I have some comments about college life and learning. There are two things that seeded these ideas. First is this article from the Wall Street Journal - For Most People College is a Waste of Time. The second is this great essay on math education by Paul Lockhart - this is not the first place I found this article, but I can’t find the other blog that linked to it. Maybe you should read these two articles and then continue here.
Read More...

Tags: rant

Yes, this blog is mostly about science and physics stuff. However, I just wanted to give a couple of comments about diving the Oriskany (I am sure there is some physics in here somewhere). Read More...

Physics of Sustainable Energy: Using Energy Efficiently and Producing It Renewably - AIP Conference proceedings

Do you like talking about energy? Cars? Alternative and renewable energy? Need more info? This looks like a good place to start. This is the presentations from the AIP-APS-AAPT forum on Energy stuff.

Physics of Sustainable Energy Presentations (both pdf and powerpoint)

I looked through some of these and there are some interesting graphs I might come back to in the near future. You might want to bookmark this page or something.

Tags: energy

(How to make your own fake moon videos - or how to undo the fake studio videos)

Stop. Don’t say it. I know the moon landings were real, but I am just trying to have fun.

Some claim that the Apollo moon landings were faked in a studio. One way to make fake films would be to film astronauts and then slow the film down so it looks like they are on the moon. If this were the case, I could speed the videos back up to “normal” speed and see what they look like. After that, I will take normal videos and slow them down to make them look like they are on the moon.
Read More...

Tags: kinematics, gravity, video, fake, units

Starting Assumptions (estimations)
How many drive-throughs are there in the U.S.A.? When I think of drive-throughs, I think of McDonalds. Wikipedia says there are 31,000 restaurants world wide. I am going to say there are around 20,000 in the U.S. that have drive-throughs. So then, how many total drive-throughs? In my town, there are two McDonalds and probably 8 other major drive-throughs (Wendy’s, Burger King, Taco Bell etc....). This will give an extremely rough estimate of 100,000 drive-throughs in the U.S. (drive-through fast food).

There are also other kinds of drive-throughs. Drive-through banks, starbucks, pharmacy, liquor (yes, they exist). All of these will have different times, so I will first just deal with the fast food drive-throughs.

How many cars go through the drive-through a day and how long do they idle? I am going to estimate that the average over 8 hours a day is 2 cars in the drive-through line with an average wait time of 2 minutes. Yes, at lunch time there is a longer line, but sometimes there is no line. This is my estimation and I am sticking to it.

Calculating the hours of idle time
From this, I can calculate the average idle time. If there are 100,000 drive-throughs and for 8 hours there are two cars idling (I guess the wait time does not matter), that would be 1,600,000 idle-hours per day (100,000 x 8 hours x 2 cars). How much fuel does this use? Anecdotal claims from the internets say that cars use around 0.3 gallons per hour idling (I would have guessed higher than this). For this calculation, I will use 0.25 gallons of gas per hour idling. So, the total fuel per day wasted in drive-through (just restaurants) would be: 400,000 gallons.

Comparing to the U.S. oil used per day
Now to compare this to the 20 million barrels of oil used per day. 1 barrel of oil produces about 20 gallons of gasoline. So 400,000 gallons of gas saved would be 20,000 barrels of oil saved. This is just 0.1% of the oil used per day. Not nearly as much as the claimed 3% savings from tire pressure (although that is for people that don’t already have properly inflated tires). Also, that 3% is for individual savings, not for the whole nation.

Slow Down
I still think the best way to save oil is to drive slower.

Either way, the real issue is (as stated in the time article) how much would we get from off shore drilling? How much can we save by changing stuff.

Tags: energy

In this post, I am going to talk about real and not real forces as well as the fake centrifugal force (if you don’t like the word “fake” you could replace that with “fictitious”)

First, an example: suppose you are in a car at rest and press the gas pedal all the way down causing the car to accelerate. What does this feel like? If I weren’t skilled in the art of physics, I might draw a diagram something like this:

Yes, maybe someone would add gravity and the chair pushing up, but this shows the important points. What is this force of acceleration? What causes this? This is EXACTLY the same thing as centrifugal force. If you think centrifugal force is real, this also should be real. I think this is enough discussion to show that this force (and centrifugal) is not real, but I will continue. There is another mystery: why does it feel like there is a force pushing you back when you accelerate? (if you have read all my blog posts, you may have a hint to the answer).

Let me replace the person with a model of a person. Here is my model (very simplistic)

In this model of a person, there are 4 masses each connect to the adjacent “atoms” with a spring (I represent the springs as rectangles because of my laziness). Now suppose I push on this model from both sides with equal forces.

I put these big bars on the side to make it clear the force was applied to both “atoms” on that side. So, when these two forces are applied, 1) the object stays at rest and 2) the horizontal springs are compressed.

