1. Assume your hybrid car gets 38.0 miles per gallon (mpg) and the current price per gallon of regular, unleaded gasoline is $2.52. The car’s gas tank holds 11.5 gallons. a. How far (in km) can the car travel on a tank of gas? Capacity of tank = 11.5 gallons 1 gallon can be used to travel 38 miles 11.5 gallons = 11.5 * 38 = 437 miles b. What will be the cost of gasoline for a 160-mile trip? Amount of gasoline required for 160-mile trip: 1 gallon covers 38 miles, therefore 160-mile trip would require 160/38 = 4.21 gallons Cost of 1 gallon = 2.52 * 4.21 = $10.61 c. How far (in miles and km) can the car travel on $10.00 worth of gas?
CHM 111 NAME: __DJIMMY FRENCH___________________________
Dimensional Analysis
RECORD ANSWER WITH CORRECT UNITS AND CORRECT SIG FIGS. IN BOX PROVIDED – USE SCIENTIFIC NOTATION IF CONVENIENT. SHOW UNIT CONVERSION PROCESS IN SPACE PROVIDED BELOW EACH QUESTION FOR FULL CREDIT.
1. Assume your hybrid car gets 38.0 miles per gallon (mpg) and the current price per gallon of regular, unleaded gasoline is $2.52. The car’s gas tank holds 11.5 gallons.
a. How far (in km) can the car travel on a tank of gas?
Capacity of tank = 11.5 gallons
1 gallon can be used to travel 38 miles
11.5 gallons = 11.5 * 38 = 437 miles
b. What will be the cost of gasoline for a 160-mile trip?
Amount of gasoline required for 160-mile trip:
1 gallon covers 38 miles, therefore
160-mile trip would require 160/38 = 4.21 gallons
Cost of 1 gallon = 2.52 * 4.21 = $10.61
c. How far (in miles and km) can the car travel on $10.00 worth of gas?
Gallons in $10 worth of gas = 10/2.52 = 3.97 gallons
1 gallon covers 38 miles
3.97 gallons would give 3.97 * 38 = 150.86 miles
2. The world record for an adult male running 1.00 mile is 3.72 min. Calculate this speed in m/sec.
Speed = mile/min = 1.00/3.72 = 26.8 = 7.21 m/s
3. Lake Superior is the largest of the Great Lakes, with a volume of 2900 mi3. How many liters of water are contained in Lake Superior?
The volume of the lake is superior is 2900 m3
Need to find the amount of water contained in the lake,
Converting 2900 m3 into liters.
1 m3 = 1000 liters.
Therefore, 2900 m3 = (2900*1000) liters = 2900000 liters
4. If the average American throws away 4.5 lb of trash each day, and the population of the US is estimated to be 311 million people, calculated the number of metric tons of garbage thrown away in the US each year. (1 metric ton (t) = 1000 kg, assume 365 days in a year)
5. A hectacre (1.0000 x 104 m2) is a metric unit of area analogous to an acre. How many square feet are in a 5.0 hectare farm?
6. The Deepwater Horizon oil spill released approx. 35000 barrels of crude oil per day into the Gulf of Mexico for 87 days. An oil barrel is defined as 42 gal.
a. Calculate the rate of crude oil released in L/hour. (Assume 24 hr in one day.)
b. A case of water at a local “warehouse store” contains forty (40) 500. mL bottles. The total volume of the Deepwater Horizon oil spill was equivalent to how many cases of water?
7. It requires1200 kg of coal to produce the energy needed to make 1.0 kg of aluminum metal. If a single soda can requires approx. 15 g of Al, what mass of coal would be needed to produce a six-pack of cans?
8. A recreational runner has an average speed of 5.9 mph. How many km does she cover in 98 min?
9. The daily dose of ampicillin for the treatment of an ear infection is 115 mg/kg of body weight. If ampicillin tablets are available in 250. mg size, calculate the number of tablets that a 33.5 lb child must take per day.
10. The density of pure copper is 8.89 g/cm3 (at 20 ˚C).
a. Calculate the mass in kg of a copper cube with dimensions 1 ft 4 in on all three sides.
b. Calculate the volume in in3 of a 5.0 kg bar of copper.
11. A spherical basketball has a diameter of 10.0 inches, and is inflated to a total air pressure of 1.6 atmospheres (atm). [( Volume of sphere = 4/3 πr3 ), 2.54 cm = 1 in, 1 atm = 14.696 psi]
a. Calculate the volume of the basketball in L.
b. Calculate the total air pressure in units of psi (pounds per square inch).
12. Six concrete posts are used to support a waterfront pier. Each post has dimensions 14 in x 14 in x 15 ft. The average density of the concrete is 2.4 g/cm3. ( 1g = 1 x 10-6 metric ton)
a. Calculate the volume of concrete (in m3) needed to make one post.
b. Calculate the total mass in metric tons (t) of all six concrete posts.
13. Earth’s surface area is 5.1 x 108 km2, its crust has an average thickness of 35 km and an average density of 2.8 g/cm3. The two rarest (non-radioactive) elements in the crust are ruthenium and rhodium, each with an abundance of 1.0 x 10-4g/metric ton crust. What is the total mass of these two elements in the earth’s crust? (1g = 1 x 10-6 metric ton)
14. A 200mg piece of gold is hammered into a sheet measuring 2.4ft x 1.0ft, what is the thickness of the sheet in meters? Density of gold is 19.32g/cm3 (1in = 2.54cm, 12in = 1ft)
15. A 15.0cm long cylindrical tube, sealed at one end is filled with ethanol. The mass of the ethanol needed to fill the tube is found to be 9.64g. Calculate the inner diameter of the tube in cm.
Density of ethanol = 0.789g/mL.(volume of a cylinder = πr2 l )
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