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8

Here is an entertaining mathematical answer. (Or at least, I find it entertaining, anyway.) Let us take seriously the idea that we can treat radians as a unit, and proceed from there. This means that when we write an expression like $\sin \theta$, the argument $\theta$ must have units of radians, whereas the result (I'll assume) is just a number without any ...


4

An average person uses approx. 1500-2500kcal/day. Since one kcal equals 4148J in SI units, that's between 6.2-10.4MJ per day. A day has 86400 seconds, which brings us to an average power consumption of 72-120W... about as much as a light bulb. :-) Physical exercise varies between light (300kcal/h) at an additional 350W to very strenuous at probably six ...


2

I think your problem is that you didn't change the units in the constant g. It has a value of approximately $9.8ms^{-2}$. Notice that it depends on meters. To obtain the correct result, you should use $980cms^{-2}$. Notice that this constant is off by a factor of 100, so that the result (after the square root) is off by a factor of $\sqrt{100}=10$.


2

When you work "fairly hard", your body can produce about 200 W of power - enough for two incandescent bulbs. Top athletes can produce more - in short bursts. Your body is roughly 25% efficient in converting "calories" (which are actually kilo calories) to Joules - meaning that if you work out hard enough to burn 600 kcal per hour, then you actually produced ...


2

A (kilo)calorie is a unit of energy, while a watt is a unit of power, which describes the rate at which energy is expended. So a 100W bulb is using 100 joules a second. A kcal is about 4184 joules, so a 100W bulb takes about 42 seconds to consume (really: convert into light and heat) a kcal. The joule is the SI (derived) unit of energy. Units of energy ...


2

The Dimensions of Angle depend on one's viewpoint and purpose (of using dimensions). Likewies the Units (and implicitly scale) of angle also depend on the local customs and practices that support those viewpoints and purposes. Personally, I want Angles to be a dimension, particularly for error detection and correction in scientific and engineering ...


2

The property of Caesium that makes it such a stable oscillator is the lone electron in its $6s$ orbital. All other electrons in the lower energy levels take a symmetrical electron configuration and leave the $6s$ as an "outsider". The spin of the Caesium nucleus can cause a so-called hyperfine transition in that $6s$ electron which has a very specific ...


2

Every atom, including cesium-133, emits (or absorbs) electromagnetic waves (light or its generalization to invisible colors) when the electrons jump from one state in the atom to another. The electromagnetic radiation is a periodic process in which the electric (and similarly magnetic) fields at a given point of space behave as $$ E = E_0 \cdot \cos (2\pi f ...


2

Both are correct. It is a matter of personal preference which you decide to use. It makes the graph easier to understand if axes are labelled in small numbers; it also makes the graph less cluttered. So either you would label the x axis "Pressure in units of 10^6 Pa" or "Pressure in MPa". Labelling the x axis as "Pressure in Pa" and using marker values ...


1

I think this question has been asked already several times, for example : How do we know that $F = ma$, not $F = k \cdot ma$ Are Newton's "laws" of motion laws or definitions of force and mass? Why isn't it $E \approx 27.642 \times mc^2$? Constants of proportionality depend on the nature of the equation and the system of units. Their ...


1

No. Beside the already mentioned examples here some real problems with different dimensionless quantities and why they cannot be mixed. :( Starting with angle velocity units: Hertz (Hz) for frequency $f$ measured in periods per seconds (which is equivalent to $\frac{2 \cdot \pi}{s}$) or Angular frequency $\omega$ measured in $\frac{rad}{s}$ You can ...


1

In an exam, Alice scored $50$, Bob scored $40$, Eve scored $10$. Now to raise the class mean, the teacher decided to add $20$ points to every students. So Alice's score becomes $70$, Bob's score becomes $60$, and Eve's score becomes $30$. Now Alice complained to the teacher, "my score was higher than Bob's by $10$ marks, and you see, according to the ...


1

Celsius and Kelvin are two scales that differs only for an additive factor, but the single increment corresponds to the same temperature difference. In other words, an object become "hotter" in the same way if you rise its temperature by 1K or 1°C. You can use conversion formula in differences, just make sure you use it for both terms and keep in mind that ...


1

Of course, you can do it with Matlab, Mupad, Maple, Mathematica or even the Smart Math Calculator. Use this method: First define your variables with your units of choice, then tell the programm what the conversion factors from the given units to the target units are, for example, if you have km/h and need m/sec define 1km as 1000m and 1sec as h as 60² ...



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