Now what if I just apply 1 of these forces:

Notice that the compression is EXACTLY the same before (Eye-dentical). Hey wait! How do I know that this one force would compress this exactly the same? Well, you or I could easily model this and in fact I have done so for a previous article (weightlessness and gravity)

If the above model looks the same, it means a person would feel the same. The only difference is that this person would be accelerating. The point of this story is that when a person accelerates, it FEELS like a force is pushing on you in the opposite way. One note: when you accelerate, it doesn’t feel exactly the same as if someone was pushing on you. When someone pushes on you, they are exerting a force on just part of you. When you accelerate, it feels like something is pulling on ALL of you.

Ok, now on to circular motion and centrifugal force. In the above case, what if I took a “picture” of the velocity vector after 1 second? The two vectors would look like this:

And using the definition of acceleration:

I can find the direction of the acceleration by finding the change in the two velocity vectors:

Ok, so maybe we are all happy with this? (I am happy) Let me move to circular motion. I will once again “take a picture” of the velocity vectors for an object moving in a circle.

Now, I can do the same thing as before to find the direction of the acceleration. (it is ok to move a vector as long as you don’t change its direction or length)

Key points: 1) the velocity did change (although only in direction and not in magnitude). 2) This change in velocity means the object accelerated. 3) in this case, the acceleration is towards the center of the circle.

This would make it “feel” like a force is pushing outwards. It is this force that people call centrifugal force.

Whenever one is thinking about forces, it is important to realize that forces are an interaction between two objects and there are only a few real forces. They are:

• Gravity - an interaction between objects with mass
• Electromagnetic - an interaction between objects with electrical charge
• Strong nuclear - an interaction between hadrons (protons and neutrons are two examples of hadrons)
• Weak nuclear - an interaction between quarks and leptons

Anything that is a real force should be one of these. Gravity is an easy one to pick out. What about me pushing on a book? That would be the electromagnetic force because the atoms in my hand are interacting with the atoms in the book (and that is what prevents my hand from going through the book).
What about centrifugal force? What are the objects that are interacting? (hmmmm.....) Which of the fundamental forces is it? (hmmmm.....). Well, it must not be a real force.

Don’t get me wrong, sometimes the idea of a centrifugal force is useful, but that does not make it real.

Tags: astronomy, forces, circular motion

Can you believe it? Have you seen this video?


Are you thinking what I am thinking? WOW. How could these people not follow my rules for cool internet video. Once again, here they are:

1. Keep the camera stationary. This way I don’t have to keep moving the origin in the movie.
2. Don’t Zoom. Same reason, this video followed that rule.
3. Include a clear and obvious calibration object. A meter stick would work, or even a Kobe Bryant (I can look up his height). Maybe it could be a Ford F-150 that has a known length. Something!
4. Include the mass and height of all people involved.
5. Use high quality video.
6. Don’t talk about fight club - oh wait, wrong list.

Despite failure to follow all these rules, I have managed to analyze this video. Really when I saw it, I said “wow” - was that real? It looked real, but who would get shot up that high? (it is on break.com, so fake is a possibility).
Read More...

Tags: kinematics, video, energy

I am always looking for videos to analyze. Here is a site with many high speed videos. The clips seems to be in low resolution and in Windows Media Format, but still looks like there are some good ones.

High Speed Videos (Dr. David Alciatore at Colorado State University)

Tags: video

I could make a way to pretend this is physics, but really it’s just funny.

Here is a picture a friend of mine took of the Chicago Tribune with his phone while he was walking to work.

I have tried to talk about energy and perpetual motion machines before (and how they can’t work). Surprisingly, people keep coming up with ideas about energy creation that just shouldn’t work.

http://www.lhup.edu/~dsimanek/museum/physgal.htm

This site is very comprehensive in covering the different ways people make mistakes about perpetual motion machines. Great examples also.

Tags: energy

I must have previously mentioned my online lectures (mini-lectures) in astronomy. Well, I got quite behind in my postings. In an effort to complete the semester, I have added some more videos - namely

• Doppler effect
• Blackbody radiation
• Telescopes
• Introduction to the terrestrial planets

I posted all these videos on Vimeo - but you can find links and descriptions here

Tags: astronomy

So, here is a video (from break.com - so you know it is likely fake).

Extreme Catapulting - Watch more free videos
If for some reason, you can not view this video, here is the plot.
1) Guy wears parachute and brings a portable thing like a see-saw.
2) Guy approaches large crane dropping a large mass repeatedly (I assume to flatten a dirt road)
3) Guy sneaks up an puts the see-saw under the area that the mass drops on and then stands on the other end of the see-saw.
4) Mass drops, guy shoots up and parachutes down. Read More...

Tags: forces, video, fake, energy

I usually create posts focused on physics and science stuff, but I like to talk about learning also. Today I will talk about the question that comes up with faculty. Should you have attendance count as part of the course grade?
Read More...

Tags: teaching, lecture, attendance, rant

So, I always try to get on Digg (a social content system) - specifically to promote my stuff. Anyway, Digg introduced a new recommendation engine. The basic idea is to find submitted stories similar to stories that a user has “dugg”.
Read More...

I have been thinking about gasoline (I can’t help it). In an effort to show my students different energy sources, I realized the power of gasoline. There is a reason we have an oil-based energy system, its cheap (still cheap comparitively) and it has lots of energy. Yes, we need to move past oil that is clear. Yes, fossil fuels lead to pollution and green house gases. But still, it is important to realize why we are here.
Read More...

