2.7: Plausibility checks
- Page ID
- 103432
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)A plausibility check is a calculation or validation procedure that is performed to verify if the obtained solution to a certain problem is correct.
The main takeaways from this section are the following:
- If your answer passes all plausibility checks, then the answer is probably correct.
- If your answer does not pass a plausibility check, then the answer is probably wrong and the failed check will likely provide you information where the mistake is, such that you can fix it.
- Therefore, if you learn properly to perform plausibility checks, you will not need a solution anymore to check if your answer is correct.
- Note that you can also perform a plausibility check at every intermediate step of the solution. This helps to find the step with the mistake.
- For professional engineers there is no solution manual. To avoid making mistakes, which can have a huge impact, they always need to check the plausibility of their calculations, to be close to \(100 \%\) sure of their answer.
- Therefore checking the correctness of answers (without solution manual) is one of the most important skills an engineer should acquire.
- For this reason we do not give students answers to all problems, since if one uses a solution manual to verify the correctness of answers, one never learns how to properly perform plausibility checks.
- If you, despite the plausibility checks, do not manage to solve a problem, always ask explanation from your professor, teacher or colleagues.
Here are some examples of questions you can ask yourself to check the plausibility of an answer:
- Does the quantity in the answer have the right units?
- Are units on both sides of the equation equal? (Sec. 2.2)
- Is the sign of the answer correct when comparing it to the question? E.g. in a problem where a ball is falling downward due to gravity, and the \(y\) axis points upward, is \(v_{y}\) negative?
- Does the value of the answer make sense? (not more than 10 times smaller or larger than expected?). E.g. in a problem where a mass is accelerating due to gravity over a surface, its acceleration can never exceed the free fall value \(g\).
- When you substitute the answer in the equations used, do you get back the given values? E.g. if you have found the solution \(x(t)=c_{1} t^{2}\), from the initially given acceleration, check by twice differentiating that \(a(t)=2 c_{1}\).
- When projecting forces on axes, does the length of the vector correspond to that of the components? E.g. \(v_{x}^{2}+v_{y}^{2}+v_{z}^{2}=|\overrightarrow{\boldsymbol{v}}|^{2}\).
- Does the net force vector \(\sum \overrightarrow{\boldsymbol{F}}\) point in the same direction as the acceleration \(\overrightarrow{\boldsymbol{a}}\) ?
- Do the chosen axes form a right-handed coordinate system?
- Does \(\sum \overrightarrow{\boldsymbol{F}}=m \overrightarrow{\boldsymbol{a}}\) and the other laws of Newton and Euler hold if you substitute the final answer back into them?
- Can methods of work and energy be used to double check the solution?
- Are all given constraint equations satisfied if you substitute the final answer into them?
- Is there any other information given that can be verified with the answer?
Of course there are many more plausibility checks that can be performed, which really depend on the type of problem under consideration.