Rhett Allain is an Associate Professor of Physics at Southeastern Louisiana University. He
enjoys teaching and talking about physics. Sometimes he takes things apart and can't
put them back together.
This is an ad for someone's online homework service (I am not saying who). The important part, that you might not be able to read, says:
"Make Learning Part of the Grade"
I think I can interpret this logo in two different ways. Both of these interpretations are not too helpful.
Isn't that what a grade is supposed to be?
Maybe you already know that I am not a big fan of grades (grades and obedience, the point of grades). So really, what is the purpose of grades? I think of a couple of things, but most people should be able to agree that they somehow (magically) evaluate what a student has learned. Right? So, in this sense, isn't learning already a part of the grade?
Grades as a motivation for learning
The other interpretation is that they are saying - give grade credit for learning. I think that is just plain silly. Using grades as motivation is moving in the wrong direction. Oh, I know what you are saying: if you don't grade it, they won't do it. I can't think of a good analogy for why this is a bad idea. Oh well.
I would like to continue my attack on the show Sport Science - ESPN. In this short episode, they are comparing the power of NFL player Marshawn Lynch with that of a truck. You can watch it here if you would like.
There are two things that are not quite right with this episode, first, the power thing. I will save the friction problem for another post. So, if you didn't watch that clip, the basic idea is that Marshawn pulls some heavy tires. Sport Science then calculates the power needed to do this and then repeats a similar thing for a truck. Quick review. What is power? In short, power tells you how fast you can either do some work or change your energy.
For the case of someone pulling something, I assume that the power would be based on the work this person does. Let me keep it simple. If you are pulling something in the same direction the object is moving (at a constant speed), the work done is:
Fairly straight forward, right? Sport Science puts some motion sensors all over Marshawn's body. They say this is so they calculate the power, but it looks like it is just to make this animated skeleton move like him.
What actually is known about Marshwan pulling stuff?
He pulls some tires and a sled with a weight of 585 lbs (2600 Newtons)
The sled is pulled 5 yards (4.6 meters)
Not exactly sure about the time this takes (because they made part if it in slow motion) but I would guess it is somewhere between 5 and 11 seconds. I counted 11 in the actual clip.
Sport Science claims that Marshawn produces 573 Watts per kg. (this was in the online clip)
However - there is a difference in the version that was on TV. I thought I was crazy because I didn't see this in the online version. Good thing I had taken a picture of it. Check this out.
Yes, that says Marshawn produces 57,000 watts. They even went on and showed how many TV's that could run. How did they get such a high number? My first thought was that they were just taking the weight of the tires times the distance for the work. This would be a pretty large error (that I will discuss in another post), but let me just assume this is what they did. How much work would it take to "lift" 585 pounds 5 yards?
If I let the time be 5 seconds to pull this thing (which I pretty sure it was actually longer than that), then the power would be:
Hmmmm....How can I make this work? In case you didn't realize, 2300 watts is not quite 57,000 watts. Let me approach this from a different angle. What am I pretty sure about? I am pretty sure about the time and the distance. Let me calculate what force would be needed (what force Marshawn would have to pull with) to get that power (assuming 5 seconds, which I think is low).
So, for a power of 57,000 Watts pulling something 5 yards in 5 seconds you would need a force of 62,000 Newtons (14,000 lbs). Hmmm. I am sure Marshawn is a powerful dude - but 14,000 lbs? There is something wrong.
According to Wikipedia's page on human powered transportation, an elite sprinting cyclist can produce 2000 watts for very short times. I am sure Marshawn is elite, but not 20 times more elite in terms of power output. Something has to be wrong.
Summary
Maybe the people at ESPN were thinking: "hey attach some sensors to this guy and determine his power. Oh, just put down something huge like 57,000 watts. No one will ever check that, it will be fine."
Looks like the show Sport Science (on ESPN) might take the place of Fetch! With Ruff Ruffman as the target of my bad-science attacks. Note: it looks like ESPN has the short episode I will be attacking online, so check it out.
Let me start off with the big problem (which The Onion already talked about). Why do you want to make a show about science that has really terrible science (if you can even call it science)? I really don't get that. If you want to just talk about cool sports stuff, do that. Please don't call it science. Ok. Now on to the particular attack.
In the last episode, Sport Science wanted to predict the results of the upcoming Super Bowl game between the Colts and the Saints. To do this, they looked at some stuff from the past 10 years.
