It’s a tradition. At the end of the year, I like to post “top” stuff. Here are my best graphs. I’m only going to share graphs that I created with Plot.ly—although there are some other ones out there. So, maybe I should say “best plot.ly graphs of 2019”.
Oh, you haven’t used plot.y? That’s OK. Plotly, is an online graphing platform. It’s pretty nice. The thing I really like is that you can create some data in python (with Glowscript) and send it over to plotly for beautification.
One last thing. I don’t yet know how many “best” graphs I have—I haven’t looked yet. Also, these are in no particular order.
What ball is the best to catch with during free fall?
So, by plotting twice the height by time squared, the slope of the line would give the vertical acceleration. In the graph above, the green line is for an acceleration of 9.8 m/s^2 (the value on Earth) and the red line is the average for all the Jedi. Notice that Yoda has a greater acceleration. I think that’s cool.
I always enjoy this course. The students are both diverse and great. They are at LEAST in Calc-I so that means they can probably do some algebra stuff. There are a good number of students that are in even more advanced math classes like Differential Equations and stuff. Oh, and it’s a great chance to get to know the new physics and chemistry majors.
The class isn’t too big (mine started around 30) so that it’s fairly easy to memorize names.
Maybe the best part of the class is watching student videos. OK, I really don’t like watching videos—it can get kind of boring. But I LOVE seeing students make terrible videos and then get better and start figuring things out. It’s awesome when students have never made a video and are afraid to do it, but then really get into it.
Students eventually figure out that I’m not just assessing their videos, but they are learning by making the videos.
One other thing I liked—I always like it: speed dating physics problem solving. Here is a twitter thread on speed dating (from another class).
Also, I did assign and collect homework. I didn’t really grade it (I gave them a score), but it’s like free points and maybe it helps them practice.
One last “good”. I put together this video tutorial on numerical calculations that looks at an object falling on the surface of the moon. I think it’s pretty good. Not sure how much the students used it though.
Yes, there was some bad stuff. Sometimes I felt like students were just sitting there. Even when I was doing interactive activities, they had this blank stare (it seemed). Maybe it was the class time (9:30 AM)—although that doesn’t seem too early. I really don’t know what the problem was. For the most part they were fine.
Another big problem—speed dating. Oh, I get it. Students don’t want to participate. They want to just sit there and take in the fire hose of learning (they think that works). But in the end, most of them seem to get some positive things out of the speed dating. But the room was not super great for this. It’s a standard lecture hall—so I didn’t really have places to put boards. I tried using very small boards, but it just wasn’t perfect.
One final problem—a good number of student just never seemed to fully grasp numerical calculations.
Here are some ideas for the future.
Mounted white boards. If I have to be in that lecture hall, I want to find some ways to put boards somewhere around on the walls.
Plickers. I’m ditching the TurningPoint clickers. I’m tired of constant updates that bork the system. I get it—they want me to upgrade. Not upgrading again. Oh, also with Plickers it shows the student name over their head when they vote.
More in-class stuff. More group problem solving. More activities. More focus on numerical calculations.
I should show the students more of the awesome physics (like stuff from my blog). I don’t do this enough because I get so busy with getting through different topics—but I think the students really like these things. Who cares anyway, it’s the stuff that I love.
Subtitle: “You don’t really understand something until you model it”
Here is the video. It’s great. Watch it.
The basic idea is to predict the path of water that is shot from a spinning sprinkler. In the first case, the water is shot straight out of the spinning pipe. The second case is a little bit trickier with the water shot towards the center of the sprinkler. OK, it’s not actually a sprinkler.
Of course, once a drop of water leaves the sprinkler, it will only have the gravitational force acting on it. So, if you view this from the top—a drop of water should travel in a straight line with a constant velocity. But there is a problem that makes this difficult to predict. It’s that we don’t see the path of one drop of water, we see the path of a water stream.
A water stream is a collection of water drops. Even though one drop might travel in a straight line, the next drop will be “launched” at a different location with a different velocity. This makes it look weird.
OK, so let’s get to a model. I’m going to go over the steps to build this model in VPython.
