# vector

Image of mosquito from http://bloodinurineandpainofca.wordpress.com/
Until now I thought I had come up with enough reasons to dislike mosquitoes, those tiny little blood sucking vectors of disease. With reports of the debilitating mosquito-borne virus chikungunya in the Americas (Carribean), I was ecstatic hear that researchers are working hard to find ways to control mosquito populations. As mentioned in a previous blog, only the females bite to obtain nourishment for developing eggs. According to the study authors, the female mosquito can double her own body weight after just one meal,…

"I wouldn't know a spacetime continuum or a warp core breach if they got into bed with me." -Patrick Stewart
It's the end of the week once again, and so it's time for another Ask Ethan segment! There have been scores of good questions to choose from that were submitted this month alone (and you can submit yours here), but this week's comes from our reader garbulky, who asks:
Why does gravity decrease the further away you are from the object? I've read that it does decrease with distance squared but not why it does this.
This question seems so simple, and yet the answer -- to the limits of our…

It is that part of the semester where the Right Hand Rule (RHR) comes out. Really, the best part is the students taking the tests. They make all these funny motions with their hands. That makes tests more entertaining (for me) than they usually are.
What is the RHR?
Suppose I have two numbers. Maybe these two numbers are the length and width of a piece of paper. Now suppose I need to multiply length times width to get the area (A = L x W). Simple - right? But that is multiplication for scalar variables. How do you multiply vectors?
There are two common operations you can do with…

So, I hear you are starting your second semester of physics. One of the cool things about physics is that the second semester still uses stuff from the first semester. Maybe you forgot some of that stuff, so here are the bare essentials you will need to get by (this is assuming you are in the algebra-based second semester of physics)
Vectors
Really, just about the entire semester course is about the electric and magnetic field. Both of these are easiest to represent as vectors. So, you pretty much need to know how to deal with vectors. Here are some reviews:
How do you represent vectors…

Yes, I am going to talk about the MythBusters latest duct tape episode. A couple of pre-post points:
They call it "duct" tape. I call it duck tape. It doesn't work very well with ducts. Also, it is good for water proofing stuff - you know like a duck. For the rest of this post, I am calling it duck tape. (Wikipedia agrees there is some naming problem)
You know I love the MythBusters - right? I hope you don't think I sit around waiting for them to make a mistake so I can pounce on them (I save that for ESPN Sport Science). In this case, they just made a small mistake. A mistake that…

So, I complained about MythBuster's explanation of relative velocity. How would I explain this? I would start by saying that velocity is relative. Here is the definition for velocity:
I put the "avg" in there because it is more true. If the acceleration is zero, I could drop this. For the rest of this post, I am going to assume zero acceleration. Ok. But what is the r vector? It is simply a vector from the origin to the object. Here is a picture.
Simple, right? And so the velocity tells how this vector r changes. But wait. Who says that I used the correct origin? How do you…

In this part of the world, we have oak trees. Technically they are called live oaks - but I don't get it. Of course they are alive. I was at a soccer game and this is the tree I always look at.
Look how far those limbs extend horizontally. That branch is about 12 meters long. Why is this amazing? Have you ever tried to hold an 8 foot 2 x 4 board horizontally by holding one end? Pretty tough. How about I calculate the forces needed to hold that branch in place? I will do a simple model and then maybe later I can make it more complicated. Suppose I replace that limb with one straight…

My last Olympics post may have been a little complicated. I am going to try to make this one a little easier. In this post, I want to look at the landing portion of a ski jump. This could apply to THE ski jump, but there are some things in that even that make it a little more complicated (but I might come back to that in another post). For this case, I will consider the freestyle event - aerials. I didn't search too long, but here is a nice short video.
First, a quick estimation of how high they are "falling" from on the way down. In that video, the jumper takes about 1.5 seconds to get…

Recently, I was talking about vectors. At that time, I had to stop and recall how I had been representing vectors. Ideally, I should stick with the same notation I used in Basics: Vectors and Vector Addition. But let me go over the different ways you could represent a vector.
Graphical
Maybe this is too obvious, but it had to be said. You can represent vectors by drawing them. In fact, this is very useful conceptually - but maybe not too useful for calculations. When a vector is represented graphically, its magnitude is represented by the length of an arrow and its direction is…

Suppose you want to move an empty paper clip box by shooting it with a toy dart gun. Why would you want to do this? Don't worry about that - this is my example and I am sticking with it. Should you shoot a dart that sticks to the box or should you shoot one that bounces off? I made a video of this exact situation. Note: you could obviously come up with other objects to do this with, but I always like to use more normal stuff.
In case it wasn't clear, the first dart bounced back and made the box go much faster (and farther) than the dart that stuck (inside) the box. The usual question is…

