Self-education is, I firmly believe, the only kind of education there is. -Isaac Asimov

Trajectory, projectile motion

Posted: November 5th, 2011 | Author: | Filed under: Algebra, Mathematics, Physics | Tags: , , , | No Comments »

One of the most annoying problems I’ve had is one of Trajectory and Projectile motion. The reason that these problems are so frustrating though is not because of the actual physics (which conceptually is quite easy) but because of the algebra. It can be quite confusing knowing where to move things around. In projectile motion problems, this becomes even harder because there are some intimidating trig functions that need to be resolved.

So let’s do one as an example which is a bit intimidating just because of the algebra, I’ll do the step by step derivation.

During volcanic eruptions, chunks of solid rock can be blasted out of the volcano; these projectiles are called volcanic bombs. Figure 4-51 shows a cross section of Mt Fuji in Japan.

(a) At what initial speed would a bomb have to be ejected, at angle \theta_0=35^\circ to the horizontal, from the vent at A in order to fall to the foot of the volcano at B, at vertical distance h = 3.30 km and horizontal distance d = 9.40km? Ignore for the moment , the effects of air on the bomb’s travel. (b) what would be the time of flight?

volcanoes are scary.Luckily, they’ve given us a picture to see what is happening.

 

 

 

First let’s take a look at what the question is looking for and then we’ll delve into how to work it. The question specifically is asking for the speed as it leaves the volcano.  So what we are looking for is the MAGNITUDE of the initial velocity. But this is kind of perplexing because we’re not given a lot of information, we’re given the height (h) the distance (d) and the angle. Let’s make a table of what we have and what we need.

anglexy
theta = 35 degreesx = 9400 m (converted from km)y = - 3300m (converted from km)
a = g =- 9.8 m/s

Not a lot of information, but we have an equation to help us with this. The path of the trajectory of a projectile is given by the equation:

y=\tan(\theta)x-\frac{gx^2}{2(V_0\cos(\theta)^2)}

We know that we are solving for the magnitude of the initial velocity. so let’s do that

y=\tan(\theta)x-\frac{gx^2}{2(V_0\cos(\theta)^2)}

 

\tan(\theta)x-y=-\frac{gx^2}{2(V_0\cos(\theta))^2}

 

\tan(\theta)x-y=-\frac{gx^2}{2(V_0\cos(\theta))^2}

 

2(V_0\cos(\theta))^2\tan(\theta)x-y=-gx^2

 

V_0\cos(\theta))^2=-\frac{gx^2}{2(\tan(\theta)x-y)}

 

V_0^2=\frac{x^2}{\cos(\theta)^2}\frac{g}{ 2(\tan(\theta)x-y)}

 

V_0=\frac{x}{\cos(\theta)}\sqrt\frac{g}{ 2(\tan(\theta)x-y)}

Note how the square roots were saved for last in the equation, this is because these were the trickiest parts.

But look now! We are 90% of the way done with part a! Now it’s all just plugging in our known values!

V_0=\frac{9400m}{\cos(35^\circ)}\sqrt\frac{-9.8\frac{m}{s^2}}{ 2(\tan(35^\circ)9400m-(-3300m))}

This comes out to about 255\frac{m}{s}

Easy! See that we just needed to think about the algebra, and the rest of the problem came together!

Now lets do part b. In this I’ll just give you the equation since it’s a simple manipulation

x=V_0\cos(\theta)t

 

\frac{x}{V_0\cos(\theta)}=t

Hey we have all these values!

\frac{9400m}{255\frac{m}{s}\cos(35^\circ)}= 45s

It’s solved! Go get yourself a drink!

Problem is from 91 in Halliday & Resnick’s Fundamentals of Physics

gcj compiler install errors Debian/Ubuntu

Posted: October 14th, 2011 | Author: | Filed under: linux | No Comments »

So on debian I’ve been having some problems with packages with gcj included. These packages :

openoffice.org-gcj
libxsltc-java-gcj

Were the ones causing the most problems, I looked at /var/log/dpkg.log and found the following line:

2011-10-13 23:39:09 status unpacked libxerces2-java-gcj 2.9.1-4.1

After some googling I found this post and used the following to fix the problem

sudo mv /usr/bin/rebuild-gcj-db /usr/bin/rebuild-gcj-db.back; sudo aptitude update; sudo aptitude upgrade

That seemed to fix it. Hope this helps someone.

Days 5 6 and 7 of not smoking, the home run!

Posted: August 6th, 2011 | Author: | Filed under: Self Improvement | No Comments »

I feel so thankful that I have family and friends who are so encouraging. I was able to accomplish my goal of not smoking, I won’t be picking up that habit any more.

Here are the graphs for days 5, 6 and 7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

As you can see the graph gets really sharp on day 7, this is because I didn’t choose to use the smoothing option in open office.
What is really cool is now I don’t have any cravings at all. By day 8 I wouldn’t have known I was a smoker. Do I miss smoking? Not really. I find that I have a lot more energy, I read more and concentrate more on tasks. Smoking was really just a distraction.

I hope these posts encourage others to quit. I can’t give you a specific reason to quit, only you can do that for yourself. But cataloging my cravings, and making an effort out of it, really helped.

Day 4 Or how I stopped worrying and learned to love to blog

Posted: August 5th, 2011 | Author: | Filed under: Self Improvement | No Comments »

Okay so it’s been about a month and change since I’ve posted, but I have good news! I have not smoked a cigarette in that time. I have also moved into our spacious new house, and am happier than ever.