Build a bar
Don’t try to do everything at once. Let’s just make a spinning bar—I’ll add water balls later. Here is what that spinning bar looks like.
Let me go over some of the important parts of this code.
The bar is an object of type “box”—this is a prebuilt object in VPython. It has two important attributes. The position (pos) is the location of the center of the box. The size is the vector with length, width, and height.
I added a ball so you can see the center (it’s not needed).
The variable “omega” is the angular velocity of the rotation. You can change this if you like.
The variable “theta” is the angular position of the bar—this is used for something later.
In the loop, the rate(100) tells the code to not do any more than 100 loops per second. Since I have a time step of 0.01 seconds, this means 100 loop would take one second—it would run in “real time”.
Don’t worry about line 16 (update theta)—at least not for now.
Line 18 is the important part. There is a rotate function in Vpython. You need to pick the angle (in this case it’s dtheta which is the angular velocity times the time step), the axis of rotation (the z-axis) and the origin of rotation (the origin).
But it works.
Add a single water
The next step is to add a single ball of water to the end of the sprinkler bar. It’s not going to do anything except to “ride around”. Here’s what that looks like. It’s really the same thing except with that ball of water.
GlowScript 2.9 VPython
#Length of sprinkler - just leave this
cent=sphere(pos=vector(0,0,0), radius=0.03*L, color=color.red)
#CHANGE THIS - rotation rate of sprinkler
#CHANGE THIS to -1 to make balls shoot IN
#this is just a spacer to make the scene look nice
tint=0 #this is the "clock" for shooting water
#CHANGE THIS - this is the water ball production rate
f=15 #water per second rate that balls are made
water=water+[sphere(pos=r,radius=0.04*L, color=color.cyan, v=(-1*cross(r,vector(0,0,omega))+a*vwater*r.hat),
water2=water2 +[sphere(pos=r2,radius=0.04*L, color=color.cyan, v=(-1*cross(r2,vector(0,0,omega))+a*vwater*r2.hat),
for ball in water:
for ball2 in water2:
This is what the output looks like. Actually, this is an animation for the case of the water shooting inward (since I already had the gif).
Now for some comments on the code.
When the water ball gets a certain distance away (I think I set it to 3*L), I change the water ball velocity to vector(0,0,0) and then I make it invisible. Otherwise the view would just keep expanding and it would look weird.
I don’t have any other important comments, but I can’t have a one bullet list.
I’m way behind on this one. My plan was to write up something when this question came up in the summer section of algebra-based physics. It was a great question and deserved a full answer. Also, I wanted to make this a tutorial on trinket.io—but maybe I will do that after I write about it here.
So, here’s how it goes. We start off the semester calculating the electric field due to a point charge and then due to multiple point charges (you know—like 2). After that we get into the electric potential difference. Both the potential and the field follow the superposition principle. If you calculate the value due to two charges individually, you can add these together to get the total field or potential.
But there is a big difference. The electric potential difference is a scalar value where as the electric field is a vector. That means that when using the superposition with electric fields, you have to add vectors. Students would prefer to just add scalars—I’m mean, that seems obvious. Does that means that you could just find the electric potential difference for some set of point charges and then use that potential to find the electric field? Yup. You can. And we will.
Let me start with the definition of the electric potential difference. Since it’s really just based on the work done by a conservative force (the electric field), this looks a lot like the definition of work.
Yes, that’s an integral. Yes, I know I said this was for an algebra-based course. But you can’t deny the truth. The “a” and “b” on the limits of integration are the starting and ending points—because remember, it’s really an integral. Also, the “dr” is in the direction of the path from a to b. It doesn’t technically have to be a straight line.
What about an algebra-based course? Really, there are only two options. The most common approach gives the following two equations for electric potential.
The first expression is the electric potential of a point charge with respect to infinity (so the starting point for the integral is an infinite distance away). The second expression is the change in electric potential due to a constant electric field when there is an angle between the field and the displacement.
Oh wait! I forgot to list the value of k. This is the Coulomb constant.
Students can understand the second expression because it’s pretty much the same as the definition of work (for a constant force). The first equation is mostly magic. The one way you can show students where it comes from is to do a numerical calculation of the electric potential difference since they can’t integrate. Did I write about that before? I feel like I did.