As you can see, they looked at 4 things for the two quarterbacks playing in the game: height, weight, age difference, and state they were born in. From this, they concluded that Peyton Manning "has the edge". I am paraphrasing what they actually said, but this is basically what it was. So? What is the deal. The deal is that Sport Science fell victim to one of the classic blunders - the most famous of which is "never get involved in a land war in Asia" - but only slightly less well-known is this: "Never confuse correlation with causation."
Really, this is a classic blunder. It means that just because in the past, two things have happened together (like if the Saints won every time I wore my lucky underwear) that doesn't mean that my lucky underwear made them win (but it doesn't mean that it DIDN't make them win either). I think xkcd said it best:
So, I put together part of my online textbook (finally). Let me give a little history and insight into this 'textbook'. Ok - I blog, I am sure you got that part already. When I write a post, I like it to start from the basic ideas so that anyone could find it and get what I am saying about some physics thing. Well, I started to realize that there were some things that I kept repeating (like how to add vectors). Instead of re-writing this every time a post had vectors, I made a post Basics: Vectors and Vector Addition. Then, I realized that I could keep doing this and slowly build up a textbook. That is what I did.
What I have so far is not complete. It is only material that would be considered the first semester of an introductory algebra-based course. But it is a start. Also, there are no homework problems so it is sort of short.
Another thing about textbooks. Where are publishers going with textbooks? It seems they are not quite sure. Online stuff is getting more popular. Perhaps publishers would like to sort of "rent" an online service for the books. Maybe this would work. However, the big problem is that they are trying to figure out how to make a business model work. For me, I don't care about that so much. That is why I put the book out there - essentially for free (except for the sidebar ads).
The Future
I am not sure about the future of published books, but for me:
Add more content. I think there are some holes in my "first half". Also, I need to work on the second half.
Add examples. This is an easy change, but it takes some time. I need to match up my blog posts with topics in the text. For instance, my post about Iron Man is a great example of work-energy.
Make a downloadable version of this. Pdf seems like a good format, but also one of these ebook formats (if it isn't too difficult).
I am still perplexed about textbooks. Here are the problems I see textbook publishers having:
Textbooks are too expensive
Many students don't even use the textbook, or just use them to look up something like a formula
Textbooks are essentially in the same format that they have been in for a long long long time
So what do you think about textbooks and the future of textbooks?
The following is a collection of some of my posts that can be put into a simple and quick textbook-type thingy. I am not really sure you would call this a textbook, but maybe you would. This does not include everything you would normally find in a traditional textbook, but clearly it is not traditional. I tried to keep it to just the fundamental ideas. As I write more stuff that is appropriate, I will add it.
In terms of the level of this material, I would think it would be appropriate for advanced high school physics or introductory college-level physics.
I plan to update this list with examples (from Dot Physics and other sites) as they relate to the topics. This will take time though. Maybe in the future, I will put this together as a pdf or ebook format or something.
One final note, if you find this useful and actually use it in some way, please let me know (by adding a comment or sending me an email.
Not sure if this is the BEST order to read through these. In fact, you may just read the ones you find useful. Really, I still don't know exactly the best way to use these but I wanted to put them in some organized manner. Hopefully, I will be able to add more topics, like electricity and magnetism stuff.
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 represented by the direction of the arrow. Here is an example:
I think the biggest negative to this representation (other than being difficult to get numerical answers for adding) is that it is not too easy to represent in 3-dimensions. For the following representations, I will try to relate them to the graphical representation.
Magnitude and Direction
In algebra-based courses, maybe this format is popular. Basically, you just give the magnitude of the vector and the angle (from the positive x-axis) that the vector is pointing. Here is an example (using the same vector from before):
And in magnitude-direction format, it would be:
I am not too found of this format. First, if you want to add vectors, you need to find components. Second, students often get confused with this angle always being measured from the same axis (it doesn't have to be the x-axis, that is just what is common). Oh, if you want to do this for a 3-D vector, it really isn't worth it. You would need two angles. Well, in some cases it might be worth it.
Components
With the component method, the idea is to just give the amount the vector is in each of the coordinate directions. Here is an example.
