Friday, July 12, 2013

Why is it deadly to hit concrete when falling from a high place?

This one goes back to a central concept in physics called the impulse-momentum theorem. The impulse momentum-theorem relates a change in velocity with the force that causes this change in velocity.

Warning: What follows is a little graphic.

Say suicidal Johnny leaps off a tall building. On his way down, Johnny speeds up and gains a lot of momentum. When he hits the ground below, he stops suddenly. His momentum goes from a large amount to zero. This happens because the ground exerts a large impulse on Johnny. That impulse is equal to the force the ground exerts on Johnny times the amount of time it takes for the ground to stop Johnny. The latter is very short, as unlike a mattress, concrete is hard. Johnny stops over the course of a few milliseconds. The force from the ground has to be very large in order to compensate for the tiny time interval and still provide the impulse needed to stop Johnny's fall. The force is so large that it causes all kind of damage to suicidal Johnny's body.

Related post: How do ducklings get away with falling from great heights without getting hurt?

Monday, July 1, 2013

Why do golf balls have dimples?




Golf balls have dimples so that they are less sensitive to air resistance and go further when hit. You might think air would flow more easily around a smooth ball and so such a ball would cut through the air more easily. But that is not the case.

A smooth ball carries around itself a pocket of still air. Around that, there is turbulent air. A small bug on the surface of a smooth ball is actually protected by this thin layer of thin air and will not feel a wind as the ball flies. This layer of thin air increases the effective size of the ball and a larger ball has a harder time cutting through air. It will not be able to fly as fast and won't go as far.

A dimpled ball creates air turbulences around itself as it cuts through the air and so it doesn't have this handicap of looking like a bigger ball. It cuts through air more easily and goes further.

Reference:
The Physics of Baseball: Third Edition, Revised, Updated and Expanded, 2002, Robert Adair

Friday, June 14, 2013

Why is it so much more miserable in the summer when it is humid?

"It's not the heat, it's the humidity." Well, really, it's both. The heat makes it necessary for the body to cool off, while the humidity makes the process difficult. The inability to cool off is what makes it feel so uncomfortable when it's hot and humid. In a related post, I talk about how sweating is an efficient way to draw heat out and away from the body. The mechanism works best when the sweat can evaporate off of the skin quickly. The evaporation process is what takes the heat away from the body. When it is humid, the sweat has a hard time evaporating and instead sits on the skin. It no longer helps us cool, or at least not very much. All it does is make us feel gross. Meanwhile the body still wastes water producing sweat (more of it in fact, in a doomed effort to speed up the cooling process), so one has to drink a lot, even if it may feel like simply breathing should supply all the water we need.

An aggravating factor on hot an humid days is that the water vapor in the air traps the heat from the Sun. Water vapor is an often ignored, but effective green house gas. When the air is dry, the temperature drops quickly at sunset and nights are cool. Hot and humid days tend to stay hot even after the sun goes down (love those muggy nights!). The lack of relief in the evening and overnight makes it that much more miserable.

Saturday, June 1, 2013

Why do we sweat when we are hot?

While it feels gross, sweating is an effective way of cooling down the body. It utilizes the difference in thermal energy contained in a liquid versus that contained in a gas. A gas contains more thermal energy (because the gas molecules move fast) than a liquid. Therefore turning a liquid into a gas requires an input of energy.

When it's hot, our body wants to expend some thermal energy so it can cool to a comfortable temperature. When sweating, our body takes some of our water and puts it out on the skin, where it comes in contact with air. In air, the sweat evaporates. The water turns into water vapor, from its liquid form to its gas form. This requires an input of thermal energy, which our body is happy to provide. The water vapor floats away, carrying that extra energy with it and helping us keep cool.

To replenish the sweat, we need water and that is why when it's hot, we feel thirsty and have to drink a lot of water.

Tuesday, May 21, 2013

Why does water at 95 degrees Farenheit (35 degrees Celsius) feel cold when air at the same temperature feels hot?

The simple, somewhat dumb answer to that is that water is more effective at cooling the body than air.

95 degrees Farenheit is lower than body temperature so heat will naturally flow from the body into the surroundings, resulting in a cooling of the body. Both in air and in water, it is movement of the surrounding medium that helps the transport of heat from our skin to the surrounding air or water. In water for instance, 95 degree water comes in contact with our 99 degree skin. There is a heat exchange where the water warms up and the skin cools. The heated water then moves away and gets mixed with the rest of the cooler water, while heat from within our body rushes to the skin to warm it back up again. The cycle then begins again.

The difference between water and air is that the process is much more rapid in water than in air. Warmed air sits on the skin for a lot longer than the warmed water. So it takes a lot more energy from our body to maintain the 99 degree temperature in 95 degree water than it does in air. As a matter of fact, the cooling process in air is so inefficient that with 95 degree surrounding air, our body fails to cool if we exert ourselves and moving around feels uncomfortable. We start sweating in an attempt to remove heat from our body faster.


Wednesday, May 15, 2013

Isn't there a better way to pick reading glasses?