Tags: gas, energy

I often have a discussion with students about science. It usually starts with a student claiming that they really aren’t a “science person” they are more of a “___________” person. (where the blank can be english, history, art, etc). There are several important things about “I am not a science person”, but today I would like to compare science and history because really, they are not that different.
Read More...

You see this all the time in textbooks:

This is often described as “the acceleration due to gravity”. Is this really the best thing to call this? No. A better name would be “the local gravitational field” and list it in units of:

Read More...

Tags: gravity, kinematics, forces

• Moon Landing Theory. This is the theory that in 1969 people ACTUALLY landed on the moon. There are many people that claim this did not actually happen. Both sides of this argument should be discussed. Here is a good place to start - (Bad Astronomy)
• Global Warming Theory. Some claim that the Earth is in a warming trend and that this trend is caused by human activity. Of course, this is just a theory. Another theory is that global warming is directly correlated with the number of pirates in the world. Here is an article on the relationship between temperature and pirates (see - its a real theory)
• Flying Spaghetti Monster Theory. Really, this one isn’t as much a theory as it is a FACT. This is the notion that there is a flying spaghetti monster that does stuff. It is not really considered a theory becuase it is in wikipedia, the source of all truthiness.
• Oblate Spheriod Earth Theory. Many textbooks descirbe the Earth as a sphere, or better as an oblate spheriod. This really neglects the whole other side of the debate about the shape of the Earth. For information about the Flat Earth Theory - see the online stuff.
• Light Wave-Particle Duality Theory. ALL textbooks in physics talk about light being both a wave and a particle. Why? Well, it seems that Einstien sort of suggested this as an explanation to the photoelectric effect. It turns out that the photoelectric effect can be explained with classical wave theory and a quantum theory of matter.
• Hydrino Theory. This theory claims that hydrogen energy states can lowered past the accepted ground state value hinting at near unlimited energy possibilities. Of course, there is no experimental evidence to support this theory, nonetheless it should still be debated just like the theory of evolution.

I know I left off some great theories that should be debated, but I just can’t think any more. If you are a Louisiana teacher, feel free to contact me if you need materials to debate these theories in your class.

Really, don’t think of the LA Science Act as a limitation but more as an opportunity. Also, with great power, comes a greater responsibility to do good.

Tags: fake

So how much would be enough to be useful? I am going to ballpark 500 Watts (although certainly less could also be useful). What kind of flow rate would one need to get this? I will assume some type of stream where someone could produce a 1-meter vertical drop.


How much energy would you get from moving a mass of water m down 1 meter? The change in gravitational energy of a mass of water would be:

Suppose I want 500 Watts, that would be 500 Joules/sec. Suppose also I have 1 kg “pieces” of water. Each piece would give 9.8 Joules (at best). So how many of these pieces of this water would I need each second? I would need 500/9.8 = 51 pieces per second. This would give a flow rate of:

Of course this assumes 100% conversion from gravitational energy to electric energy. Clearly that is not going to happen. If I assume a 50% efficiency, then I would need a flow rate twice that - 102 kg/sec.

Suppose all this water was coming through a pipe, how fast would it have to go? If I have a 1 inch pipe, then I would need to first look at the volume flow rate.
Assuming water with a density of 1000 kg/m³ then the flow rate would be:


How fast would the water have to flow to get this?

How long would this pipe have to be to get 0.051 m³?
Well, the cross sectional area would be:

So, if the volume = 0.051 m³ then the length would be:

If all of this moves through in a second, that would make a flow speed of 100.6 m/s or 225 mph. Seems kind of fast.

Tags: energy

I don’t think I even need to do a video analysis of this motion, all the important info is given. I will assume that air resistance did not play a signficant role (and that is a good assumption - or good enough - see this for example: motion of a falling tennis ball). So, here is the situation.
Part 1: guy falls 35 feet 5 inches (10.8 meters).

For this part of the motion, it will be easiest to use the Work-Energy theorem to determine his velocity RIGHT before hitting the water. (note that I am assuming the 10.8 meters is the distance to the surface of the water, but really it doesn’t matter much). The work-energy theorem states:

In this example, I will assume just the person as the system. This means that the only change in energy will be the change in his kinetic energy and the gravitational force will do work. The two things to start with are the gravitational force (close to the surface of the Earth):
Here g is the gravitational field (9.8 N/kg) pointing down.
And kinetic energy:

When calculating the work done by gravity, the gravitational force and the displacement are both down. This means that the work done by gravity will be a positive quantity. This gives:

Putting in some numbers, I get:
for the speed of the guy right BEFORE he hits the water.
Now I can apply the same idea when he hits the water. The only difference is this time he starts at the above speed and ends at rest - also there is another force acting on him, the water.