Ok, that’s a good start. Now for a problem.
Electric potential due to two point charges
Suppose I have two charges that are both located on the x-axis. Charge 1 is at the origin with a charge of 6 nC. Charge 2 is at x = 0.02 meters with a charge of -2 nC. Here’s a diagram—just for fun.
Let’s start off with the electric potential—as a warm up. What is the value of the electric potential (with respect to infinity) at the location of x = 0.02 meters? Using the equation above for the electric potential due to a point charge, I need to find the potential due to point 1 and then the potential due to point 2—then just add them together (superposition).
First for point 1.
Now for point 2.
This gives a total electric potential:
Finding the Electric Field
Now to find the electric field at that same point. I don’t know how to say this in a nice way, so I will just say it. Since the electric potential is calculated based on an integral of the electric field, the electric field would be an anti-integral. Yes, this means it’s a derivative. But wait! The electric field is a vector and the electric potential is a scalar? How do you get a vector from a scalar? Well, in short—it looks like this.
That upside delta symbol is the del operator. It also looks like this:
Yes, those are partial derivatives. Sorry about that. But you do get a vector in the end. But how can we do this without taking a derivative? The answer is a numerical derivative. Here’s how it works.
Suppose I find the electric potential at three points on the x-axis. The first point is where I want to calculate the electric field. I will call this . The next point is going to be a little bit higher on the x-axis at a location of . The final point will be a little bit lower on the x-axis at . Maybe this diagram will help.
When I take these two end points (not the middle one), I can find the slope. That means the x-component of the electric field will be:
Let’s do this. I’m going to find the x-component of the electric field at that same location (x = 0.02 meters). I don’t want to write it out, so I’m going to do it in python. Here is the link (I wish I could just embed the trinket right into this blog post).
Umm..wow. It worked. Notice that I printed the electric field twice. The first one is from the slope and the second one is by just using the superposition for the electric field. Yes, I knew it SHOULD work—but it actually worked. I’m excited.
Also, just for fun—here is a plot of the electric potential as a function of x. The negative of this slope should give you the x-component of the electric field.
Here you can see something useful. Where on this plot is the electric field (the x-component) equal to zero? Answer: it’s where the slope of this plot is zero (yes, it’s there). Remember, just because the electric field is zero that doesn’t mean the electric potential is zero.
How about this? See if you can find the electric field due to these two charges at a location y = 0.01 and x = 0.0 meters. This is right on the y-axis, but now the electric field clearly has both an x and a y-component. That means you are going to have to do this twice.
It’s the beginning of a new school year—and I’ve got you covered. You want to do something with coding in your physics class, but you don’t know where to start? I’m going to give you a jump start.
I know you are nervous, but don’t worry. You don’t need to be a ‘l33t h4x0rz’ (that’s cool-speak for elite hacker). You just need to get started. Just remember, everyone had to start programing at some point. They all did it—so can you.
What the heck do you call it?
I like to call this stuff “numerical calculations”. I think this is the best name for it because it sort of describes what’s going on. Here’s the general idea:
Take a physics problem (or any problem, really).
Break the problem into a bunch of small and easier problems.
Maybe make some approximations.
Solve all the small problems by using numbers.
Numbers are the key. You have to use numbers in a numerical calculation. The other solution is an analytical calculation. This is the process of solving a problem in terms of known functions—like the trig functions. For an analytic solution, you don’t really have to put in the numbers until the end.
Of course, there isn’t a huge difference in these two solutions (analytical vs. numerical). A great example from Bruce Sherwood (in a discussion at the recent AAPT meeting in Utah) points out the following:
Suppose you get a solution for a mass oscillating on a spring. The analytical solution will be in terms of the cosine function. But then, how do you get values for something like ? Well, you put it in your calculator or you look it up in a table. Oh, you could find the value for cosine by summing an infinite series. But you see—we are back to a numerical calculation.
That’s not exactly what Bruce said, but that’s the basic idea.
Here are some other names for numerical calculations that you might see:
Coding in physics
I’m drawing a blank here—there must be some other words.
