Physics (not) by the numbers: work and energy

I tutor several physics students right now, and I find myself starting a lot of conversations with the phrase ‘let’s look at this conceptually for a second’. Don’t get me wrong, I love math, but sometimes we have to step away from the numbers and formulae and use our words.

Work and energy are good topics to tackle conceptually. Like many words, they have very specific meanings in physics that differ from the colloquial usage.

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…If there were only three bulbs wired in parallel, could I refer to it as a three-ring circuit?

For whatever reason, there are nine light bulbs installed in our living room ceiling (three recessed, controlled by two different switches, and six on a zigzag-shaped fixture, controlled by a single switch). I clearly think this is an excessive number, as evidenced by the fact that, a few weeks ago, I was working away happily in what I felt was a perfectly adequately lit room. The SigFig then walked in, looked up, and pointed out that most of the bulbs in the fixture had burned out. A single light bulb soldiered on amongst its burned-out brethren.

I did what any scientifically-minded person would: I started thinking about circuits.

Anything that runs on electricity contains some form of circuit. Simple circuits consist of electrical energy sources (such as batteries or home electric grids), resistors that transform that electrical energy into other forms of energy (such as heat and light), and wires to connect these elements. Circuit diagrams show how the parts of the circuit are put together.

BasicCircuit

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Up, down, on top, on bottom, strangely…

…and with charm.

You’ve probably noticed that I like puns; when I spent a lovely Saturday afternoon participating in a charm bracelet walk with a couple of friends in nearby Snohomish, a certain quark pun of questionable propriety ran through my mind. However, what really got my science-gears turning was the sight of skydivers as they descended into the nearby fields.

Air resistance is a topic I’ve tackled on many different occasions, including a post on this very blog. (If you haven’t tried the activity described at the end of the post, go for it now!) Parachutes work because air, being a fluid, exerts a force on objects that move through it. As the surface area of an object increases, the air has more space to push on it, thus increasing the total force exerted on the object. A parachute has a large surface area and a relatively low mass, meaning that the large upwards force due to air resistance is only minimally canceled out by a smaller downward force due to gravity. After a quick review of freebody diagrams, we can see that the net force on the parachuted skydiver is actually upwards, yet he continues to move downwards.

This counterintuitive detail trips up many students. What we have to remember from Newton’s Second Law (Force=mass*acceleration) is that our net force shows the us the direction of our acceleration, not our motion. Let’s define the downward direction to be positive. An upward net force indicates a negative acceleration; since acceleration is a measure of how quickly an object’s velocity is changing, and our skydiver is not changing direction, a negative acceleration represents a reduction in speed. Our analysis of the forces shows us that the skydiver is slowing down, and that’s exactly what we see.

You can experience this phenomenon even if you have a fear of heights. Like air, water is a fluid and exerts a force analogous to air resistance. Tape rocks or small weights along one edge of a clean trash bag. Take it to a pool (preferably one owned by friends of yours) that is about five feet deep (four, if, like me, you are a shade under five feet tall). Start running through the pool, then spread your arms out and hold the trash bag behind you, weighted end down, like a cape. The water will exert a force on the trash bag and you’ll slow down.

(This should go without saying, but PLEASE don’t try this unless you have permission.)

I knew from a young age that we had chemistry together…

…or at least that we took chemistry together. It’s the SigFig’s 30th birthday, and, while we’ve only been dating for a few years, we’ve actually known each other since high school. We took a handful of classes together, one of which was chemistry, and his milestone birthday has me feeling nostalgic.

One of the first labs we did in our chem class was the classic separation lab. You start with a mixture of substances such as salt, iron filings, and sand, then plan and execute a procedure to separate the substances. It was really a lab preparedness warmup: the activity helped students learn about lab safety and how to develop and follow procedures. In retrospect, I’d classify it as more of an engineering activity than a scientific investigation.

The primary difference between science and engineering is that the goal of science is to answer questions (What does the structure of an atom look like?), while the goal of engineering is to solve problems (How can airplanes become more fuel efficient?). There’s definitely a lot of overlap, and progress in one field is frequently dependent upon progress in the other. Scientists use tools that engineers build, and engineers use scientific discoveries to build new things.

The SigFig became an engineer, so I guess something from that class stuck with him. (Besides me, of course.)

Scientific Pet Peeves #2: To paraphrase Dr. Seuss…

…a fraction’s a fraction, no matter how small. It’s mildly irritating that many people seem unaware of this.

To fill the silent void of an empty house during this stint of unemployment, I’ve been rotating through the options that YouTube, NetFlix, Hulu, and various network sites have to offer. Nothing too heavy; it’s generally just background noise as I work on job applications, knit, write this blog, etc. You may recall that I’m a huge fan of game shows and cooking shows, and Food Network’s Cutthroat Kitchen fills both of those niches nicely.

If you’re not familiar with the premise of the show, four contestants each have $25,000 to bid on opportunities to sabotage their opponents. After each round of cooking, one contestant is eliminated until the last chef standing wins the amount of money he/she has remaining. To add a bit of dramatic flair (and likely a bit of a psychological element), the contestants are issued their auction money in the form of 250 hundred-dollar bills.

Naturally, many of the contestants are giddy at the opportunity to hold that amount of cash: “I’ve never held this much money before, not even a fraction of it!”

Um, yes, you have. Have you held a one dollar bill? Then you have held a fraction of 25,000 dollars: 1/25,000. A fraction is just any portion of a whole, regardless of how small. (It can even be more than the whole, if you’re willing to get into improper fractions.)

A child holding his or her first penny still has a fraction of 25,000 dollars, even if it’s a little trickier to convey. A penny is generally expressed as .01 of a dollar, so we could write the fraction as .01/25,000. However, fractions are more intuitive when there are no decimals within them; .5/2 is equivalent to 1/4, but the latter is much easier to picture. To get rid of the decimal in that case, we multiplied the top and the bottom by 2. (Recall that 2/2, 3/3, 42/42, etc., are all equal to one, so multiplying by them does not change the value of the fraction.) Since .01 x 100 = 1, we can multiply the top and bottom of .01/25,000 by 100 to get 1/2,500,000. It’s a small fraction, but a fraction nonetheless.