Singularities and my daughter’s head

I am still quite overwhelmed with returning to work. I am finding it difficult to balance teaching, which really takes as much time as you are willing to give it, spending quality time with my daughter, and finding time for my own interests (am I allowed to have those anymore?).

While I am not quite ready to get back to blogging about Physics and my little girl, I saw an article in the New York Times, courtesy of a facebook post from the Agnes Scott College Math Department.

The article, entitled Singular Sensations has a really interesting description of singularities and how they relate to our life, including the back of my daughter’s head:

Check it out and I will be returning soon to talk more about Physics and my daughter and probably my teaching as well…

Crawling and electrical outlets

My daughter has just started moving. We are fortunate that she started moving later than some other babies we know.  We have had a blissful 10 months of not having to chase after her and put up gates in the house. Alas, that is all over now.

She is not crawling exactly, but she scoots forward. She reaches forward onto her hands while sitting and uses one leg to pull herself forward and drags the other leg behind. I have seen many of her cousins doing something similar, at pretty high speeds. This may turn into a standard crawl someday soon, or maybe not. Either way, she is definitely moving around, and faster every day.

Last week, I put her down on the floor in the bedroom so I could pick up some clothes to do some laundry. She usually goes straight to playing with our window shades, which is relatively safe. That day, though, I turned my back for just a second and she went straight across the room to the electrical outlet. Yikes! I had not yet put the safety plugs in upstairs. It is crazy how she always goes straight for the electrical outlets. They are right at eye level and are apparently quite fascinating.

So why are electrical outlets so dangerous for little ones?

First of all, can she even get her little fingers in those tiny little holes? In order for an electrical connection to be made, she needs to touch the metal connections. Even with her very little fingers, I do not think she could get them into the outlets. That being said, I certainly do not want to let her try!

I think the real danger is probably having her put one of her toys into the outlet and making an electrical connection that way. Many of her toys are plastic or rubber right now, which do not conduct electricity effectively, but she does love to play with metal things. Also, she gets into everything now that she is mobile and I let her play with anything that does not seem dangerous, so it is not unlikely that she would find something to put into that outlet.

What happens if she does manage to get something into the electrical outlet (finger, fork, etc.)? The outlet has 120 V of potential – that means that it has energy that is ready to start flowing. If you ‘complete the electrical circuit’, i.e. give that energy somewhere to flow, it will start flowing – through you.

So how much current will flow through your body if you touch an electrical outlet and what is a dangerous level? Ohm’s Law tells us that voltage, V, (that 120 V for a standard household outlet) is related to current, I, and resistance, R, through the following equation:

The amount of current that flows through us depends on our resistance to that current.

So what is our resistance? That turns out to be a complicated question because it depends on things like how dry (or wet) our hands are, and how much contact we make with the metal wires. If we connect with the wires over a large area of our bodies, our resistance is lower – it is easier for current to flow through us.

Dry skin has a larger resistance than wet skin. This is fortunate for me as a teacher. I accidently shocked myself with a 500 V source in the lab once, but my hands were covered in chalk and the contact between my hands and the wire was small. It was definitely not a pleasant shock, and I felt dizzy for a little while after, but there was no serious or permanent damage. On the other hand, I have also shocked myself on a 120 V outlet in a lab (no chalk) and it was quite painful. Who knew the life of a physicist could be so dangerous?

But I have not answered the question. What is our resistance? I had my students measure their resistance in a teaching lab using very small metal probes (small area of contact). They measured from one hand to the other and found that they had a resistance of about a megaohm – that’s one million ohms. However, an article on Electric Shock on Wikipedia cites the International Electrotechnical Commission as showing adult resistances at 100 V of ~2000 ohms. They use larger contact areas, but you never know when you shock yourself how much contact you will have, so it is much safer to assume your resistance will be low.

Okay, let us assume, to be safe, that our resistance is about 2000 ohms and the voltage of the outlet is 120 V. From the equation above (Ohm’s Law), we can calculate that this situation would send 60 milliamps (mA) of current through us. That does not sound like a lot, right? Well, an amp is a LOT of current. The same Wikipedia article cited above states that humans can feel 1 mA of current. Currents as low as 60 mA (and sometimes lower) can cause fibrillation of the heart muscles, which can lead your heart to stop.