But I also like numerical calculations because it doesn’t explicitly say “computer” in it.
Why do numerical calculations in physics?
Let me be brief and just list some points.
Numerical calculations are just part of physics. There are countless physics problems that can only be solved numerically.
Once students get the idea of numerical calculations, they can solve more interesting problems that would otherwise be inaccessible to them.
What about other fields? Meteorology, digital animations, protein folding, economics…the list goes on.
Tools. The tools for numerical calculations are both free and easy to access. You don’t need to install anything and you could even do it on a smart phone (not recommend—but possible).
Finally, numerical calculations helps student understand physics. I’ve always been surprised that when working on a problem with students on a computer, they ask questions. But these questions are rarely about computer syntax. They are usually things about vectors or forces. It’s awesome.
Who is this for?
I’m going to get you started—so this tutorial is geared towards very introductory classes. I use this same stuff in a physics lab for an algebra-based physics course at that college level. I think this would be fine for high school classes also.
If you want more advanced stuff—this might also work as an introduction. For my calculus-based physics course, I start with more complicated stuff.
Also, I am careful to emphasize that students (and faculty) don’t need any prior experience with coding.
Where to start
I like to have a workshop format for my lab or class. I use a projector at the front of the room to go over some points and then stop and let the students work on code either individually or in groups (here is a version of my presentation—feel free to use it). I tell students to bring a computer or tablet if possible. Otherwise they will be in groups of 4 per computer (which is not ideal). Of course some students don’t want to get involved, so a 4 person group is what they want.
Here is the general outline of the workshop format lesson.
Give an overview of numerical calculations (motivation).
Start with an object moving at a constant velocity in one dimension. Let them solve it analytically (hopefully, this is a review).
Next have them take this SAME PROBLEM but solve it by breaking into 7 time steps—but still solving it on paper. NO COMPUTERS YET.
I actually give them a table to fill out. It has 7 rows with columns for time, time step, and position. After a short time, I stop them and go over the calculation for the first row (and maybe the second). Some students can finish this table very quickly, and others not so quick.
Next, they do this same set of calculations with some python code. I give them this program that runs as it is and I go over each line.
So, the students run the code and then modify the code to answer some questions such as:
Where will the car be at a different time? Say 2.2 seconds.
What if you change the velocity the 0.62 m/s, where will it be after 2.2 seconds?
What if the car starts at -0.5 meters?
Stuff like that. Really, I just want them to be able to run the code, read the output, and change the code. It’s sort of a coding ice-breaker.
I’m not going to go over the rest of the workshop—but it’s all there (and more) on the trinket.io site along with the instructor slides. After that first small activity, the students do the following:
A similar problem but with a constant (non-zero) acceleration. This is great because you get a different final answer for the numerical calculation that depends on the size of the time step.
How to make graphs (or at least print out values) so you can get more data.
Solving a problem with two cars—one moving at a constant velocity and one accelerating. This is the classic “police chase” problem. I set up the program (not all the way) but I let them figure out how to change the while loop to get it to run. It’s great because students come up with their own ways of making it work. Sometimes, this is where I stop the class.
Mass oscillating on a spring.
What do you need?
If you want to do this in class, you need some computers or tablets and some time. You could probably do this in sections, just break it into 30 minute activities if you like.
Some other things to consider:
Make sure you work through the material first. It’s important to really know what’s going on so that you can easily help students when they get stuck.
If a group has a program that’s not running right, I really try to get them unstuck. If it’s a silly syntax error, I try to find that right away so they don’t get frustrated.
If you have any questions or need help. let me know.
Here are some things I need to share regarding this meeting. Overall, it was great to see everyone. As usual, the conversations were the best. I regret that there were some people I did not get to meet or talk to—maybe next time we will meet up.
Blog vs. WIRED
One question that came up multiple times was about this blog vs. my posts at WIRED. How do I decide where a post goes? OK, here is my explanation.
In the beginning, there was a blog. A blog was super informal and free form and alive with comments. It was like the 60s and I was a hippie. A physics hippie. I don’t know if this early blogging era was like the 60’s or maybe the wild-wild west. Well, the comments eventually turned into the wild west with a shoot out at the O.K. Corral.