I can then use this to find the force the water exerts on him:

This would be great, but it turns out that a better measure of what a person can handle is in terms of the acceleration. So, solving for the acceleration of the person:

Now to get this in terms of “g’s”, where 1 “g” is 9.8 m/s². This would give an acceleration of 35.4 g’s. Is this ok?
Well, instead of going out and taking human g-force tolerance data, I will use NASA’s data as listed on wikipedia. This says a human can take 35 g’s “eyeballs in” if it is for less than 0.01 minutes. (eyeballs in means the acceleration is in the opposite direction that your eyes look)
So, how long was this guy accelerating? If I assume a constant acceleration, I can use the definition of average velocity where his average velocity while stopping would be 7.275 m/s.

So, it looks like this is within the range of what NASA recommends. No wonder this guy is a professor, his jump is NASA-approved.

Tags: acceleration, video, gravity, energy

Once again, time to crank out my favorite video analysis tool - Tracker Video Analysis (free). In order to do a complete analysis of the video, I need to scale it somehow. I first thought of using the height of the astronaut, but I could not find that data (plus he is wearing that space suit). Instead, I used the length of the PLSS (Primary Life Support System) the big back pack thing.

This site - http://www.myspacemuseum.com/plss.htm gives the length of the PLSS as 26.4 inches (0.67 meters). Now to the data:

Here is a plot of the vertical motion of the astronaut during the jump. I fit a quadratic function to the data shown in the graph. This gives a downward acceleration of 1.4 m/s² which would correlate to 1.4 N/kg gravitational field. This is very close the the official Wikipedia value of 1.6 N/kg. I think there are two problems with this video. First, I need a better quality video - this one as duplicate frames. Second, I probably need a better item to use to scale the video. Nonetheless, this does not look like an a jump in a studio on Earth.

Tags: video, acceleration, gravity

I like this demo because it is simple and clearly, anyone can do it (my 4 year old daughter did it). Here is what you do:

• Get an object (like a glass) and a piece of paper or cloth. Make sure the glass is not wet or too sticky on the bottom. If you use a cloth, make sure it does not have a hem on it.
• Place the glass on the paper with about 1/2 of the paper hanging over the edge of the table.
• Here is the scary part. Pull really, really fast. Pull the paper DOWN. When you pull it down, the paper comes out and more importantly, the paper does not go UP. If you hesitate, you will lose.
• If you want to go a step further, say that you will make the trick even harder by adding water to the glass (this actually makes the trick easier). Then repeat the above steps. Make sure you don’t get water on the outside of the glass.
• You can put other stuff on the paper as well. Just remember, the heaver the better. Also, the more breakable, the cooler you will look.

So, how does this work? The key here is the following:
Which, is essentially Newton’s 2nd law. I can also write this as:
This shows how the momentum changes with force and time.
Is there a net force on the glass? Yes, but the time is very small, so you will notice the momentum does not change much. In fact, in the video, my two year old pulled the paper slowly. I caught the glass, but it would have fallen.

Why is it easier when you add water? No one really cares about the momentum of the glass, you care about the velocity. Momentum is:

So, for a full glass, the change in momentum is about the same (if the force and the time are the same - really neither of these are the same). If the mass increases, then the velocity of the glass will not need to increase as much.

Tags: forces

Perhaps you already noticed the links on the side “Astro Course”. Hopefully, someone, somewhere will find these useful. It is clear that that person will not be me (I really can’t handle listening to myself). So, who might find these useful? If you are interested in some aspect of astronomy (or physics) maybe you will like this. Also, if you are teaching or taking an astronomy course it might be useful.

I tried to break the lectures in to short focused presentations under about 10 minutes. There is very little math and I would consider the course to not have a math prerequisite. At this point I have lectures covering the motion of the sky, history of astronomy and force, motion and energy.

Tags: astronomy, video

I like Car Talk. I also like their puzzler. One week - here was the puzzler. The basic idea:

What is the probability of make a two way trip and being at the exact same spot at the exact same time of day?


The answer is 100%. Here I have drawn a graph of position as a function of time.

Notice that as long as they leave to go back before they arrived on the way there, the two lines should cross. When they cross, the two functions will have the same values for position and time.

Tags: velocity

First, let me give a personal note to Kobe and his friends:

1. When making a video, please do not wear dark colors. Also, it would help if your outfit had distinguishing patterns on it. This video is very difficult to analyze because it is hard to see where you are (legs and arms and stuff). It would help if you wore a bright red cap or something.
2. Your other video (of you jumping over a pool of snakes) was much easier to analyze because you didn’t change your body position. Whenever possible, please do that again.
3. I must give bonus points to your film crew. Thank you very much for not moving the camera while he is jumping and for having a nice perpendicular shot that does not need perspective correction (I still haven’t figure out how to do that).
4. Finally, I know these jumps may be fun, but please be careful. Oh, the quality of videos on youtube pretty much sucks. I found one somewhere else that looked much better but it had repeating frames.
5. Oh, one more. The next time you do a jump, send me a note and I will analyze it as soon as possible.

