Miscellaneous Archive
Some past science snippets and physics tips... enjoy!
Snippets from science
Energy densities compared
The term energy is widely used these days... from the news to everyday conversations. What's amazing about this 'thing' is that for anything to happen anywhere - whether inside a plant, our bodies, a car - it must obey the conservation of energy. This means that if one type of energy increases - say, the energy of motion of an object (kinetic energy) - then this can only happen either by converting energy from another type already inside the object, or by transferring energy to the object from someplace else. Converting or transferring - that's it. When we start walking across the floor our body gains kinetic energy, and this energy is converted from the chemical energy contained in food molecules inside our cells. (If we were instead pushed across the floor then this energy would have been transferred to our body by the push.)
So how much energy is contained in various chemicals? One way to look at this is through energy density: the energy released per mass of a chemical undergoing a normal, everyday, reaction (see common chemicals here, with energy density ranked along the x-axis). Hydrogen - whether gas or liquid - tops the list at about 140 MJ/kg; it burns to water and is really light. Next at around 50 MJ/kg are mostly hydrocarbons containing only carbon and hydrogen; they burn to carbon dioxide and water and their constituent elements are still pretty light. The third clump at about 20 MJ/kg are mainly hydrocarbons that also contain oxygen; they still burn to carbon dioxide and water, but bring some oxygen atoms along which increases their mass. Today's batteries, meanwhile, although improving, bring up the rear at about 1 MJ/kg.
So with the energy stored per kg by hydrocarbons such as gasoline being 50-60 times greater than that stored by batteries, it'll take a while (if ever) before we can fully replace the former by the latter. Watch out for new developments though, and continue to explore science - for human ingenuity (unlike energy) is limitless.
The connection between mind and movement
Ever wondered why trees don't have brains? Or which single study tip might be most helpful to us? The answers, respectively, can be found here and here, and together they convey some amazing benefits from haptic learning.
Trig nomenclature
Why are sin, cos and tan named as they are? Matthew Conlen explains all.
Curiosity, and what is 'right' anyway?
Why do we adopt 'x' as the unknown...? Terry Moore explains.
This cartoon by Angela Melick illustrates how almost every statement (and model) in science can be both 'right' - useful and correct for the intended purpose - and also 'wrong'. In science, as in life, context is everything.
Tips for studying physics
What vectors are (and aren't)
A common entity we often encounter when doing science to make useful predictions is the vector. We may recall that this 'thing' has a magnitude (with appropriate units) and a direction. So, for example, velocity is a vector (the wind might be travelling at 3 m/s in a direction due-north, or at 12 m/s in a south-west direction), as is, for example, electric field (a field of 4 N/C pointing to the north, or 12 N/C pointing south-westerly). Note that 1 N/C is 1 V/m, so either N/C or V/m work ok here.
Anyway, what's great about vectors is that while they have magnitude (with units) and direction, they do not have a location. So you can draw/place them anywhere you wish. You may have already known this - perhaps you've been adding vectors by doing tail-to-tip additions and figuring out what final vector you end up with. So you're used to moving vectors around the page until the tail of one connects with the tip of another. You preserved the magnitudes and directions (so the vectors were unchanged), but happily changed their locations. As we often find in science, it's useful to know what something is, as well as what it's not.
Dimensions revisited
Last month I mentioned that expressions within sine, cosine, and tangent operations have no physiclal units. More generally, for any formula in science we can only meaningfully add or subtract terms with the same units - for example, we can add kg to kg to kg..., but never, say, kg to s2 to m3. So, no matter how complicated a formula may be, the physical dimensions of all terms that are added or subtracted must be the same. Knowing this can help a lot!
Dimensions and trig formulae
Considering sin, cos, and tan... it's helpful to remember that any expression within these operations must be dimensionless. Each one can be represented by a power series, and there's no law of nature that allows us to meaningfully add, for example, kg to kg2 to kg3..., etc. Thus, no matter how complicated an expression is within a sine, cosine, or tangent, it must have no physical dimensions. Knowing this can save time and possible hiccups with the algebra!
Why study physics?
For you:
- excitement of doing something intellectually stimulating... learning something new each day
- accomplishment of solving problems... satisfaction from doing/building/understanding it
- the international nature of the subject... physics societies exist in almost every country around the world
- every event in nature is due to physical interactions... it's fun to identify, understand, and then harness these in a beneficial way.
For employers/wider society - physics graduates can:
- understand and parse complicated concepts
- communicate complex procedures and results to a wide audience
- collect and analyse large data sets
- use a plethora of hands-on and mathematical tools, while still open to learning more
Check out Elon Musk speaking here (from 18 min onwards) about the benefits that physics-based thinking brings. Also see the Canadian Association of Physicists for some careers that studying physics can lead to.