# Video on Dimensional Analysis

The need to relate different attributes of a physical quantity is fundamental to most areas of study. To do this, it is necessary to use dimensional analysis.

This video explains what dimensional analysis is and how to apply it. It also covers unit conversions and how to use them, specifically converting Amperes to Coulomb and hours to seconds.

## Unit Conversions

Many, if not most, parameters and measurements in chemistry and physics have a corresponding dimensional unit. Understanding how to calculate these units is a key skill for these disciplines.

In order to convert a given number of a physical quantity into an equivalent number using another unit, the ratio used must cancel the existing unit in both the numerator and denominator. Orienting the conversion factor correctly to accomplish this is known as dimensional analysis.

This video covers the basics of dimensional analysis (also known as the factor label method) and includes several practice problems. It also covers the metric system and English units including the use of sat proportion word problems.

A physical quantity can be expressed with a different set of units, but each of these must be related to some common standard. In this video, you will learn how to use a variety of conversion factors to simplify and clarify your calculations. This process makes working with larger and smaller numbers more convenient.

## Power of an Electric Eel

The electric eel can deliver a high voltage shock to a predator, enough to cause significant injury. But how does the fish channel so much power into a single discharge? It relies on the fact that water conducts electricity so well.

The eel’s nervous system synchronizes thousands of disc-shaped, electricity-producing cells packed into its specialized electric organ. Each cell can acquire a potential difference of 1/10th of a volt by controlling the flow of sodium and potassium ions (charged atoms) across membranes. Linked together in arrays, the electrocytes can generate up to 0.5 kW of electrical power.

The researchers measured the peak current in the subject’s arm during each high-voltage discharge and estimated the return path resistance, based on the eel’s body-water interface and the large surface area of the trunk compared to the arm. Together, these estimates indicate that the eel transferred 3.9 W of energy to the target during each leap. That is an order of magnitude more than the amount of power imparted by a law-enforcement TASER.

## Enem Exam Questions

The enem exam is taken by roughly 5 million students each year and covers a wide range of subjects. Its questions are designed to be able to be answered in a variety of ways, from multiple-choice answers to essay writing. In this video, the speaker explains how understanding dimensional analysis and unit conversions can help students solve these questions, even if they don’t know the content or formulas involved.

While the enem exam isn’t mandatory, it has become a common method for universities to select students in Brazil. It is often compared to the vestibular, which is mandatory. Both exams are used to rank schools nationally based on student performance. However, a recent report revealed that the enem league table has major flaws when it comes to school quality. This may explain why some schools appear to be better than others in the league tables, despite these schools being close in terms of raw averages.

## Prefixes

A key tool in understanding dimensional analysis is the distinction between stock quantities and flow quantities. The dimensions of a stock are fixed (length, mass, time), while the dimension of a flow is dependent on other variables such as velocity. The dimension of a flow is expressed in terms of other base quantities, like length and mass, or by a combination of these units, such as kg/m3. A quantity that is measured in more than one combination of units is called a derived unit.

The rule that a physically meaningful equation, inequality or ratio must have the same dimensions on both sides of the equation is called dimensional homogeneity. This is a simple sanity check that can be used to evaluate a mathematical formula and protect against many simple errors. For example, the expression F = mass times acceleration is dimensionally homogeneous because the dimensions of mass and length are compatible.