Ok, now on to the analysis. Question: was the jump fake? Well, one way to answer this is to look at his acceleration in the air. This is somewhat problematic because he is not a rigid object while in the air. To compensate for this, I will mark the location of his important body parts and plot the motion of his center of mass. Again, I use Tracker Video Analysis to get x,y positions of each part in each frame. I tracked the motion of his calf, thigh, trunk, arms and head. To find the y-value of the center of mass, I used:


I used this table (http://oregonstate.edu/instruct/exss323/CM_Lab/bsp_deleva.htm) to get the percentage values of a typical person’s body parts (that way I did not need the total mass). Doing so, I obtain the following plot:

Where I have fit a quadratic function to the center of mass plot. Relating this fit to the kinematics equation:
so, the A value in the fit is 1/2 times the acceleration. This means that the acceleration (in the y-direction) is twice the A value for an acceleration of -11.6 m/s². Yes, I know this is not what would be expected (the expected value of -9.8 m/s²), but I think it is ok.

• First, you will see that the data fits a parabola very well (the listed RMSE of 0.015 - this is root mean square error - 0 would be a perfect fit).
• Next, why would this be off? I calibrated my data from the poor quality video using the height of Kobe Bryant as 1.98 meters (as listed on wikipedia). He was never standing up nice and straight except when his arms were over his head (making it difficult to see his head). So, this could be a cause for the different acceleration.
• Lastly, I really guessed about the location and percentage of mass for Kobe’s body parts.

Also, I looked at his horizontal positions (and did the same thing as above)

Here you can see that his horizontal motion is fairly constant (for his center of mass). This is what you would expect for a jump. There is no force in the horizontal direction (while in the air) so there should be no horizontal acceleration. Notice that the motions of the body parts CAN have acceleration, but as a whole, non.

As a comparison, I did another analysis of a jumper - but this jumper used a trampoline. This is video of some world-record trampoline dunk.

Notice that this quality is even worse than the Kobe video (but they do give a nice sideways view - thank you Japanese show people. Here is the data for the horizontal and vertical motions:


First, note that this analysis shows a vertical acceleration of -6.76 m/s² with a much higher RMSE (and with much poorer quality video). The horizontal motion shows constant velocity (as expected).

Conclusion: The jump seems real. He is a professional basketball player, so one would expect that he can jump. I am sure I have seen some other video of a person jumping over a moving car, so not an impossible stunt (though still impressive).

Next, was some there some sort of trickery involved? First, let me look at the car. Doing an analysis for the motion of the car (just in the horizontal direction although it is clear it is going down hill).

Here is the plot of the position of the car. You can see that it is moving at a fairly constant velocity (9.79 m/s or about 22 mph). The question I originally thought of “was it turning around him or something”. This doesn’t say for sure, but I would think it would have a non-constant velocity in this case.

Did the camera play some type of perspective trick? Here is an image of two frames overlapping:

This shows Kobe and where he was standing and how that compares to the position of the car at a later time. From this it looks like he was standing very near to the front right tire of the car (clearly not in the middle). This suggests that perhaps there was trickery involved. It really would be foolish of him to jump over a car without trickery. What if he missed by just a little and injured himself - that would not be good for his basketball career, would it?

Conclusion: In my opinion (for what its worth), Kobe has the ability to jump over a moving car. It am not sure if trickery was involved.

Next: I had planned to include an analysis of a jump that was fake, but apparently these are difficult to find. When I find one, I will post that.

Tags: kinematics

Suppose you drive such that your speed is like this:

This would obviously give you an average speed of 50 mph. Here you are increasing your speed for 2 minutes and then coasting for 2 minutes. Note that the the following graph would be unrealistic:

The biggest problem is the infinite accelerations going from 60 mph to 40 mph and back from 40 to 60. Well, perhaps this is just a very high acceleration. Then this would really defeat the goal of pulse and glide as you would be using your brakes to slow down and that would just be a dumb way to lose energy.
What if you did the following:

Hey its the same as before! No, its not. In this graph, you increase your speed from 40 mph to 50 mph over 2 miles, not two minutes. You then decrease your speed for 2 miles. It turns out this does NOT give an average speed of 50 mph.
Clearly, we are talking about one dimensional motion here (and by we, I mean me). So, I will use the following:
Suppose I drive 60 mph for 2 miles and then 40 mph for 2 miles (which is not what the above graph says (it has non-constant speeds - but I will proceed anyway). My average speed is NOT 50 mph. Why? Let me do this the long way. My average speed is my change in position over my change in time.

Here, I know x₁ and x₂ (the distance traveled at each speed, but I do not explicitly know the times. I can find the times using:

Substituting these in for the times:

In this case, x₁ = x₂ so:

So, if the driver drives 60 mph then 40 mph for the same DISTANCE, then the average speed would be:

Great, you may say - but that doesn’t apply to pulse and glide, as you (I) stated above. Anyway, who would drive by watching the mileage markers instead of the clock?
Nonetheless, the same idea applies to second graph with regards to distance.

Really, I am just using this pulse and glide to talk about average velocity - see, I tricked you. But I think I would like to explore this pulse and glide technique a little more. I am confused on how this saves energy significantly. If you just drive slower, it seems that would be better (less energy loss to air resistance). It seems the claim is that the car engine is more efficient while speeding up than it is maintaining speed. This seems odd, but I am not too familiar with the efficiency characteristics of the car engine.

