# numerical

I can't let it go. There is more here to explore. First, I can't believe that I looked at braking and then turning but not turning then braking. And what about braking while turning? I will model braking and then turning - but it won't stop here.
Consider a few motions. I could turn and then brake (which I am looking in this post). Another option would be to brake and then turn. I already showed that this takes a longer distance than just stopping. Braking and then turning in general won't work. Suppose I brake and slow down to a certain speed. Now I am a certain distance away from…

I have seen several videos similar to this.
Real? Fake? How many tries did this take? Let the analysis begin. Before I do any analysis, let me state that I think this is not fake. I do not know that for sure, just my first guess.
How would I tell if it is real or fake? This is tricky. I can't really get a good trajectory of the ball to make some measurements on it because of the camera angle (next time people, make sure you set the camera up perpendicular to the plane of motion and far enough away to avoid perspective problems - thanks!) Really, the best I can do is to look at the…

(alternate title: how to make pretty graphs in vpython)
I am happy. Finally, I can use the visual module in python (vPython.org) and plotting with Matplotlib. Maybe this isn't such a big deal for many of you, but for me, it never worked until now.
In the past, I blogged about plotting in vpython vs. matplotlib. My conclusion was that it was easier in vpython, but prettier in matplotlib. So, why not just use matplotlib? There are a couple of things that make vypthon very attractive.
Vectors. Vpython has a built in vector class (or function - I don't know what I am talking about). There…

Title: Chased by zombies
When I heard word about the ScienceBlogs Zombie Day, I knew I wanted to participate with a post - but I had no idea what to do. My first thought was to somehow talk about living off the electric grid in the case of a zombipocolypse - you know, like how big of a solar panel would you need?
But you know what? Physics is difficult - but modeling is easy. How about I model something? How about a model for the motion of a zombie horde? This will be great.
Zombie motion model
What do I want in my model? What are the constraints? What real-life situations can I use to…

While I am still fresh on the Space Jump topic, let me take it to the extreme. Star Trek extreme.
SPOILER ALERT
But really, is this a spoiler alert if it is from the trailer of a movie that has been out forever? Of course, I talking about the latest Star Trek movie where three guys jump out of a shuttle and into the atmosphere.
So, in light of the Red Bull Stratos jump, how would this jump compare? First, my assumptions:
This Star Trek jump is on the planet Vulcan. I am going to assume this is just like Earth in terms of gravity and density of air.
The jumpers in Star Trek have on stuff…

A new video from the Red Bull Stratos Jump guys came out. Here it is:
This reminds me of an unanswered question about the Stratos jump that I didn't address on my last post on this topic. Commenter Long Drop asked about how much Felix would heat up as he falls from 120,000 feet. This is a great question. The first, off the bat answer is that he won't heat up too much. Why do I say this? Well, when Joe Kittinger jumped from over 100,000 feet and didn't melt. Still, this is a great thing to calculate.
How do you calculate something like this? I will look at this in terms of energy. For…

I already looked at ESPN's Sport Science episode where they calculate that Marshawn Lynch produces 54,000 watts when pulling some tires. Yes, that is way too high. However, what would happen if some was actually that powerful? What could that person do? How fast could they run 100 meters? That is what I am going to calculate.
First, I am going to assume that Marshawn has a mass of about 100 kg. Also, let me say that he can produce 54,000 watts no matter what his speed.
Take a short time interval. During this time, Marshawn will increase his speed from say v1 to v2 this would be a…

I happened to catch two parts of two different episodes of Meteorite Men - a show about two guys that look for meteorites. In both of the snippets I saw, they were talking about a debris field for a meteor that breaks up. In these fields, the larger chunks of the meteorite are further down in the field. Why is this?
Let me approach this first from a terminal velocity view. This requires a model for air resistance. I will use the following:
Where:
rho is the density of air
A is the cross sectional area of the object
C is a drag coefficient that depends on the shape of the object
v is the…

This is a requested post. Clearly, I do requests. The idea here is that I am going to give all the details needed to determine the equation of motion (and then model it) for a basic pendulum. Warning: this post is a little more advanced than my normal posts. There are some prerequisites. You need to understand derivatives. I will assume that you do. Here is a pendulum. (and this time I will stick to my variables)
Like I said before, this is a tricky problem unless I use some tricks. The problem is that the tension the string exerts on the mass changes. Here is my trick: think about a…

Looking back at part I of this idea, I don't think I did a very good job. Let me summarize the key things I wanted to say:
Normally, there are two ways of modeling the motion of an object:
Calculating the forces on the object and using the momentum principle or Newton's second law (which are the same thing). I called this the Newtonian way. The problem with this method is forces that constrain the motion (like the normal force). These forces have a variable magnitude to make the object stay on a particular surface.
Defining some variables that describe the system as it is constrained.…

