.416 L / s (to 4 significant figures)
• f) 0.02488 ft³ to cm³
• (0.02488 ft³ / 1) * (12 in / 1 ft)^3 * (2.54 cm³ / 1 in)^3 = 704.5 cm³ (to 4 significant figures)

2.

• a) How many liters of wine can be held in a wine barrel whose capacity is 39 gal? 
• (39 gal / 1) * (3.785 L / 1 gal) = 150 L (to 2 significant figures)
• (b) The recommended adult dose of Elixophyllin^®, a drug used to treat asthma, is 6 mg/kg of body mass. Calculate the dose in milligrams for a 150 lb person. 
• Convert 150 lbs to kilograms: (150 lb / 1) * (1 kg / 2.2 lb) = 68.1818 kg.
• Calculate the dosage: (68.1818 kg / 1) * (6 mg / 1 kg) = 400 mg (to 1 significant figure)
• c) If an automobile is able to travel 239 mi on 11.5 gal of gasoline, what is the gas mileage in km/L? 
• (239 mi / 11.5 gal) * (5280 ft / 1 mi) * (12 in / 1 ft) * (2.54 cm / 1 in) * (1 m / 100 cm) * (1 km / 1000 m) * (1 gal / 3.785 L) = 8.84 km/L (to 3 significant figures)
• d) A pound of coffee beans yields 50 cups of coffee (4 cups = 1 qt). How many milliliters of coffee can be obtained from 5 g of coffee beans?
• (5 g beans / 1) * (1 kg / 1000 g) * (2.2 lb / 1 kg) * (50 cups / 1 lb) * (0.2365 L / 1 cup) * (1000 mL / 1 L) = 100 mL (to 1 significant figure)

3.

• a) If an electric car is capable of going 235 km on a single charge, how many charges will it require to travel from Boston, Massachusetts to Miami, Florida, a distance of 1486 mi, assuming that the trip begins with a full charge. 
• (1486 mi / 1) * (5280 ft / 1 mi) * (12 in / 1 ft) * (2.54 cm / 1 in) * (1 m / 100 cm) * (1 km / 1000 m) * (1 charge / 235 km) = 10.2 charges (to 3 significant figures)
• b) If a migrating loon flies at an average speed of 19 m/s, what is its average speed in mi/hr? 
• (19 m / 1 s) * (100 cm / 1 m) * 91 in / 2.54 cm) * (1 ft / 12 in) * (1 mi / 5280 ft) * (60 sec / 1 min) * (60 min / 1 hr) = 43 mi/hr (to 2 significant figures)
• c) What is the engine piston displacement in liters of an engine whose displacement is listed as 450 in³? 
• (450 in³ / 1) * (2.54 cm / 1 in)^3 * (1 mL / 1 cm³ ) * (1 L / 1000 mL) = 7.4 L (to 2 significant figures)
• d) In March 1989, the Exxon Valdez ran aground and spilled 240000 barrels of crude petroleum off the coast of Alaska. One barrel of petroleum is equal to 42 gal. How many liters of petroleum were spilled?
• (240,000 barrels / 1) * (42 gal / 1 barrel) * (3.785 L / 1 gal) = 38000000 L (to 2 significant figures)

4. The height of a horse is usually measured in hands instead of in feet, where 1 hand equals 1/3 ft (exactly).

• a) How tall (in centimeters) is a horse of 17.7 hands?
• (17.7 hands / 1) * ((1/3) ft / 1 hand) * (12 in / 1 ft) * (2.54 cm / 1 in) = 180 cm (to 2 significant figures)
• b) What is the volume (in cubic meters) of a box measuring 8 2.7 11 hands?
• Calculate the volume of the box in hands: v=lwh = 8 * 2.7 * 11 = 237.6 hands³
• Convert cubic hands to cubic meters:
• (237.6 hands³ / 1) * ((1/3) ft / 1 hand)^3 * (12 in / 1 ft)^3 * (2.54 cm / 1 in)^3 * (1 m / 100 cm)^3 = 0.2 m³ (to 1 significant figure)