Hopefully I will return to this topic.

Tags: speed, velocity

Tags: energy

To many students, it looks like class is the most important part of a course and where all the learning should take place. It is the part you SEE after all. In fact, the classtime is just a small part of real learning. What goes on under the water? Reading, homework, contemplating about the issues etc. This is much more important and takes much more time than that spent in class.

I don’t think so. Here are my reasons:

• In most areas, it is illegal to ride a bike on the sidewalk
• I am on a road where the speed limit is 25 mph, I typically go around 20 mph.
• There is plenty of room for cars to pass me if they wish, I don’t recall having slowed down someone
• Riding on the sidewalk (in my opinion) is just down right dangerous.

I don’t think these people realize what would happen if a bike going 20 mph collided with a pedestrian. So, I will do a couple of quick calculations. You see, this way, those people that yell at me will see the error of their ways (I am sure they read my blog).

How can I describe what it would be like to be hit by a bike? I think people are generally familar with collisions in football. How would this compare?

Football:
Let me make some very basic assumptions. Suppose a football player runs straight at a quarterback and tackles him. This is a situation I would not want to be in, especially without protective gear. Here are my completely guessed values:
Quarterback, at rest. Mass = 100 kg (like 200 lbs) Call this m_q
Tackler moving at 12 mph (5.4 m/s), mass = 120 kg (like 260 lbs) Call this m_t and v_i


After the collision, suppose they stick together. In a collision, momentum is conserved (because there are no significant external forces). Thus the momentum of the tackler plus quarterback before the collsions is the same as the momentum of the two together after the collision (assuming they stick together). This means: (I am going to write everything in terms of horizontal components, but I will leave off the x-subscript notation)

This can be used to calculate the final velocity of the two guys (they could be girls)

There are many ways to “characterize” a collision. The final velocity does not tell you much. What is interesting is to look at the loss of kinetic energy. Before the collision, only the tackler is moving, so only he has kinetic energy. After the collision the two players together have kinetic energy, but it will be LESS than the initial kinetic energy of the tackler. So where did all the kinetic energy go? It went into the impact in the form of increase in temperature, sound and deformation of the two objects. Its this last part that is important.
*Note: it is also important to look at how long the collision lasts - but this is very difficult to explore since it depends on so many things such as the materials the guys are wearing and the configuration of the players during impact.
So, what is the change in kinetic energy for this collision? Well, the initial kinetic energy would be:
and the final KE will be:

This gives a change in KE of:
Note that this will always be a negative value meaning that the KE will decrease (as I stated previously).
Let me now put in some values for the assumptions above:
So, what does that mean? Well, it is a value I can use to compare a collision with a bike. As a reality check, 795 Joules is the amount of energy needed to lift 178 lbs 1 meter (about 3 feet).

Ok, let me now consider a collision between a person biking and another person.
mass of Bike + biker = 75 kg (this is like m_t)
mass of pedestrian = 65 kg (this is like m_q)
initial velocity = 20 mph = 8.9 m/s (like v_i)
Now I can just plug these numbers into the same expression:
This is more than the football player (in case you didn’t notice).
How heavy would the tackler have to be to have this same change in KE?
I will solve the above expression for m_t:

It is very possible I could have made an error here (since I did the algebra while writing the equations in LaTeX). But at least the units look ok - so I will assume it is correct. So, what would the mass be? If a 100 kg player was tackled by another player going 5.4 m/s, that player would have to be 164 kg (or about 360 lbs).

This is not good. Consider also that merely knocking someone over on a sidewalk can cause serious trauma to the head (most pedestrians don’t wear helmets).

The moral of the story: Bikes on sidewalks can be dangerous (if they are going fast). Obviously, if one is not going too fast, its not much of a problem. I feel that anyone that complains about bikers on the road should let one ride past them at 20 mph, that is pretty fast. Also, bikers should be nice too. Can’t we all just get along?

Tags: rant, bike, energy, momentum

The teacher has a whole bunch of knowledge. The students sit in the class. The teacher then gives this knowledge to the students which they then give back to the the teacher on a test.

Here is my analogy of class and learning. Enrolling in a class is like joining a gym. You join a gym to increase in physical fitness (say you are trying to lift more weight). Well, how does this happen? How can you become stronger and lift more weights? Could you just go to a class and watch someone else lift weights? No, that wouldn’t help you too much. To get stronger, you need to exercise. You may have a trainer. What does the trainer do? He (or she) is like your mentor. He (or she) helps you do the exercises correctly. Sometimes the trainer will spot you so you don’t get hurt. The trainer may offer encouragement and suggest a schedule of exercieses.

So, in a class, what is the role of the teacher? The teacher can not MAKE you learn, to learn the students must do the work. The teacher is like the trainer. It doesn’t matter how muscular I am, that will not help you get muscular. You (the student) must do the exercises. Such is the same with learning. If a student in not actively engaged in some manner, no real learning will take place. One has to think and struggle with the material in order to understand it.