This post has been sitting in my mind for quite some time. Really, it is about mechanics - not about pendulums. What is the goal in mechanics (classical mechanics, if you like)? Generally, it is to find out how something changes over time. If you could get an equation of motion, that would do it.
As Matt (Built on Facts) did a while ago, it can be shown that you can get the equation of motion for a mass on a spring with normal Newtonian mechanics or with Lagrangian mechanics. Let me summarize two different ways of looking at the motion of an object.
The Newtonian Way
Maybe that isn't the…

I already attacked the 2008 Punkin Chunkin Show. So, now I going to give the chunkers some tips. In case you aren't familiar, the Punkin Chunkin contest has teams create devices to launch a pumpkin. They have different categories, but I am going to focus on the air-powered devices. The basic idea is to make an over sized pneumatic potato gun. Here are the things I was inspired to think about.
It seems all the canons were aimed at about the same angle. Did they guess at the angle? Or is this trial and error? What would be the best angle for a pumpkin launch?
Does the optimal angle of…

I am sad to say the following comes from a school that I attended. This was from an alumni newsletter regarding the activities of one of the physics faculty.
"Since the time of Archimedes, sciences advanced along two avenues, through new experiments and through theory...."
I have a problem with just that first part, but it goes on:
"For many centuries, theoretical physicists devised clever mathematical methods to describe many physical phenomena, yet some of the most important ones - like the properties of matter, of proteins and living things, or of weather patterns - are far too…

If you didn't catch the latest MythBusters (yeah! new episodes), they did something straight from the physics textbooks. Just about every text has this example of shooting a bullet horizontally and dropping a bullet from the same height. The idea is that they should hit the ground at the same time. No one but the MythBusters could actually show this demo with a real gun.
The Physics
I am going to do some calculations, but I want to first write about the physics that accompanies this idea (and you can actually do it your self without the gun). What physics principle does this demo show?…

There were a couple of things that bothered me about the MythBusters' myth where they fired bullets in the air. The myth was that a bullet fired in the air could kill you. The first problem is that it is not a myth. There are several reported cases of people being killed from bullets that were fired in the air. The Mythbusters tested this by finding out how fast a bullet would be going if fired straight up. A couple of problems:
First, they measured the terminal velocity of a tumbling bullet, not a spinning one. I really don't know how long a bullet will stay spinning, but I guess this…

You know I like the Mythbusters, right? Well, I have been meaning to look at the shooting bullets in the air myth for quite some time. Now is that time. If you didn't catch that particular episode, the MythBusters wanted to see how dangerous it was to shoot a bullet straight up in the air.
I am not going to shoot any guns, or even drop bullets - that is for the MythBusters. What I will do instead is make a numerical calculation of the motion of a bullet shot into the air. Here is what Adam said about the bullets:
A .30-06 cartridge will go 10,000 feet high and take 58 seconds to come…

I have been reflecting on my recent failure to realize that the Giant Water Slide Jump was fake (more analysis here). I think the guys that made this video did a really good job on several levels. First, the motion appears to do two important things:
shows constant acceleration in the vertical direction
shows constant velocity in the horizontal direction
That seems like such a simple thing, but it is surprising how often fake videos don't have those two elements. Maybe they were not close, but with the error associated with the panning and zooming camera, it seemed close enough. Also, to…

Every introductory astronomy text and most intro physics texts talk about tides. The usual explanation is something along the lines of:
The moon exerts a gravitational force on the Earth and all the stuff on the Earth.
This force decreases with distance (1/r2).
Thus the moon pulls greater on one side of the Earth than the other
This doesn't matter except for oceans which can move.
BOOM. Two tides a day due to a bulge on the side close to the moon and the opposite side.
Oh, the Earth is slowing down.
Really, that is what almost all intro texts say. Go check for yourselves.
Yes, the tides…

I created another screen cast showing how to get started with a numerical calculation for one of my classes. In this case, the students are attempting to model the motion of an object falling with air resistance. The following example doesn't show the steps including the air resistance, but maybe it is enough to get someone started.
Record your screencast online

Here is another one from a great podcast - Buzz Out Loud. I totally can't remember which episode it was, I listened to a several in a row mowing the lawn and doing outside type work. Anyway, the discuss was along the lines of:
Could an iphone tell if your parachute didn't open with its accelerometer?
The first and simplest answer would be "no". When you are skydiving, you quickly reach terminal velocity such that you are no longer accelerating. Maybe the built in GPS could use elevation data, but it seems like that is rarely used (and not very accurate). There is perhaps a way that work…