Depending on the voltages and contact situation, electrical shocks can also cause serious burns. I had minor burns on both hands when I was shocked by the 500 V lab source. (I should note that I am always very careful around electrical sources and in both cases of being shocked, I was working with wires that had been previously damaged  – a good example of why you should always have broken or old wiring repaired immediately.)

Okay, I am convinced. I should cover up my outlets and keep my daughter safe! So far we have just put in some standard outlet covers, though I have read in several places online that these covers are too easy for toddlers to remove. Fortunately, my daughter is too young to have figured that out yet (and trust me, she has tried!). As she gets older, and stronger, and more coordinated, and smarter, we may have to come up with better ways to keep her safe.

We are definitely entering a new stage of parenting. It is amazing to watch her learn to move and explore her world and I am very much enjoying it, but with every new development comes new challenges.

Jingle Cubes

We had some visitors come and stay with us last weekend. My daughter is really wary around strangers, so I was very happy that she handled the visitors so well. She relaxed enough to stop giving them the evil eye and went on to smile and play with them some. At one point, one of our visitors mentioned what a nice set of alphabet blocks she had and I was so confused. My daughter doesn’t have any blocks.

I looked up and responded, “Oh, you mean the jingle cubes.”

My husband and I discussed at one point that normal parents probably don’t refer to their child’s toys by the proper geometrical shapes. But these are clearly cubes:

And these very beautiful jingle cubes (they each have a bell inside them so they jingle when my daughter shakes them) were made for us by a mathematician, so I think we should call them cubes.

Of course, geometry has never been my strong point, so I may have to do some research if I want to continue this trend of calling her toys by their right names.

We definitely have spheres (left below), cubes (above), and cylinders (right below) of many different types. Here are a couple:

And of course, it will be important for my daughter to know that this is a ‘truncated icosahedron’: (Mathematica Website)

 It has 32 faces and is apparently also the shape used for soccer balls. So this seems important for her to know, right?

My daughter does not have a set of blocks yet, but we are hoping to get her a nice set of wooden blocks, maybe for her birthday. I think I may have to just resort to calling them blocks unless some of my mathematician friends can help fill in the empty place in my brain where geometrical shapes should go.

Of course, at some point, I think we should just call a giraffe, a giraffe and not worry about its shape:

For those of you who are physicists out there, you know that geometrical shapes are not really important since we tend to approximate chickens as point particles and cows as spheres. Anything else is too complicated for us.  For those of you who are not physicists and wonder why we care about chickens and cows…well, I am not sure I can explain physics humor, but we think it’s funny. Ah, my poor kid is going to be so embarassed by her mom.

The jingle cubes will always be jingle cubes, though. And they have been a favorite of my daughter’s for a long time. First, they were so big, she needed both hands to grab them and they helped her learn hand coordination. Then, she loved to chew on them (like everything else). Then, her hands grew and her coordination improved so that now she holds one in each hand and shakes them and knocks them together to make music. Maybe soon she will start to stack them, and then (in the distant future) use them to spell words. They really are fantastic, multipurpose jingle cubes.

Baby Thermometers

Babies have very limited methods of communicating what they want or what is wrong with them. Crying can mean any number of different things. At this point, I am fairly good at figuring out when my daughter is tired or hungry or upset about strangers or just bored. However, sometimes she just cries and gets very upset for no clear reason and it is difficult to figure out what is wrong.

A couple of weeks ago, my daughter was very fussy and needier than usual and just refused to nap. After a while, I decided that there was definitely something wrong and that she seemed sick. One of the main tools for determining if our child is sick is our thermometer. Being a scientist (or a geek, if you prefer), I am of course interested in how different thermometers work and how they measure my daughter’s temperature.

While it seems that there are a wide variety of baby thermometers – ear thermometers, rectal thermometers, under arm thermometers and forehead thermometers – the most common types fall into just two categories of operation. The rectal and under arm thermometers use contact between the skin and a metal component on the thermometer to read temperature while the ear and forehead thermometers use the radiation emitted by your baby’s body to calculate temperature. These thermometers use very different techniques to measure temperature than the bulb thermometer many of us grew up with.

Contact Sensors

The metal contact sensors are most commonly electrical sensors. There is a thermistor in the metal detector portion of the thermometer. This is a resistor that changes its resistance depending on temperature. To understand how this works, we need to think about some simple electronics.