Let me explain my categories

Random: Really, does this need an explanation? This is stuff that doesn’t really fit anywhere or just some random rant of mine.

Math: You may know that I like helping people with math (or maybe you don’t know). Math stuff goes here.

Physics: This is where all the meat is. Most of this stuff is aimed at a level that a good high school student or an introductory physics major in college could understand.

General Science: This is other science stuff. Originally, I made this for topics related to science at the elementary education levels. Most people should be able to get something from these topics.

Learning: This is a new category. You may or may not know that I enjoy teaching. But really what is teaching? What is learning? Here you find my ideas about how people learn and what class is or should be all about.

(yes, you could argue the answers are slightly ambiguous - but there is still a “best” answer)

The answer is of course d. A star. Do most people get this correct? No. I polled some students and the most common answer was “Jupiter”. Why do people get this incorrect? I think that an understanding of the solar system and where the stars are is not in the common knowledge of people.

Tags: astronomy, question

Tags: HP

This girl seems to be thinking about vision as something that comes out of your eye. This is not how we see stuff. Take for instance the moon. Can you see that? Of course you can. Is it greater than 17 miles away? I would say yes (actually on the order of 241 thousand miles). What about a star? The star Alpha Centauri is 4.4 light years away (2.6 x 10¹³ miles).

In fact you can see things MUCH further away than 17 miles. You see things when light from that object reaches your eye. In the case of a star, that light is produced travels 4 light years and enters your eye. In the case of the moon, light from the Sun reflects off the moon and enters your eye.

For the 17 mile limit of seeing stuff, this has nothing to do with the human eye, it has to do with the curvature of the Earth. Maybe this is what this girl meant, but she explicitly said “the human eye can only see...”. This is a common idea that seeing has to do with something “vision” coming out of your eye. A good test to see what people think is to ask the following:

“What would happen if you were in a TOTALLY dark room? Could you see anything?” I will not tell you the answer to this question. If you don’t know, you should try it out. (it has to be completely dark).

Here are some other interesting posts about seeing:

• How does shiny stuff work?
• Well, I thought I had more - but they are on my old server, sorry.

Tags: light

Before going into details about this question and Tom and Ray's answer, I must say that this has most certainly been discussed on the car talk forum. Please forgive me if you have already stated this somewhere else. So, instead of just focusing on the correct explanation (which I will also do) I think this is a good opportunity to look at common ideas about force and motion.

First, the correct explanation:
Here is a diagram of a car crashing into an immovable wall.
First, the car going 60 mph crashing into an immovable wall. Here is a a diagram (drawn by myself)

What is important in this analysis? The key thing is that the car gets compressed as it crashes into the wall. Let me suppose it compresses an amount d. During this time, there is a force acting on the car from the wall pushing on it (there is also the ground and gravity acting on the car, but they are equal and opposite and thus cancel). So, let me assume the force the wall exerts on the car is F_wall. Whenever you have a force acting over a distance, the best way to analyze it is by using the Work-Energy principle. This basically says that (for this case):
Where v₁ is the initial velocity (in this case 60 mph). This expression could be used to solve for the force needed to be exerted on the car by the wall in order to stop it in the given distance.

Now to look at two cars hitting head on:

I am showing the cars as being compressed the same amount as before. One way you could explain this is that they have to both stop in the middle (how could one car push more than the other if they are the same?) Also, imagine that the there is a thin sheet of paper at the location where they collide. If the paper didn't tear, it would look like this paper is an immovable wall. So, how does this work. Well, in order for the same car to stop in the same distance, it needs the same force. BUT WAIT! There are TWO cars now. That really doesn't matter. This goes back to Newton's third law with basically says:
For every force there is an equal and opposite force - or as I like to put it: "Forces have two ends" or "Forces are an interaction between TWO objects". Really you can think of it as the force between the two cars. The force between the two cars would be equal to F_wall. Thus the left car would exert a force of F_wall on the right car and the right car would exert a force of F_wall on the left car. This does not mean the force has to be twice as much since it is acting on two cars. Forces are ALWAYS an interaction between two objects.

Now what about the misconceptions?

Here are the key parts of the conversation (mostly paraphrased - I intentionally left out some stuff that was not related to the physics):
Tyler: Presents the question. My dad says that two cars colliding at 60 mph each is equivalent to one car going 120 mph colliding into a brick wall.
Ray: I believe this is correct.
Tom: Your dad is correct.
..
Ray: Give us your rationale, maybe you will sway us.
Tyler: The argument is that there is a certain amount of force, right? These two cars approach...these two cars approach each other, but that force is getting divided two objects, each car. If you are driving into a stationary wall, all of that force is going into one car. So if you are driving 120 mph into a brick wall, that is 120 mph worth of force. Whereas if you are driving into another car, and they are each going 60 mph, that is only 60 mph of force.
Tom: Yeah, the other car is sucking up some of the danger here.
..
Ray: my impression from high school physics is that it is equivalent to hitting the wall at 120 mph

What can be learned form this discussion? First, I believe that Tom, Ray and Tyler are all thinking of force as a property of an object. This is a common idea in normal discussions, and you can see this above with the following statements:

• "60 mph of force"
• "that force is getting divided between two objects"

Both of these statements are made by Tyler, who I assume was trying to argue that two cars colliding is equivalent to colliding with an immovable wall. His arguments seem to suggest he is saying they are different.

