calculation
rallain | April 28, 2009In the second Cat in the Hat book (I think it is the second one), the Cat reveals that he has more smaller cats under his hat. They are labeled A - Z with Z being so small you can't even see. Question: What is the sequence of sizes for successive cats? How big would Cat Z be?
Here is the first picture that Cat reveals Cat A. It is not trivial to measure their relative sizes because they are in different positions. I drew two circles, one around each head and looked at the circle sizes.
So, Cat has a head that is 165 px tall and Cat A has a head 61 px tall. Let me call the total length…
rallain | April 21, 2009First: Car Talk is awesome. I wish I could come up with some class activities that help students become as good at trouble shooting and critical thinking as Tom and Ray are. Anyway, they are quite entertaining.
So, my Dad called and told me he heard a discussion on Car Talk about the effect DC to AC converters and accessories plugged in to it and how they would effect gas mileage. I skimmed through the last Car Talk podcast, but couldn't find it. He must have heard a re-run on the radio or something (he doesn't really believe in podcasts). Let me calculate the effect a number of things…
rallain | April 12, 2009I already talked about increasing the temperature of a pool. My father commented that he thought the pool level rose by like half an inch when the temperature increased (by about 10 degrees F). So, this leaves the question: Is my father crazy, or is this possible? Or are both true?
Does water expand when it warms up? Yes, except when it melts. Why does this happen? Liquids are actually very complicated, but here is a basic answer. Take a look at this PhET gas simulator, I know it is for gases not liquids. I think we can make it behave like a liquid if you increase the gravity to the…
rallain | April 11, 2009It is spring break, so we are at my parents house for a couple of days. The kids like it because there is a pool, a heated pool even. It really isn't that cold outside, but yesterday the water measured at 62 oF. So, with some help from the kids, we cleaned out the pool and turned on the heater. We also put a cover on it, hopefully to help it heat up some more.
This is perfect for a quick calculation. Is it reasonable that the pool could get up to a swimable temperature by tomorrow? Let me first make some assumptions and data:
15,000 gallons of water in the pool. This is about 57 m3.…
edyong | April 3, 2009
Say the word 'statistician' and most people might think of an intelligent but reclusive person, probably working in a darkened room and almost certainly wearing glasses. But a new study shows that a monkey in front of a monitor can make a reasonably good statistician too.
Tianming Yang and Michael Shadlen from the University of Washington found that rhesus macaques can perform simple statistical calculations, and even watched their neurons doing it. Psychologists often train animals to learn simple tasks, where the right choice earns them a reward and the wrong one leaves them empty-…
rallain | January 25, 2009When you pour a beer, there is this foamy top called the head. The size of the head decreases over time. What is this process dependent on? Clearly, little bubbles of beer are popping. Does each bubble have an equal probability of popping? Do only the bubbles on the top (or bottom) pop? I became aware of this idea from a colleague. Maybe he was going to do an analysis, but I haven't seen it yet. If you do (Gerard), I am sorry for doing this before you. This may have been investigated before, but in the spirit of re-doing everything I have not searched for previous beer head studies.…
rallain | December 29, 2008In part I of this post, I talked about the basics of projectile motion with no air resistance. Also in that post, I showed that (without air resistance) the angle to throw a ball for maximum range is 45 degrees. When throwing a football, there is some air resistance this means that 45 degree is not necessarily the angle for the greatest range. Well, can't I just do the same thing as before? It turns out that it is a significantly different problem when air resistance is added. Without air resistance, the acceleration was constant. Not so now, my friend.
The problem is that air…
rallain | October 14, 2008**Pre Reqs:** [Kinematics](http://scienceblogs.com/dotphysics/2008/09/basics-kinematics.php), [Momentum Principle](http://scienceblogs.com/dotphysics/2008/10/basics-forces-and-the-moment…)
What are "numerical calculations"? Why are they in the "basics"? I will give you really brief answer and then a more detailed answer. Numerical calculations (also called many other things - like computational physics) takes a problem and breaks into a WHOLE bunch of smaller easier problems. This is great for computers ([or a whole bunch of 8th graders](http://scienceblogs.com/dotphysics/2008/09/…
rallain | October 2, 2008Gas prices may be trending down, but they are still quite high. How can we save gas? One of my colleagues suggested we can save gas by getting rid of all drive throughs. This means it is my job to estimate how much could be saved.
**Starting Assumptions (estimations)**
How many drive-throughs are there in the U.S.A.? When I think of drive-throughs, I think of McDonalds. [Wikipedia](http://en.wikipedia.org/wiki/Mcdonalds) says there are 31,000 restaurants world wide. I am going to say there are around 20,000 in the U.S. that have drive-throughs. So then, how many total drive-throughs?…
rallain | September 28, 2008When mowing the lawn, I like to listen to podcasts. One of my favorites is [Buzz Out Loud](http://bol.cnet.com). This weekend, I was listening to episode 817 and one of the topics of discussion was MySpace and their DRM free music stuff. [Wired](http://blog.wired.com/music/2008/09/myspace-launche.html) had a description of what they were going to do. That is not my point. The point is the claim that you could make an infinite number of playlists. How about I calculate (or estimate) the number of different playlists one could make.
First, the idea behind the idea. Calculating the number…
rallain | September 26, 2008On a previous episode of The MythBusters, Adam and Jamie made a lead balloon float. I was impressed. Anyway, I decided to give a more detailed explanation on how this happens. Using the thickness of foil they had, what is the smallest balloon that would float? If the one they created were filled all the way, how much could it lift?
First, how does stuff float at all? There are many levels that this question could be answered. I could start with the nature of pressure, but maybe I will save that for another day. So, let me start with pressure. The reason a balloon floats is because the air…