Science: Dimensional Analysis Across Disciplines
Using units to solve problems in science
Science: Dimensional Analysis Across Disciplines
Using units to solve problems in science
Science - Grade 9-12
- 1
A car is traveling at 72 kilometers per hour. Use dimensional analysis to convert this speed to meters per second.
Convert kilometers to meters and hours to seconds.
The speed is 20 meters per second. The conversion is 72 km/h × 1000 m/1 km × 1 h/3600 s = 20 m/s. - 2
A medicine dosage is 12 milligrams per kilogram of body mass. A patient has a mass of 58 kilograms. How many milligrams are needed for one dose, and how many 250 milligram tablets is that?
First find milligrams, then divide by milligrams per tablet.
The calculated dose is 696 milligrams because 12 mg/kg × 58 kg = 696 mg. This is 2.78 tablets because 696 mg ÷ 250 mg/tablet = 2.78 tablets. In real life, a healthcare professional would decide how to round or adjust the dose. - 3
In a chemistry lab, you need 0.500 moles of sodium chloride. The molar mass of sodium chloride is 58.44 grams per mole. What mass of sodium chloride should you measure?
You should measure 29.22 grams of sodium chloride. The calculation is 0.500 mol × 58.44 g/1 mol = 29.22 g. - 4
A sample of aluminum has a mass of 135 grams. Aluminum has a density of 2.70 grams per cubic centimeter. What is the volume of the sample?
Density can be written as grams per cubic centimeter, so use it as a conversion factor.
The volume is 50.0 cubic centimeters. The calculation is 135 g × 1 cm^3/2.70 g = 50.0 cm^3. - 5
A stream has a flow rate of 3.2 cubic meters per second. Convert this flow rate to liters per minute. Use 1 cubic meter = 1000 liters.
Convert cubic meters to liters, then seconds to minutes.
The flow rate is 192,000 liters per minute. The calculation is 3.2 m^3/s × 1000 L/1 m^3 × 60 s/1 min = 192,000 L/min. - 6
Light travels at about 3.00 × 10^8 meters per second. How far does light travel in one 365 day year, expressed in kilometers?
Convert one year into seconds, multiply by the speed of light, then convert meters to kilometers.
Light travels about 9.46 × 10^12 kilometers in one year. The calculation is 3.00 × 10^8 m/s × 60 s/min × 60 min/h × 24 h/day × 365 days × 1 km/1000 m = 9.46 × 10^12 km. - 7
A gas tank is pressurized to 2.45 atmospheres. Convert this pressure to kilopascals using 1 atmosphere = 101.3 kilopascals.
The pressure is about 248 kilopascals. The calculation is 2.45 atm × 101.3 kPa/1 atm = 248.185 kPa, which rounds to 248 kPa. - 8
A snack contains 230 food Calories. One food Calorie equals 4184 joules. How much energy is in the snack in joules?
Food Calories are capital C Calories, and each one is 4184 joules.
The snack contains 962,320 joules of energy, or about 9.62 × 10^5 joules. The calculation is 230 Cal × 4184 J/1 Cal = 962,320 J. - 9
A car uses 6.5 liters of gasoline per 100 kilometers. How many liters of gasoline are needed for a 450 kilometer trip?
The trip requires 29.25 liters of gasoline. The calculation is 450 km × 6.5 L/100 km = 29.25 L. - 10
An electric power source produces 820 grams of CO2 for each kilowatt-hour of electricity. A household uses 650 kilowatt-hours in a month. How many kilograms of CO2 are produced?
After finding grams of CO2, convert grams to kilograms.
The household produces 533 kilograms of CO2. The calculation is 650 kWh × 820 g CO2/1 kWh × 1 kg/1000 g = 533 kg CO2. - 11
A bacterium is 2.5 micrometers long. Convert this length to millimeters and meters. Use 1 millimeter = 1000 micrometers and 1 micrometer = 10^-6 meters.
A micrometer is much smaller than both a millimeter and a meter.
The bacterium is 0.0025 millimeters long and 2.5 × 10^-6 meters long. The conversions are 2.5 micrometers × 1 mm/1000 micrometers = 0.0025 mm and 2.5 micrometers × 10^-6 m/1 micrometer = 2.5 × 10^-6 m. - 12
Ocean water has a salinity of 35 parts per thousand by mass, which means 35 grams of salt per 1000 grams of seawater. How many grams of salt are in 2.5 kilograms of seawater?
There are 87.5 grams of salt in 2.5 kilograms of seawater. The calculation is 2.5 kg seawater × 1000 g/1 kg × 35 g salt/1000 g seawater = 87.5 g salt. - 13
Newton's second law is F = ma. If mass is measured in kilograms and acceleration is measured in meters per second squared, what base units make up one newton of force?
Substitute the units for mass and acceleration into F = ma.
One newton is equal to 1 kilogram meter per second squared. This comes from multiplying mass units by acceleration units: kg × m/s^2 = kg·m/s^2. - 14
At standard temperature and pressure, 1 mole of a gas occupies 22.4 liters. A container holds 5.60 liters of oxygen gas. How many oxygen molecules are in the container? Use Avogadro's number, 6.022 × 10^23 molecules per mole.
Convert liters to moles first, then convert moles to molecules.
The container holds about 1.51 × 10^23 oxygen molecules. The calculation is 5.60 L × 1 mol/22.4 L × 6.022 × 10^23 molecules/1 mol = 1.51 × 10^23 molecules. - 15
A storm drops 2.4 centimeters of rain evenly over a rectangular field that is 80 meters long and 50 meters wide. What volume of water falls on the field in cubic meters and in liters?
Convert the rain depth to meters before multiplying by the field area.
The storm drops 96 cubic meters of water, which is 96,000 liters. The area is 80 m × 50 m = 4000 m^2, the rain depth is 2.4 cm × 1 m/100 cm = 0.024 m, and the volume is 4000 m^2 × 0.024 m = 96 m^3.