Why do people try to associate a force with a property of an object when it should be associated with an interaction BETWEEN two objects? I am not completely sure. I can say that ideas of force and motion are not as easy as one would think. Even Aristotle got these ideas wrong (though he did not explicitly talk about forces). It seems that people want to associate something with the object. I guess all people are object-oriented.

Another interesting aspect is the idea of doubling. Why is one car going at 120 mph colliding into a wall the same as two objects colliding into each other? I think the reason this is stated is by using ideas of relative velocity. If you are in a car traveling 60 mph towards a car that is going 60 mph, it looks like that car is going 120 mph towards you. Using this reason, Tom and Ray would be correct, but they forgot one important aspect. We are assuming the wall does not compress, but the other car does. This means that for two cars colliding, they BOTH are compressed and absorb energy. If the wall does not compress (even though it really would a little), it would not absorb any energy.

Tags: work, energy

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
http://auto.howstuffworks.com/question424.htm

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 20% efficient at converting this energy to mechanical energy.
• The alternator is 70% efficient at converting mechanical energy into electrical.
• At highway speeds, air resistance is the dominating factor in fuel efficiency (this might be wrong)
• The air resistance force can be modeled as F_air = (1/2)ρ C A v²
• I will assume an "average" car that has combined C_dA of 9 ft² or 0.84 m² (where C_d is the coefficient of drag and A is the cross sectional area. Also, ρ is the density of air, about 1.2 kg/m³)
• An average trip of 50 miles (I completely made this up).
• My mythical "average" car gets 25 mpg when going 70 mph

Now to Calculate
First, for this 50 mile trip going at 70 mph, how much gas is "spent" on daytime running lights? Well, a 50 mile trip at 70 mph would take:

During this time, the lights are running at 100 watts, this is the same as:

How much gas does this require? Using the information from the above, I can write an expression for how much energy a certain number of gallons of gas would produce using the alternator. Note in this expression, the 0.2 and 0.7 are the efficiencies of the engine and alternator.

Solving this for "gallons of gas"

Note: this wouldn't change much if driving 71 mph, the time would be about the same.

Now for the slowing down part.
How much energy would be saved by driving 70 mph instead of 71 mph? What is the energy lost due to air resistance? To calculate this, I can calculate the work done by the air resistance (which would be equivalent to the energy lost). Remember that work is
In the case of air resistance, the force of air and the direction of motion are in the opposite directions. This means that the work done by friction is:
where these are the magnitudes of the vectors (d is the distance traveled).
Since I am not really concerned with the work done by air resistance, but rather the CHANGE in work done in going 71 mph vs. 70 mph, I can just calculate:

Now to convert this into gallons of gas. Note: I only need to include the 20% efficiency of the engine and not the 70% efficiency of the alternator.


The Answer
So, there you have it. Slowing down from 71 mph to 70 mph saves more gas than turning off your daytime running lights. There are people that say daytime running lights are a waste of gas, but they don't seem to be that big of a problem. If you are really concerned, you could slow down. That will have a much bigger impact on fuel useage. (Just imagine how much you would save if you slowed down to 55 mph). Plus, daytime running lights are likely safer (that is what they claim, and it makes sense).

Tags: energy, cars

I try to stress to people that driving faster on shorter trips doesn't really make THAT big of a difference in time. Also, you can save money by driving slower. This was essentially the idea behind my optimal commuting speed calculator. The problem is that this calculator doesn't really work if you don't get paid by the hour. I decided to make a graph anyway that shows the decrease in your efficiency (and thus increase and how much you spend on gas) at the same time showing how much time you save. That way, you can use your own weighting of the importance of time.

For this graph, I used an efficiency of 25 miles per gallon when driving 70 mph. The trip distance is 20 miles and the cost of gas is $4 per gallon.

You can see going 90 mph instead of 50 mph save you 10 minutes, but cost more than $2.50 dollars MORE than going 50 mph.

Tags: energy, cars

Step 1. Get the movie. I used Mpeg Streamclip to get the movie in quicktime format from flash video.
Step 2. Get some stuff to calibrate the video. I first tried searching for that particular pool in the video so I could find out how big it was. Epic Fail. Next I went to wikipedia to get the dimensions of Kobe Bryant entity. He is 1.98 meters.
Step 3. Analyze the video. Here is the vertical motion of Kobe.

From this, we (me and you) can see a couple of important things. First, it is a parabolic graph. This indicates the acceleration is constant. Second, I can obtain a value for this acceleration. It will be twice the coefficient of the x² term. This means that the acceleration of Kobe while jumping is 9.56 m/s². This is close enough to the expected value of 9.8 m/s² that the video seems real. But I will continue (because it is difficult for me to stop).

Let me now look at the horizontal motion:

This is clearly a straight line indicating that there is no horizontal acceleration. This is also an indication of non-fakedness.

What can be learned