OK, this one is not a question a 3-year old would ask, but more like a 40 year old with (until then) 20/20 vision would ask. It is a question that cropped up in my life very recently for which some simple physics comes VERY handy.

Most people develop presbyopia somewhere in their late thirties to early forties. The eye loses its flexibility and the ability to adjust the lens for near vision. Seeing far is still OK, as that is the eye's relaxed position. That is when one has to go shopping for reading glasses. Reading glasses, like prescription lenses, are rated by their power, which is just 1 over the focal length of the lenses.

I found lots of websites with reading charts to help me pick the power of my reading glasses. I found these charts completely useless. The issue with them is that I can still focus, it just takes effort. It is only recently that I realized that the chronic fatigue and headaches I have been living with for a few months now were likely partly due to my declining eyesight. It's hard for me to tell which line of small characters on these charts I can no longer read. I can read all of them (especially when it is an easily recognizable sentence), it just takes increasing effort. How much effort is too much effort? I found that very subjective and could not decide.

When faced with a problem, a physicist goes back to the underlying principles. In this case, the thin lens equation:


f is the focal length of the lens and 1/f is the power of the lens (in diopters). Stronger lenses are more curved, have shorter focal lengths, and higher power. s is the distance between the lens and the object we are looking at, and s' is the distance between the lens and the image formed. Distances must be measured in meters. Translated to our problem:

The left hand side is the power of the lens, what we are trying to determine. s is the distance between our eyes and whatever it is that we are looking at: the book lying on the desk, the computer screen, a project in our hands. s' is a little more abstract, but translated to our problem, it is the distance at which we wish the thing we are looking at were. It is the distance that is comfortable for us. The book held at fully stretched arms length for instance.

In the case of reading glasses, s' must be entered as a negative number.

To find the power lenses that you need, do the following:
1) Determine s'. That is the toughest part. The goal is to find the minimum distance of comfortable focus. That is the s' we are looking for. To find it, stand at increasing distance from an object that has fine details on it. Start at reading distance. Relax your eye completely. You will see two objects. Slowly bring the object into focus until there is just one object. Go slow. Resist the temptation to bring the object completely into focus if it doesn't do that without extra effort. You will have to tune into your newly discovered lack of ability to focus and practice. If you do it right, you will discover with dismay that at reading distance, the object is all blurred. Progressively move away from the object until you can bring it into a single object and in sharp focus without strenuous effort.

That's your minimum distance of comfortable focus. Translate that distance to meters (or measure it with a metric ruler), put a negative sign in front of it, and stick it into the thin lens equation.

2) Determine s. s is I think pretty standard for everybody. You may need different power glasses for different purposes. For instance, if you are using your glasses to look at a computer screen on your desk at work, it's probably something like 0.50 meters away from your face (measure it). On the other hand, if you are working on crafts or reading a book, you are holding your work closer to 0.30 meters away from your face.

In my case, for instance, I have discovered that my presbyopia is more serious than I would have thought for something I was not noticing or at least misinterpreting as tiredness. My minimum distance of comfortable focus is around 1.5 meters. That is to say, holding things at arms length don't make it much more comfortable to read. In the thin lens equation, my 1/s' is -0.67. If your near point is greater than 5 meters (that is you can't find a point where it starts to be comfortable to focus), use 0 for 1/s'. It means your minimum distance of comfortable focus has moved to "infinity" and 1/infinity is zero (in physicist's math).

So for a computer screen fairly far from my face, the power I need is






Such glasses would be rated "+1.33" at the store. Ready-made reading glasses go in increments of 0.25, so I am somewhere between a +1.25 and a +1.50. I went with +1.25. The slightly lower power can be compensated for by moving my computer screen back some.

For close work, the power I need is







That is, glasses rated as close to "+2.33" as possible.

When you shop for reading glasses, you will notice that the maximum power is +4.00. This corresponds to someone who has a near point at infinity (the worse it can get), trying to look at work 0.25 meter (25 cm) from their face (the closest you would normally be looking at things). In many states, you can't buy reading glasses over the counter when they are much stronger than 2.75 diopters.

To summarize, the first term on the right hand side of the thin lens equation depends on what you are trying to do, while the second term depends on the quality of your eyesight. While determining s' is still subjective (that's the nature of the problem), I still prefer this method. Determining s' is a traceable source of uncertainty, while the reading chart is just complete black magic. I did find a use for the reading chart at the store, but not the way they suggested using it. I stood a reading distance away from the chart and tried the "comfort focus" method detailed above while wearing different strengths reading glasses. The ones that were the right ones brought the chart into sharp focus with the minimum of effort.

Saturday, May 11, 2013

Why is it not my birthday today?

I heard this one today at a birthday party. The conversation went like this (the little girl was watching the birthday girl unwrap her presents).

Little girl: I want a present too!
Mom: Not today.
Little girl: Why not?
Mom: Because it's not your birthday.
Little girl: Why is it not my birthday today?
Mom: ....

Yeah, I'm stumped too.