Hold on. I am not finished. Yes, I wrote these components as vectors so that:
Often you will see textbooks sort of stop here. In this case they may say something like:
It is important to realize that this notation is NOT the magnitude of the vector Fx and Fy. The magnitude of a vector has to be a positive number. To really use these, you need unit vectors. This is what they look like:
The little ^ over the x means that it is a unit vector. A unit vector is a vector that has a magnitude of 1 with no units. This means that the Fx vector could be written as:
And maybe now you can see why that negative sign is important. The vector Fx is in the opposite direction as the x-hat vector and that is why you need a negative sign. So, using this notation, you could write the vector F as:
Some textbooks like the you i, and j instead of x and y - this would look like:
Same thing, different looks. Don't forget units though. Vectors have units, if you leave them off you are probably a mathematician (just kidding). Also, this notation can be expanded to three dimensions by adding a z-hat or k-hat component. Another nice thing is that these vectors are all set up and ready to add. If you have a vector in component notation you are ready to rock.
I guess the reason textbooks use the magnitude-direction format some is that it may be easier to relate to real life. In real life, I would measure the magnitude and direction of a force and then have to calculate the components.
Same thing, but another way
I really like the physics textbook Matter and Interactions by Ruth Chabay and Bruce Sherwood. The way that textbook consistently represents vectors is as:
I like this notation. It is short and it emphasizes the components as well as the idea that all forces are 3-dimensional. The short thing is really good for lazy people like me. Also, it matches up really nicely with vectors in vpython. Here is how I would write that vector in vpython:
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: which dart had a greater change in momentum? You could also look at this in terms of impulse. First, the momentum principle:
In this form, it says that the product of net force and time the force is acting on an object is the change in momentum of that object. For this case, there is a collision. So, the important points for a collision are that the forces between the two colliding objects have are equal and opposite and that they last for the same amount of time. This means the the change in momentum of one object is the negative of the change in momentum of the other object.
With that idea, you can see already which has a larger change in momentum. When the dart bounced off (instead of sticking into) the box, the box had a higher speed (and went farther). So since the change in momentum of the box was larger in this case, so was the change in momentum of the dart. Time for another picture. Here is the dart bouncing off the box.
If the dart bounces back at a little bit lower speed, the change in momentum (in the x-direction) will be:
This is where many people make the mistake in saying the change in momentum is 2 kg*m/s. Ah ha! That is the change in the magnitude of the momentum, not the change in the momentum. You see, they are different.
Since the change in momentum for the dart is the same (but opposite direction) as the change in momentum of the box, it increases in momentum by 8 kg*m/s (and it started at zero). Now, here is a diagram for the case where the dart sticks. (I will assume that it starts with the same initial momentum)
So, in this case, the change in momentum of the dart is: (in the x-direction)
This means that the box must have a change in momentum of 2 kg*m/s (and thus is slower than the case where the dart bounced off).
I am sure I have talked about this stuff before, but it came up recently in a discussion so I figured I should put it here.
Let me draw a picture of learning.
The path of learning goes through the swamp of confusion. Suppose you are in a class and you are confused. This is good. If you are not confused, you are not going through the learning process.
All too often I see a student put their big toe in the swamp. It is icky, so they stop. Their thoughts are:
This can't be the right way. I am sure I made a wrong turn somewhere. I can't possibly go through this. If this IS indeed the way to go, I must be dumb or I wouldn't be confused.
The only way you can get to the mountain peak of understanding without going through the swamp is if you already understood the idea. The real unfortunate thing is that students rarely see the swamp. Too many of their courses have a path that takes through a quick tour of the rose garden. Sure, it smells nice - but did you get anywhere?
I know, my analogy isn't perfect. A student may say: "well, if the swamp is in the way, why don't you just take me to the mountain in your helicopter?" In this case, I switch analogies. Can you become a better runner by riding really far in a car? Or do you have to run?
This one has been on my mind for quite some time. What kind of power source would you need to run a lightsaber? I was actually worried recently about this post when I saw the Discovery Channel show "Sci Fi Science". In that particular episode Michio Kaku talks about how you would actually build a lightsaber. The episode was a little silly, but the science wasn't too bad. In end Michio decides to build a type of hand held plasma torch. Doing this, he estimated that the lightsaber would need a power source on the order of mega-watts.
He didn't do what I was thinking. I am thinking about the scene from Phantom Menace where Qui Gon tries to cut through a door at the beginning. It looks like this:
Comment Notes:
Usually, I save this for the end. However, let me go ahead and pre-emptively address some comments (that are similar to what happened with the flying R2-D2 thing.)
Yes, I know light sabers are magic. I also know that they run on these cool crystals. This will not stop me from making an estimate anyway.
Oh, I know I am estimating some quantities. That is ok. At least I can get a ball park figure for this.
Rhett Allain is an Associate Professor of Physics at Southeastern Louisiana University. He
enjoys teaching and talking about physics. Sometimes he takes things apart and can't
put them back together.
