# air resistance

You can call it football if it makes you happy. Anyway, this is a popular story going around. The physics of the magic curving soccer kick. Here are two ends of the spectrum.
First, there is the lower, easier to consume version from io9.com
Physics forced to come up with whole new equation to explain "impossible" soccer kick
I will summarize this article for you:
"Have you seen these crazy soccer kicks where the ball curves? It happens because the ball spins and physics. Here is a video"
Oh, and they have a diagram - which doesn't seem to come from the original paper and they also have…

You know I have trouble letting stuff go, right? I am still thinking about these crazy long basketball shots. Here are some more thoughts.
Really, there are two things I am interested in. First, commenter Scott Post suggests that the drag coefficient might be around 0.25 instead of 0.5. I don't know. For the discussion before, it doesn't really matter. My point was to see a numerical model for a falling ball would be similar to the time and distance from the video. Changing the drag coefficient to 0.25 gives values that are still close to the video. So, I still think the video is real…

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…

The oil spill is still in the news (sadly). One thing that keeps coming up is the speed that the oil bubbles rise to the surface. This is important in different oil-capture methods. The common statement is that smaller bubbles of oil can take quite a long time to reach the surface and larger bubbles can take about 2 days.
This is one of those cases where things do not scale quite the same. Suppose there is a spherical oil bubble rising at a constant speed. Here is a force diagram for such a bubble:
If this drop is going at a constant speed, then all these forces have to add up to the…

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…

Crazy, but I was on CNN Saturday night. They contacted me at the last minute to talk about the Red Bull Stratos Jump. Here is a screen shot to show that I am not making this up (or that I have awesome photoshop skillz).
Looking back, maybe I looked like an idiot. Really though, it wasn't my fault. I thought we were going to talk about physics. The first two questions threw me for a loop. Here are the two questions and my response (roughly paraphrased):
Will Felix survive the jump?
Answer: I guess so.
Is there a scientific reason for this jump?
Answer: I thought we were going to talk…

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 meant to mention this earlier since it happened a little while ago. There is this "mini-conference" with three schools: Southeastern Louisiana University, Southern Mississippi University, and the University of South Alabama. The purpose is to give students (and some faculty) a chance to present their work at a smaller conference. I really enjoy this, mostly because it is small and I get to see lots of undergrad talks. There are two talks that stuck in my head.
Dr. Jiu Ding "Dynamical Geometry: From Order to Chaos and Sierpinski Pedal Triangles"
Jiu Ding is a mathematics professor at…

Check this out.
So, the guy jumps from 150 feet into some cardboard boxes. Why are the boxes important? You want something that can stop you in the largest distance to make your acceleration the smallest. Here is my Dangerous Jumping Calculator. Basically, you put in how high you will jump from and how much distance you will take to land and it tells you your acceleration.
You will probably need this G-force tolerance info from wikipedia.
One problem - this calculator doesn't really work for this case. It doesn't take into account air resistance. Does air resistance even matter in this…

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…

I ride my bike and mostly the wind makes me unhappy. On a very few days the wind is with me on the way to work and then changes so that it is with me again. But most days the wind is fairly constant. So, if the wind is constant then shouldn't everything even out? (Even Stephen).
Assumptions:
Let me start with the assumption that I (a mere mortal) can output at a constant power (but not 57,000 Watts like some people). I will also assume an air resistance force that is proportional to the square of the relative air speed. Here is a diagram.
A couple of quick things to point out. First,…

I had so much fun creating graphs for the Red Bull Stratos Space Jump calculation, that I figured I should make some more.
Can you fall faster than terminal velocity? That is the question.
Air Resistance
Air resistance is a force exerted on an object as it moves through some stuff - air in this case. The magnitude is usually modeled as:
Rho is the density of the stuff the object is moving through
A is the cross sectional area of the object
C is the drag coefficient of the object - this depends on the shape (a cone would be different than a flat disk)
v is the magnitude of the velocity of…

Red Bull is sponsoring this sky dive from really really really high up - Stratos: Mission to the Edge of Space. Seems dangerous. The basic idea is that Felix Baumgartner will take a balloon ride up to 120,000 feet and jump out. Here are some questions:
Will he reach supersonic speeds?
The Red Bull site says: "can Felix react to a 35 second acceleration to mach 1?"
How about the claim that he will free fall for 5 minutes and 35 seconds? That seems pretty short.
In 1960, Joe Kittinger jumped from 102,800 feet. Will 20,000 feet make a large difference?
Assumptions
Clearly, this can be a…

Since my previous post on R2-D2 flying was so popular, I thought I would follow it up. I was going to add these two points in the comments, but a separate post seems to make more sense.
Point 1 - R2 flies at a constant speed
Well, he obviously doesn't always have to fly at a constant speed. However, in the clip I was looking at there are two important things in the analysis. What angle is R2's thrusters at? Is R2 flying at a constant speed? I found a much better quality version of the flying R2 from Billy Brook's site. That helped out a lot. So, on to Tracker Video Analysis (I always…

You know I can't help but like Star Wars. Even with the new stuff, I watch it. Recently, I was watching the Clone Wars cartoon and noticed something odd about the way R2-D2 flies. I know what you are saying...."the odd thing is that he flies at all. Why didn't he fly in episodes 4-6?" Who knows. Here is the best image I could get of R2-D2 flying (from wookieepedia).
What is wrong? Well, maybe you can't tell from the image I posted. Here is a diagram of flying R2-D2.
If R2 (I can call him that because we are good friends) was flying like that, why would that be a problem? That would…

In 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…

Which wastes more fuel? (and thus produces more carbon dioxide). This is a difficult to question to answer for a variety of reasons. The main reason is that a speed change from 71 mph to 70 mph is different than a reduction from 56 to 55 mph.
First, let me be clear that the question of how much fuel is wasted using daytime running lights (or DRL as they are called) has already been addressed. The first source I found was howstuffworks.com
Assumptions
The daytime running lights on a car run at about 100 watts (for the pair)
The energy density of gasoline is 1.21 x 108 Joules/gallon.
A car is…

In my previous post on launching a pumpkin (punkin chunkin) I essentially just looked at what happens to the pumpkin after it is launched. How fast would you have to shoot it to go 1 mile? The answer seems to be around 1000 mph and they are currently shooting them around 600 mph.
The question for this post, how fast can you launch a pumpkin so that it does not smash into smithereens? First, why would it smash at all? Here is a diagram of a pumpkin being launched while still in the tube.
The pumpkin launcher works by releasing compressed air inside the tube. This means that the force…

Last night I saw the newest episode of MythBusters. One of the myths they revisited was the exploding water heater. Well, it turns out that I had an analysis of this first explosion, but I didn't move it over when I switched software. So, here it is.
In case you never saw the first episode of exploding water heaters, here is the important part:
If you are impatient, here are the answers (from the video analysis):
Time of flight = 11.8 seconds
Max height = 167 meters = 548 feet
Launch speed = 234 mph
Speed on impact with the ground = 76 mph
First, from re-watching the video, I can see (…

Not really. Here are the details (and some data) for the Millikan Oil Drop Experiment without the oil drop that I talked about previously (originally from The Physics Teacher - lucky you, it was a featured article so it should still be available (pdf)).
The basic idea that Lowell McCann and Earl Blodgett from U of Wisconsin propose is to do an experiment similar to the oil drop experiment, but not so squinty (if you have done the oil drop experiment, you know what I mean). Instead of dropping charged oil in an electric field, they drop containers with metal nuts in water. The goal is to…