Consider a very simple electronic circuit like the one below:

A battery provides a voltage – 9 Volts in this picture. A constant current travels around the circuit because there is just a single path through the loop. An ammeter is a device that is used to measure the current – this is a measurement of how much charge passes through that point in a given amount of time.

Ohm’s Law tells us that voltage, V, is related to current, I, and resistance, R, as follows:

So what happens when my resistor is sensitive to temperature? When you put the resistor in contact with your body, it heats up and its resistance decreases. The battery voltage stays constant, so as the resistance decreases, the current through the system must increase. This makes sense, right? If there is less resistance to the flow of charge, more charges will pass the ammeter in a given amount of time.

By measuring this current, and knowing the voltage of the battery, you can easily calculate the resistance of your temperature sensitive resistor using the equation above. The resistance vs. temperature is something that is very well known by the manufacturer, so once you know the resistance, you know the temperature of your baby who is in contact with the thermometer.

The circuit in your thermometer has a few more components, but this basically how it works. And it does all the calculating for you and just displays a temperature.

Infrared Sensors

If you bring your child to the doctor’s office, they will likely take his or her temperature using an infrared sensor. This is what my nurse uses. She takes a device with a flat, round end and lightly moves it across my daughter’s forehead and reads out the temperature. This is very fast and is great for a kid (like mine) who hates to be touched by strangers.

How does this work? If you remember, a few weeks ago, we talked about Blackbody Radiation. Our bodies emit light, but it is in the infrared where we cannot see it with our eyes. The peak wavelength emitted from our bodies is about 9 microns (Check out the PhET website to see for yourself). The amount of light and the peak wavelength of the light both depend on the temperature of our bodies.

The thermometer uses a thermopile to measure the radiation coming from our bodies (How Stuff Works). Heat from our bodies heats two pieces of metal that make up the thermopile. A voltage is created between the pieces of metal that depends on the heat of our bodies. (Wikipedia)

How do we measure this voltage and turn it into a temperature? We could use the same circuit that we used above. This time, have a constant resistor and use the thermopile as our voltage source. We can measure the current to determine the voltage created by the heat from our bodies and determine the temperature from that voltage.

The infrared sensors are very fast, which is definitely a plus with a screaming, squirmy baby. Both types of thermometers work best when the temperature is taken inside the body – a rectal thermometer or ear thermometer. However, we were discouraged by the hospital from using a rectal thermometer on a newborn because they said it is to easy to cause them harm because they are so tiny. And ear thermometers can be a little tricky because they need to be aimed at the baby’s eardrum to get an accurate reading.

We have one of the forehead thermometers at home so I definitely wanted to make sure I understand how they worked. It turns out my daughter did not have a fever when she was sick a few weeks ago. I did take her to the doctor, though, and she did have an ear infection. The poor kid was sick for a while since the first set of antibiotics did not work on her, but is feeling better. And is now fussy for some other completely unknown reason…

I hope my daughter continues to be healthy and not have any fevers, but I do think it is interesting to know how current thermometers make use of technology to help me figure out what is going on with my little girl.

And, of course, I am looking forward to the time when she can tell me what is wrong and there is a lot less guesswork in trying to figure out if she is sick.

Babies in motion

It is amazing how much of introductory Physics we all learn before we turn one year old. We learn it so well and internalize the information that we forget that we even know it. It is just a part of our core knowledge, like breathing and eating (other things we learn as babies).

My daughter is just learning these things for the first time. She is just beginning to explore motion. Here are some of the things that she has learned so far:

  • The smooth floor at mommy’s yoga class is good for sliding on. You can scoot while sitting up to get closer to the good toys (like yoga blocks and straps).
  • The rug is best for rolling over and standing up and sitting up.
  • The counter is not good for standing up on.
  • Sitting can be accomplished by either pulling on mommy’s hands, or both pushing on the floor and pulling on something.
  • Rolling is easiest if you first push up on your arms, or push your butt up into the air, or kick your legs up into the air.
  • Small things move when you pull on them. Parents and furniture do not.

Friction and Forces

So, my daughter has learned all about forces & friction: The smooth floor at the yoga studio has very small coefficients of both static and kinetic friction – that means it is easy to get things moving and keep them moving. In order to move, she needs to apply a force that is larger than the force of friction in order to accelerate from her current position.