When I moved to WIRED, everything was the same except it was at a different site. But I’ve been there for a LONG time (9 years?) and things evolve. My posts at WIRED are more edited and geared for a specific audience. That’s not bad, it’s just different. I don’t think I can just write whatever I want like I did in the old days. No more random posts that just talk about my cat (I don’t even have a cat).
So, that’s where this blog comes in. It’s a place where I can post whatever I want and no one can stop me. These are the kinds of things you will find here.
Random posts (like this one) that are just an outlet for me to write stuff and tell stories.
Explicit educational material. If a post needs too many equations, I would rather put it here. Many WIRED readers (while very education) don’t really get into all the equations. Also, since WIRED is paywalled it makes it more difficult for educators to access the stuff (in the off chance that they might find it useful).
MacGyver science notes. Oh sure, I post some MacGyver stuff on WIRED—but I really don’t think they want to see 50 posts on different episodes. So, those are here.
I think that pretty much covers it, so I don’t even need this last point.
In the end, I apologize for the confusion with the two blogs. Oh, actually there are three. I recently wrote a post on OneZero Medium (analysis of a car crash from Stranger Things) also. Not sure how much I will write there—but it’s still me.
What’s up with all the drone videos?
Yes, I have a drone. I love my drone. I can only hope my drone loves me as much as I love it. Honestly, I am honored that you even noticed my drone videos.
Oh, wait. You haven’t seen them? I can fix that.
In case you are curious. This is a DJI Spark. Great drone.
Here are some more short comments.
Meeting with Bruce Sherwood and Ruth Chabay was great. I wish I had a picture with both of them (I did get one with Bruce though).
Bruce made this epic comment in regards to numerical vs. analytical calculations. People claim that analytical solutions are better because you can solve a problem in terms of known functions like sine and cosine. But how do you find the value of the cosine function? YUP – numerically or in a table or in an infinite series. So, in a way all solutions are numerical. Win for numerical.
The other deep thought by Bruce was a discussion on his AJP on energy. Read that paper. This sums it up. You can not find the work done by friction. Friction is crazy hard. I think I might write a WIRED post on this.
Eric Ayars had an excellent presentation on chaotic systems. One system was a bouncing ball on a moving floor. I wonder if there is a case where the ball just stops—this could happen if the relative collision speed of the ball and floor is zero.
The 30 demos in 60 minutes was pretty good. I love these things. Even though I’ve seen many of these demos before, I always find something new. Here is their site http://30demosin60minutes.com/
I went hiking. It was super hot, but I had a great time.
Was the moonwalk fake? No, not the Apollo landings. I am talking about Michael Jackson’s moonwalk. You got to admit, he had a big impact on a lot of stuff and this is my way to give him respect – physics.
I am sure you know about the moonwalk. Maybe you can even do the dance move yourself, but how does it work? First, here is a clip of MJ doing his stuff.
As a side note, I can’t remember where I saw it but there was a great discussion of the history of the moonwalk. If I recall correctly, some were saying Michael didn’t create this move. One thing is for sure, he made it popular. Now for the physics.
The key concept here is friction. Friction is actually uber-complicated, but a simple model works for many cases. Static friction is a force exerted on an object when it is in contact with some surface but those two surfaces do not move relative to each other. Kinetic friction is a force exerted on an object when the two surfaces are moving. Suppose I have a block at rest on a table and I pull it with a slowly increasing force. This is what it would look like:
Two key things from this graph. As you pull on the stationary block, the block doesn’t move. If I pull with 1 Newton, and it doesn’t move then the frictional force is 1 Newton. If I then pull with 2 Newtons and it still doesn’t move, the frictional force is 2 Newtons. The static frictional force does what it can to make the thing not move – but not more than it can. This leads to the static friction model of:
In this model, the force is less than or equal to the product of some coefficient (that depends on the two types of surfaces) and the normal force (how hard the two surfaces are pushed together). The direction of this frictional force is parallel to the surface in the direction that prevents the object from sliding.
