Reference guides as a teaching and learning strategy: Key science units

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Reference guides as a teaching and learning strategy: Key science units

Patrick Blessinger

The Key Science Units reference guide provides the physical units and constants commonly utilized in science. These units and constants provide a basis for measurement and problem-solving in science. According to the International System of Units, a base unit is a standard unit that defines a physical quantity such as length, mass, or time. Sometimes the SI system is also referred to as the metric system. A common set of units allows for the continuity of measurement and communication across disciplines within the sciences. The kilogram has recently been redefined to depend on Planck's constant, whereas the meter is now defined based on the speed of light constant (BIPM, 2019).

Science literacy involves an understanding of the base units that represent length, mass and time. They are the meter, kilogram, and second, respectively. Most of the problems in science will be solved using these base units. The SI units are internationally accepted forms of measurement that make scientific communication clear and coherent across different disciplines and countries. This handout gives teachers and students a quick reference guide for the base units and derived units and constants that are commonly used in measurement and calculation in science.

The reference guide is organized by dimensions and units. A dimension is a type of quantity, for example, length, mass, and time. Dimensions describe what is measured without reference to any particular scale or numeric value. A unit is the scale used to quantify the dimension, how the dimension is measured and calculated. Examples of the different units of the same dimension for length include millimeters, centimeters, meters, inches feet, miles and many more. This guide also serves as a handy reference guide to explain and systemize proper terms, nomenclature, and abbreviations (IUPAC, 2023).

One of the key benefits of using reference guides as a strategy for teaching and learning is that they help reinforce comprehension and retention by providing students, especially middle and high school students, and even introductory university students without a strong science background, with a concise summary of logically organized concepts that they can refer to as they work on problems. Another benefit is that reference guides foster more independent thinking, and they save time by providing both teachers and students with a quick reference of core concepts without having to spend time searching through textbooks (Freeman, et al., 2014).

Practical Applications

Dimensional analysis is a powerful tool in science and engineering. It is a method for changing an amount expressed in one unit into an equivalent amount in another unit. This is accomplished by using suitable conversion factors. It enables the student to check on the consistency of equations, to perform unit conversions, and to simplify and solve complex problems (Cengel & Boles, 2019; Halliday, et al., 2013).

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Example 1: Derivation of the unit joule

An exercise might involve verifying the dimensional consistency of the equation for force (F = ma), where force is measured in newtons, mass in kilograms, and acceleration in meters per second squared. The joule is the SI unit of energy, work, and amount of heat. It is derived from the fundamental units of mass (kg), length (m), and time (s).

Work is done when a force is applied to an object, moving it some distance.

Formula: W = Fd where W is work (joules), F is force (newtons), and d is distance (meters).

According to Newton's Second Law, force is the product of mass and acceleration.

Formula: F = ma where F is force (newtons), m is mass (kg), and a is acceleration (m / s^2).

Substituting the expression for force into the work formula gives W = mad.

1 joule?(J) = 1 newton?(N) × 1 meter?(m).

Therefore, 1?joule?(J) = 1?kg × m^2 / s^2, expressed in base units.

The unit joule represents the energy transferred (work done) when a force of one newton is applied over a distance of one meter. This definition shows that the joule is a derived unit, combining the base SI units of kilograms, meters, and seconds.

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Example 2: Speed conversion

Convert 60 miles per hour (mph) to meters per second (m / s).

Given: 1 mile = 1,609.34 meters, 1 hour = 3,600 seconds.

Calculation: (60?miles / hour) × (1,609.34?meters / 1?mile) × (1?hour / 3,600?secs) = 26.82?m / s.

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Example 3: Energy Conversion

Convert 50 calories to joules.

Given: 1 calorie = 4.184 joules.

Calculation: 50?calories × 4.184?joules = 209.2?joules.

Example 4: Force calculation

Determine the force in newtons exerted by a 5 kg object under standard gravity (9.8 m / s2).

Calculation: F = mg = 5?kg × 9.8?m / s^2 = 49?N (weight).

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Example 5: Pressure conversion

Convert atmospheric pressure from 0.98 atm to pascals using cross-multiplication.

Given: 1 atm = 101,325 Pa.

Calculation: (1 atm / 101,325 Pa) = (0.98 atm / x Pa); 0.98 atm x 101,325?Pa = 99,298.5 Pa

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Example 6: Density calculation

Calculate the density of an object with a mass of 10 kg and a volume of 0.5 cubic meters.

Calculation: Density = Mass / Volume = 10?kg / 0.5?m^3 = 20?kg / m^3.

Example 7: Fluid pressure

Another application is to calculate the pressure that water would exert on an object at a certain depth below the surface. The total pressure at a certain depth under water is the sum of the atmospheric pressure and the hydrostatic pressure: Pt = Pa + Ph, which is Pt = Pa + ρgh, where ρ (rho) is the fluid’s density, g as the acceleration due to gravity (9.8m / s^2), and h is the depth below the surface.

Atmospheric pressure (Pa): 101,325 Pa

Density of water (ρ): 1,000 kg / m^3

Acceleration due to gravity (g): 9.8 m / s^2

Depth (h): 10 meters

Total pressure = atmospheric pressure + hydrostatic pressure

Use the formula Pt = Pa + ρgh

Substitute the values: Pt = (101,325 Pa) + (1,000?kg / m^3 × 9.8?m / s^2 × 10?m)

Calculate:

Pt = 101,325 + (1,000 × 9.8 × 10)

Pt = 101,325 Pa + 98,000 Pa

Pt = 199,325 Pa (1.97 atm or about 2 atm)

In addition, constants like Planck's constant in quantum mechanics or Avogadro's number in chemistry play vital roles in energy analysis. For example, the energy carried by photons is essential in understanding the behavior of light and matter in quantum mechanics. Similarly, Avogadro's number plays a vital role in converting the amount of substance in moles and the number of particles, especially in chemical reactions (Shankar, 2014).?

Conclusion

The Key Science Units reference guide emphasizes the importance of base units in scientific measurement and communication. This article explains basic concepts, provides some practical examples, and carries out some simple calculations to show how SI base units help ensure consistency in scientific disciplines.

This article further emphasizes how units are derived from base units and how base units are based on universal constants. Overall, the aim of the Key Science Units reference guide is to serve as a practical and helpful resource for teachers and students by reinforcing and applying key scientific unit concepts.

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References

Bureau International des Poids et Mesures. (2019). The international system of units (SI) (9th ed.). BIPM. https://www.bipm.org/en/publications/si-brochure

Cengel, Y. A., & Boles, M. A. (2019). Thermodynamics: An engineering approach (9th ed.). McGraw-Hill Education.

Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), 8410-8415. https://doi.org/10.1073/pnas.1319030111

Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics (10th ed.). Wiley.

International Union of Pure and Applied Chemistry. (2023). Green Book: Quantities, units, and symbols in physical chemistry. IUPAC. https://books.rsc.org/books/edited-volume/2097/Quantities-Units-and-Symbols-in-Physical

Shankar, R. (2014). Principles of quantum mechanics (2nd ed.). Springer.

Patrick Blessinger is a lecturer of education at SUNY (Old Westbury), a STEM teacher with NYSED, and chief research scientist for the International Higher Education Teaching and Learning Association or HETL.

Copyright ? [2024] Patrick Blessinger

Disclaimer

Opinions expressed in this article are those of the author and do not necessarily represent the position(s) of other professionals or any institution.