One of the first things we learn in Physics is that the sum of all the forces on an object  is equal to the mass of the object (mdaughter) times its acceleration (adaughter). My daughter needs to scoot with a force greater than that of friction, and then her movement will be governed by the following:

The harder she pushes off (larger Fdaughter­), the faster she accelerates. Or if the force of friction is smaller, it’s easier to move. That’s why she can scoot on the smooth floor but not on the rug yet. Her small mass also makes it easier. I have to push much harder to scoot on the floor than she does, but then again, I’m a bit stronger as well.

Okay, so sliding is easiest on surfaces with less friction – smooth floors, countertops, icy surfaces, etc. But sometimes sliding does not help her in her attempts to move.

When she is trying to stand, she needs her feet to stay still (not slide) while she pulls up. When she’s sitting on the counter and she pulls on my hands, she just slides instead of standing up. So, for standing, she needs a big friction force.

Newton’s Third Law

She has just discovered that pulling up on my hands seems to be similar to pushing down on the floor. Why? Newton (he was a smart guy) said that every action has an equal and opposite reaction. When she pulls down on my hands, my hands (without me moving) pull up on her. That helps her sit up. When she pushes down on the floor, the floor pushes up on her, also helping her to sit up.

Of course, if she pulls on smaller objects or objects that are on a smooth surface, sometimes they move! That’s just friction again – the force of friction is directly related to the weight of the object. Heavier objects experience have a bigger friction force keeping them immobile. Lighter objects experience less friction and so it takes a smaller force to get them in motion.

It is a common misconception that she can pull lighter objects because she pulls on them harder than they pull back. That’s never true. The forces are always equal and opposite. When my daughter pulls an object to her, it is because the force of her pull is greater than the force of friction (or other force) holding the object in place.

Rolling

My daughter has been rolling over for quite some time, but she’s always hated to be on her belly, so she refused to roll onto her belly. And she was so unhappy when on her belly that she just cried instead of thinking to roll onto her back.

In the past couple of weeks, though, she has remembered that she can roll over. She stays on her belly exactly as long as she wants and then rolls over. She’s also realized that she can continuously roll over and over again to move across the room. (Crawling on her belly has occurred to her but she has not yet discovered how to make that work).

We know that we need a big force to move in a line. My daughter needs to learn to push or pull (or kick) off with more force in order to scoot along or crawl. What about rolling? Is it just a matter of force? How do we rotate?

Think of opening a door. When you push a door open, it matters both how hard you push the door and where you apply that force. If you try to open a door by pushing on it very close to the hinge, you have to push very hard to get it to open. But if you push on the edge of the door furthest from the hinge, you do not have to push very hard at all. So rotating objects seems to depend on how hard you push (or pull) but also where you apply that force – how far from the point of rotation.

When my daughter lies flat on the ground and tries to roll over, she doesn’t go anywhere. She would have to have very strong abdominal muscles to make her body rotate – the force of her abs is applied very close to her center of rotation.

But she’s too smart for that. She’s already learned about torque (force times distance from axis of rotation) and gravity. So, when on her back, she kicks her legs up in the air (and sometimes her arms too), rotates just a little bit and uses gravity to make her legs and arms fall to the side and bring her around all the way. When on her belly, she can push up on her arms first, then just push off a little on one arm and her body falls to one side and rolls back over (kicking your butt up in the air and kicking off works just as well). She has already learned that she needs a lever arm to rotate. What a smart kid. 

Physics in Motion

My daughter has not yet mastered the art of motion, but she learns more about it every day. She is quickly mastering the Physics involved and will soon be ready to study energy, power, fluid motion, electricity and magnetism. By the time she’s five, I imagine she will be doing her graduate work in Physics. Or perhaps, she will be done with that and have moved on to learning new languages and cultures by then.

I love to watch her learn. If only we could all learn with the wide-eyed, fearless innocence of a baby. Not to mention the amazing brain capacity to learn a hundred new things every day. I guess if my brains were working at that speed all the time, I would also need two naps and eight meals a day.

The Conclusion to the Great Nightlight Mystery

Three weeks ago, we embarked on the Great Nightlight Mystery: Why does my daughter’s nightlight turn off in sunlight, but not when I turn on the overhead light?