The other key feature in the graph is the small jump down when the thing starts to slide. This is because the coefficient of kinetic friction is typically smaller than that for static friction. Also, if the object is sliding, the frictional force is constant.
Back to Michael and the moonwalk. The key here is: how do you make one foot slide and the other not slide? If both feet are stationary, then this is dealing with static friction. I could make the frictional forces on these two feet different by changing my center of mass. Here is a free body diagram:
Since he is not accelerating up and down, the following must be true:
These are the forces in the y-direction. They must all add up to zero so that:
There is another condition that must be satisfied. Since he is not rotating, the total torque about any point must also add up to zero. If you want more info on torque, check out this post (Note: link doesn’t work). But for this post I will just say that torque is like the ‘rotational force’. It depends on the point about which you want to rotate and is essentially the force applied times the perpendicular distance to the point of rotation. For the free body diagram of Michael, I have chosen one of his feet to be the point about which he is not rotating (I could chose any point). This makes 3 of the forces have zero torque (N2, F2 and F1 have zero torque because the perpendicular distance to point O is zero). Here I labeled the other important distances:
The only two forces that exert torque about O are the weight and the N1 force. They have opposite directions of torque because they would cause rotation in different directions. This along with the previous equation gives:
Eliminating mg, and solving for N1, I get: (I know the indices for the forces and distances don’t match)
If his center of mass is in the middle, then r2 – r1 = r1 and the two normal forces would be equal (as you would expect). If the center of mass is more towards the foot on the right, then r2 – r1 is less than r1 and N1 will be larger than N2. This will make the frictional force on the foot to the right greater and the other foot slide.
Well, what if r1 is greater than r2? One of two things would happen. Either he would fall over, or there would have to be a force pulling the foot on the left down. This is similar to Michael Jackson’s trick in “Smooth Criminal”.
Ok. So that is how Michael gets one foot moving. How does he keep one foot sliding and the other not sliding? It is really the same thing as above except that he can increase the force on the moving foot a little bit more since it is sliding. Sounds easy, but Michael could really make it look cool.
Finally, I just want to show another demo that is essentially the same idea.
I told my students I would solve this problem for them. It’s a real life problem too.
Is it possible to use a Neodymium magnet and a coil of wire to get an LED to light up?
That’s the real version. But because I was afraid students would be overwhelmed, I added the following:
The magnet has a maximum magnetic field of 0.2 Tesla.
The LED requires 1.5 Volts and 10 mA to light.
I like this problem because I don’t know the answer. Also, the answer is useful. If you want to do a physics demo showing the voltage induced by a changing magnetic field—what better way than with a hand-held magnet and a small light?
But will it even work? Let’s get started. Here is a diagram.
By changing the magnetic flux through the coil, this will create a curly electric field and an electromotive force (a change in electric potential). The magnetic flux is defined as:
Where N is the number of turns in the loop, A is the area of the loop and is the angle between the magnetic field and a vector perpendicular to the area. In the diagram above, since the magnetic field is perpendicular to the coil.
A change in flux produces a voltage according to Faraday’s Law:
Note: yes, I’m different. I think that the number of loops (N) is part of the magnetic flux and that the minus sign in Faraday’s Law doesn’t really mean anything.
Putting the flux into Faraday’s Law, I get (assuming ):
Now for some estimates. I could just estimate everything and then calculate the voltage—but instead I’m going to estimate everything except the number of turns. I can then solve for N and see if it’s reasonable.
Here’s what I have.
B = 0.2 T
A: radius = 0.01 m
Time interval = 1 second
Voltage = 1.5 V
Solving for N:
This is the perfect case to use python for your calculator. You can put your estimates as variables so that you can easily change things up. Here is my code. I get the following output.
Umm….yeah. That’s 23 thousand turns. I’m not going to do that. Even if decreased the time to 0.1 seconds, I would still need 2000 turns. Arg.
Oh, what if I just make a HUGE loop? Nope. That wouldn’t work. In my estimation for the change in flux, I assumed a constant magnetic field—this is obviously not true, but good enough for a small loop. With a big loop, you would have some of the magnetic field creating a negative flux. It would just make things worse.
What if I put the magnet on a spinning stick (run by a motor)?