Units: the hints hidden in every physics and engineering problem

academics engineering physics units
By Jeff M.

In many science and engineering classes, units can be seen as an additional step that needs to be taken into consideration when completing a problem. In some problems on the Fundamental Engineering exam, mismatched units are intentionally used in an attempt to confuse students and measure their understanding of key concepts. Nonetheless, units hold critical information about the values in the problem and how they interact. If you can understand how units are functioning in a problem, you can unlock helpful hints to solving that problem!

1. How Dimensional Analysis can be used

Through the application of dimensional analysis, units can provide important hints about how to solve a problem. As an example, let’s look at the following physics problem taken from NCEES’s 2015 Fundamentals of Engineering sample questions [1]:

Screen Shot 2022-06-01 at 10.54.17 AMThis problem provides three types of units: N/mm, N, and mm. It asked us to solve for the force required (N), while providing us with the spring constant (N/mm) and two separate lengths (mm). To solve for the required force, we must somehow get Newtons using N/mm, and mm. The simplest form of doing this is as follows:

Screen Shot 2022-06-01 at 10.55.31 AMTherefore, we now know that we must multiply the spring constant by something with the units of mm. This knowledge rules out the possibilities of multiplying the two lengths together (which would result in units of mm2) or calculating a ratio of the lengths (which would result in a unit-less number). While it’s true that any linear combination of the two lengths will result in the required units of mm, two of the most reasonable ways to use these measurements in an equation that outputs N is to multiply spring constant by either the sum or the difference of the two measurements. This gives us the two following options:

Screen Shot 2022-06-01 at 10.56.28 AMor

Screen Shot 2022-06-01 at 10.56.58 AM

The first option can quickly be eliminated as it is not one of the possible answers leaving us to estimate the answer to be C: 2,500 N which happens to be the correct answer. We have now successfully solved a practice problem for the Fundamentals of Engineering exam with only dimensional analysis and without using any equations.

2. Broader Scope and Applications

While the example above is relatively naïve, it shows the power in using the information contained in units. This information is amplified as units get more and more complicated. It’s important to keep in mind that all units break down to five major physical quantities: mass (M), length (L), time (T), electrical current (I), and temperature (Θ). Below is a table of some common units in engineering and physics and how they break down.

Screen Shot 2022-06-01 at 10.58.13 AMThis information allows us to break down any coefficient into its fundamental units and glean the maximum amount of information contained in those units. Take for example thermal conductivity k, a material property essential in many heat transfer calculations.

Screen Shot 2022-06-01 at 10.58.51 AMThis breakdown hints at which values in a given problem might need to be multiplied or divided by thermal conductivity to get the desired output. While it’s unrealistic to expect to solve all problems simply from breaking down the units of the provided values, dimensional analysis is a powerful tool especially when combined with other knowledge. Specifically, it can give you an idea of what you need to do with your values before applying an equation to them. Many engineering classes and tests provide relevant equations. By analyzing the output dimensions of that equation, you can quickly eliminate many incorrect equations for that specific problem. Admittedly, there is no guarantee that your answer is right just because your units workout, however, it is a guarantee that your answer is incorrect if your units do not work out.

Conclusion

One of the most important pieces of information provided in physics and engineering problems is the units of the given and desired values. Being able to quickly breakdown and understand the interactions of different units take much practice but is essential to becoming a proficient engineer.

Sources

[1] Fundamentals of Engineering Sample Questions, National Council of Examiners For Engineering and Surveying, 2015. https://www.engineeringonline.ncsu.edu/wp-content/uploads/sites/23/2018/02/FE-Sample-Questions-Book_2015.pdf

Comments

topicTopics
academics study skills MCAT medical school admissions SAT expository writing college admissions English MD/PhD admissions strategy writing LSAT GMAT GRE physics chemistry math biology graduate admissions academic advice ACT interview prep law school admissions test anxiety language learning premed MBA admissions career advice personal statements homework help AP exams creative writing MD study schedules computer science test prep Common Application summer activities history mathematics philosophy organic chemistry secondary applications economics supplements research 1L PSAT admissions coaching grammar law psychology statistics & probability legal studies ESL CARS SSAT covid-19 dental admissions logic games reading comprehension engineering USMLE calculus PhD admissions Spanish mentorship parents Latin biochemistry case coaching verbal reasoning DAT English literature STEM excel medical school political science skills AMCAS French Linguistics MBA coursework Tutoring Approaches academic integrity chinese letters of recommendation Anki DO Social Advocacy admissions advice algebra artificial intelligence astrophysics business cell biology classics diversity statement gap year genetics geometry kinematics linear algebra mechanical engineering mental health presentations quantitative reasoning study abroad technical interviews time management work and activities 2L DMD IB exams ISEE MD/PhD programs Sentence Correction adjusting to college algorithms amino acids analysis essay art history athletics business skills careers cold emails data science dental school finance first generation student functions information sessions international students internships logic networking poetry resume revising science social sciences software engineering tech industry trigonometry writer's block 3L AAMC Academic Interest EMT FlexMed Fourier Series Greek Health Professional Shortage Area Italian Lagrange multipliers London MD vs PhD MMI Montessori National Health Service Corps Pythagorean Theorem Python Shakespeare Step 2 TMDSAS Taylor Series Truss Analysis Zoom acids and bases active learning architecture argumentative writing art art and design schools art portfolios bacteriology bibliographies biomedicine brain teaser campus visits cantonese capacitors capital markets central limit theorem centrifugal force chemical engineering chess chromatography class participation climate change clinical experience community service constitutional law consulting cover letters curriculum dementia demonstrated interest dimensional analysis distance learning econometrics electric engineering electricity and magnetism escape velocity evolution executive function freewriting genomics graphing harmonics health policy history of medicine history of science hybrid vehicles hydrophobic effect ideal gas law immunology induction infinite institutional actions integrated reasoning intermolecular forces intern investing investment banking lab reports linear maps mandarin chinese matrices mba medical physics meiosis microeconomics mitosis mnemonics music music theory nervous system neurology neuroscience object-oriented programming office hours operating systems