First, we looked into how a spectroscope works so that we could investigate the different spectra of the lights in my house. We discovered that incandescent light bulbs contained all of the colors of the rainbow, much like the sunlight that comes through my windows. This is because sunlight and incandescent bulbs are both examples of blackbody radiation. The fluorescent bulbs, on the other hand, were only made up of a few colors of the rainbow, through when combined, the light still looks white. Finally, we looked into how the LED nightlight itself works and what colors of light is puts out.

So where does all this leave us? Let’s look at a summary of the spectra, or color outputs, of the different lights in my house:

The nightlight must have a photodetector – this is usually a semiconductor material that detects light. Just like the materials that emit light of only certain colors, this photodetector can be designed to only detect light of certain colors. My theory (I don’t know for sure) is that the detector was picked so that it would not detect light from the LED nightlight. It would then only be affected by outside light.

We checked this – our external bright LED light did not seem to affect the nightlight (turn it off) unless the nightlight was very close to the LED light bulb. The same is true for the fluorescent bulbs. However, a small amount of incandescent light or sunlight will turn the nightlight off.

Looking at the spectra above, it’s difficult to see why this is. I thought originally that the dip in light from the LED – the 500 nm blue region must be the light that the detector is sensitive to. However, the fluorescent bulb has light there. Perhaps the detector is sensitive to light in the bluish-green – that narrow area where neither the LED or fluorescent bulb emit light? I would need more information on the detector or some more sophisticated equipment than I have in my house to be sure.

The detector does seem to be wavelength dependent, though. It seems to be a poor design to me that it does not turn off in the presence of fluorescent light bulbs since many homes are switching over to fluorescent bulbs as a more efficient alternative to incandescent bulbs. In fact, there are new standards in the US designed to help phase out the inefficient high wattage incandescent bulbs. You can read more here. Since many of the more efficient light bulbs are compact fluorescents or LED light bulbs, my daughter’s nightlight will not be very useful in most houses – it will always remain on. Of course, if I open the shades, the sunlight will turn it off. I suppose the most efficient lighting will always be sunlight anyway, especially in very sunny Colorado.

What does this mean for you and your house lights? You will need to make choices between brightness, color, efficiency and cost. Sunlight and incandescent bulbs are probably easiest on your eyes, but new, better compact fluorescent bulbs and LEDs have better spectra and are much more efficient. Here are a couple of things to keep in mind:

  • BRIGHTNESS: We are used to thinking of brightness in Watts, but really that has nothing to do with brightness. The Watts are just a measure of how much power is required to run a traditional incandescent bulb. The unit of measurement ‘lumens’ is a more appropriate measurement of brightness. The Department of Energy provides the following graph to help you convert between the two:

  • COLOR: The new lighting label on the left above also includes a section entitled “Light Appearance.” This compares the light output to the light output of a blackbody of a certain temperature. If you remember from our discussion of blackbody radiation, a higher temperature means light that is more blue and less red. From the PhET simulation website on blackbody radiation, we see that the temperature of a typical incandescent is about 3000 K, and sunlight is approximately 5700 K. This can help you find a bulb that is more red (warm according to the label) or more blue (cool on the label) depending on what you prefer.

Of course, as we can see with our little handheld spectrometer, none of the lights are quite as good as just opening the shades on a sunny day – that has the best color and uses the least energy, but it is not always an option (especially at night!).

  • EFFICIENCY & COST: The new lighting label also includes an estimated yearly energy cost and lifetime. With that and the cost of the light bulb, you can figure out which light bulbs are most cost efficient. Of course, if saving energy is more important to you than saving money, you may just go with the most efficient option.

Hopefully you enjoyed our light filled April and now feel confident in your knowledge of light bulbs. I at least better understand my daughter’s nightlight and realize that if I want it to turn it off with the room lights on, I had better get an incandescent light bulb, open the shades or possibly explore different compact fluorescent and LED light bulbs until I find ones with the appropriate color spectrum.

The Great Nightlight Mystery, Part IV: Light Emitting Diodes (LEDs)

Two weeks ago, we embarked on the Great Nightlight Mystery: Why does my daughter’s nightlight turn off in sunlight, but not when I turn on the overhead light?