My dad and I had a disagreement. We were driving back from a trip and he let me take over the wheel for a while. His complaint was that I was driving too slow and it was driving him crazy. For me, I thought I was driving fast. My typical behavior is to drive 3 mph under the speed limit. That is just how I roll. In this case, I knew he wouldn't be able to handle this so I went the speed limit (70 mph).
Here is the problem. The speedometer said 70 mph. The gps thingy said the average speed was 69 mph. I think my dad feels that the gps is correct and that cars have speedometers that are…

Forgive me if I don't know the official parkour term for this move. This is where you have two walls that are close to each other and you vertically climb them. Here is a shot of Mark Witmer (from Ninja Warrior) doing the wall climb.
Doesn't look too hard, does it? Well, I think it depends on how far apart the two walls are. This is actually one parkour move that my kids like to do (Hey kids! Don't do that! Let me get my camera though because this will be perfect for my blog)
I am going to start with this second kind of wall climb. Simply because it is easier due to symmetry. So,…

pre-reqs: vectors, kinematics
I haven't done a "basics" topic in quite some time. It's odd, I have used centripetal acceleration quite often, but I never derived the expression that I use. To get to the point, the magnitude of the acceleration of an object moving in a circle is:
Also, the direction of this acceleration vector is always towards the center of the circle the object is moving in. This is really not too difficult to derive (but it does use at least one "trick"). Let me start with an object moving in a circle at a constant speed. I am going to show to instances of the object…

I am so pumped up that MythBusters is back on. Not only do I like the show, but it offers so many blogging opportunities. Their latest show featured car crashing myths. One of the myths from the episode was a redo of the myth where two trucks crash head on simultaneously crushing a smaller car in the middle.
The first test was very similar to the previous time they tested this, but faster. They towed two 18 wheelers to crash together around 50 mph and smash a stationary car. The results were impressive. However, they did not have the result of the car completely contained in the…

What is a fake force? A fake force is one of those forces that introductory texts tell you aren't real - like centrifugal force. They aren't real in the sense that they are due to one of the fundamental interactions. Basically, introductory texts (and even blogs like this one - not a bad summary of real vs. fake forces) attack the centrifugal force. This is because it is so common for students to want to use these faux forces in the wrong way. Better to just not use them at all.
Anyway, there are times when faux forces are awesome. Just to be clear, a faux force is needed to use normal…

Let's try a thought experiment.
This one comes via Buckminster Fuller: imagine you have a length of nylon rope, which you splice into a length of cotton rope, then into another length of hemp rope. If you tie an overhand knot in the rope, and push it down, through all three kinds of ropes, the knot remains a knot. The material is irrelevant, because the knot is just a pattern that has a specific set of guidelines for itself. Fuller wrote that "a pattern has an integrity independent of the medium by virtue of which you have received the information that it exists." That is to say, if you…

**Pre reqs:** [Free Body Diagrams](http://scienceblogs.com/dotphysics/2008/09/basics-free-body-diagrams.php), [Force](http://scienceblogs.com/dotphysics/2008/09/basics-what-is-a-force.php)
The time has come to look at things that are NOT in equilibrium. The most basic question to ask yourself is: *"What do forces do to an object"*? Aristotle would say that forces make things move. Constant forces make things move constantly. Actually, Aristotle said there were two types of motion:
Natural motions: These motions don't need anything to happen, they just do. Example: a rock falling. You…

**Pre Reqs:** [Intro to Forces](http://scienceblogs.com/dotphysics/2008/09/basics-what-is-a-force.php), [Vectors](http://scienceblogs.com/dotphysics/2008/09/basics-vectors-and-vector-ad…)
Hopefully now you have an idea of what a force is and what it isn't. What do you do with them? The useful thing to do with forces is to determine the total force acting on an object. At the beginning of the introductory physics course, you will likely look at cases where the total force is the zero vector. This is called equilibrium. Even if you are looking at cases where the forces don't add up to the…

**pre reqs:** [Vectors and Vector Addition](http://scienceblogs.com/dotphysics/2008/09/basics-vectors-and-vector-ad…)
This was sent in as a request. I try to please, so here it is. The topic is something that comes up in introductory physics - although I am not sure why. There are many more important things to worry about. Let me start with an example. Suppose you are on a train that is moving 10 m/s to the right and you throw a ball at 5 m/s to the right. How fast would someone on the ground see this ball? You can likely come up with an answer of 15 m/s - that wasn't so hard right?…

**pre-reqs:** trig
Think of the following two things. Temperature and wind speed. These are two different things that you could measure, but there is one big difference. Wind speed has two parts to it - how fast and which direction. Temperature is just one thing (no direction). Temperature is an example of a scalar quantity (just one piece of information). Wind speed is an example of a vector quantity - multiple pieces of information. Here are some other examples:
**Scalar:** mass, money, density, volume, resistance
**Vector:** velocity (most physicist reserve the word "speed" to mean…