First, we looked into how a spectroscope works so that we could investigate the different spectra of the lights in my house. We discovered that incandescent light bulbs contained all of the colors of the rainbow, much like the sunlight that comes through my windows. This is because sunlight and incandescent bulbs are both examples of blackbody radiation. The fluorescent bulbs were only made up of a few colors of the rainbow, though when combined, the light still looked white.

This week, we are going to look into how Light Emitting Diodes (LEDs) are different (and similar) to the other types of bulbs in my house. With this information, we should be able to not only solve the Great Nightlight Mystery, but also understand why our eyes and our wallets prefer certain types of light bulbs.

If you recall from last week, fluorescent bulbs contain a gas of molecules that glow at very specific colors due to the molecule’s changing energy levels after a high voltage is applied. LEDs work on a very similar concept. They are solids, though, so the molecules work together instead of independently like they do in a gas. This causes some differences in the output light.

The atoms in semiconductors (the materials out of which LEDs are made) are in very close proximity and work together to form bands of energy. LEDs are formed by putting two semiconductors in close proximity, one that has an excess of electrons (negatively charged particles) in a higher energy band, and one that has an excess of positive charge, or holes where the electrons can fall into, in a lower energy band. Putting these materials together and applying a current causes the electrons in the higher energy band to fall into the lower energy band. Just like in the fluorescent bulbs, the excess energy is emitted in the form of light. The color, or frequency, f, of this light is directly proportional to the energy difference between the higher and lower energy bands:

The higher the energy difference, the higher the frequency, or the more blue the light that is emitted looks. The energy bands are wider in solids than in atoms, so the light emitted has a larger bandwidth – this means that a wider range of colors is emitted, but they are still very narrow band compared to sunlight.

You have probably seen quite a few LEDs as lights on electronics. They are most commonly green, blue, or red. But the LED nightlight in my house appears to emit white light. If an LED can only emit a single band of color, how do they make white LEDs?

I read an article recently in Optics and Photonics News that discusses the various ways of making good white LEDs and talks about whether or not LED lights are ready to take over the light bulb industry (Jeff Hecht, “Changing the Lights: Are LEDs Ready to Become the Market Standard?”, Optics and Photonics News, 23 (March 2012).).

From this article, I learned that one way to make a white LED is to combine three colored LED’s – red, green and blue – so that the result looks white. It is generally less expensive and more efficient, though, to use a single blue LED and a phosphor. The LED emits light at 460 nm (blue light). This light then hits a phosphor. The energy from the light excites the phosphor to a higher energy level (yes, just like the atoms in fluorescent bulbs and the materials in the LEDs) and then atoms then fall to a lower energy level and emit light. The phosphors used in white LEDs generally emit light over a fairly broad range, from about 500 to 700 nm. The white LEDs use the very energy efficient LEDs in the blue to provide the energy (and blue light) to then get the longer wavelength light from the phosphor. The resulting spectrum looks something like this (from Wikimedia Commons):


This graph shows a big peak of intensity at 460 nm due to the blue LED (made of gallium nitride (GaN) or indium gallium nitride (InGaN) in this case – those are the semiconductor materials that make up the LED). There is also a smaller, wider peak of light covering the other visible wavelengths from the cerium doped yttrium aluminum garnet phosphor (Ce:YAG).

There are a couple of interesting qualities of LEDs that we can figure out from this graph. First, they emit a lot of blue light, so they look pretty blue. There is also a dip of little light in the blue-green (around 500 nm) so they do not emit much light there.

Using different phosphors, or multiple phosphors can change the output light to make it look more like incandescent bulbs, which emit more red light and less blue light. Bulbs with better color outputs can be less efficient, though (information from Wikipedia).

I used my spectrometer to look at my LED nightlight and another LED light bulb that we bought because we were curious. Here is the picture of the spectrum (note the blue is on the right in this picture unlike the graph above):

We can see the bright blue on the right from the LED, then the dip in light between the blue and green, then the broad green-yellow-orange-red light from the fluorescing phosphor. Just like we expected. Cool!

LEDs are very energy efficient – more so than both incandescent bulbs and fluorescent bulbs, but they are also still fairly expensive to buy in the store, so it will cost quite a bit to replace all the bulbs in the house.

Now that we understand all the light sources in the house, we can figure out why my daughter’s nightlight turns off in sunlight but not in room lights. Coming up next…