But here is what you came for some data! Here is the graph for the 4th day of quitting. As you can see, I was still struggling, but I managed to keep the cravings away by moving heavy furniture and painting!

Quit smoking graph

See all of those data points?

 

Day 4 (delayed)

Posted: June 23rd, 2011 | Author: | Filed under: Self Improvement | No Comments »

My day 4 craving graph is being delayed due to my moving, I am still keeping track, I’ll update in a few days!

About the smoking rating system

Posted: June 22nd, 2011 | Author: | Filed under: Self Improvement | No Comments »

I wanted to address the smoking craving scale I used in the previous three posts basically I based it off of the 0-10 scale that doctors use when asking patients for their pain levels:

0-1 No pain
2-3 Mild pain
4-5 Discomforting – moderate pain
6-7 Distressing – severe pain
8-9 Intense – very severe pain
10 Unbearable pain

My scale is basically parallel with cravings instead of pain

0-1 No craving
2-3 Mild craving
4-5 Discomforting – moderate craving
6-7 Distressing – severe craving
8-9 Intense – very severe craving
10 Unbearable craving – smoked a cigarette

I hope this helps clear some stuff up, I plan on making a post soon to show you all how to make your own smoking graphs using Free Software!

Day 3 without a smoke, feeling stronger than ever!

Posted: June 22nd, 2011 | Author: | Filed under: Self Improvement | 2 Comments »

Today was the 3rd day without a single puff of smoke, by far today was the hardest in terms of temptations, here are a couple of things that happened

  • Needed to take boxes to the FedEx Office, but couldn’t find anyone to help me
  • Needed to figure out house stuff (we’re buying a house) and organize everything for thursday
  • Car broke down for the second time this week, this time it was the brakes, thank goodness for AAA!
  • The first thing I did this morning was take an exam

So it was pretty stressful, but I think I handled myself well. I could have easily bought cigarettes at anytime during today but I kept thinking about how I just needed to stop using them as a crutch. I need to be able to stand up on my own without them .

Here are some of the things that happen on the third day of not smoking:

  • Nerve endings begin to regrow
  • You become more sensitive to smells and taste

I haven’t really been able to test the first hypothesis, but some evidence suggests that the second one is happening. There is a Chinese restaurant down the street, and even though I walk past it every day, and notice it’s bad grease smell today in particular almost knocked me on the ground!

Without further ado here is the graph (notice the first sharp spike, this is because I didn’t record data during my test)

Overall the values are lower than other days though, which suggests that either I am not noticing the nicotine, or that the nicotine is leaving the body (or both).

Day 2 without a cigarette (graph)

Posted: June 21st, 2011 | Author: | Filed under: Self Improvement | No Comments »

My highly scientific study on the effects of quitting smoking continues. Today was a particularly stressful day, had to get my front tires changed on our car, had to deal with realtors and mortgage companies, and I have an exam tomorrow! I didn’t give in though. These cigarettes were not going to best me!

Today’s graph is a little bit more unweidly than yesterday’s post. I think a lot of it had to do with the stuff going on. Not only did it stress me out, but it also help to distract me when I really would have wanted a cigarette.

Things of note:

Today I really felt the craving level of “2″ was totally justified. The reason for this was that there were times when I wasn’t even thinking about smoking and suddenly I’d remember to record the data. I use 9 a lot because I really feel like I am about to go to the store and buy a pack of smokes at that moment, it’s those moments that I try to take the most care in getting the data down, because I think it’s good to see how eventually the cravings go away.

All in all:

This was a pretty good day, I feel like I definitely succeeded and that even though I still have cravings, I am fighting the good fight.

13 Hours without a cigarette

Posted: June 20th, 2011 | Author: | Filed under: Self Improvement | 5 Comments »

So I’ve now gone 13 hours without having a smoke. Feels pretty good, but what would this be worth to anyone else?

When I got up this morning the first thing I did was start recording data on my cravings, I used a 0-10 scale 0 means I have absolutely no craving, 10 means that I have smoked a cigarette.

The blue dots represent the data points I put in the lines in order to show the trends between two dots.

So without further ado, here is the graph:

Some surprising things

There wasn’t a point today when I went below a 3 “craving”, hopefully this gets better with time, but I’m going to try to collect this data for a month to see any larger trends.

The cravings were highest around noon, and I think this is probably related to triggers such as food

This graph really helped me to visualize what I was going through, it helped me to see “Oh see I’ve already been through a 9 today, I can totally handle this 6″

I was tempted to buy cigarettes when I took a quick trip to the store to purchase some soda, but I thought about the graph, and it helped a lot.

I have quit before (with the help of a friend) but this time it just feels harder. I think it might be because of some personal things that will get sorted out this week.

Sources of error

The major source of error, is that “cravings” really aren’t quantifiable

I could have chosen to take data at regular intervals, but the data ended up being very close to “semi-regular” intervals anyway, so it probably didn’t affect the graph too much.

Moore’s law and physics

Posted: June 19th, 2011 | Author: | Filed under: Physics | No Comments »

The Hindu has an article of a review of Micho Kaku’s newest book “The Physics of the Future”. In particular they point out that Moore’s Law cannot last forever. They give a few good reasons why, but I think it’s very intutitive as to why, and I think they only touched on it slightly.

The second hurdle before Moore’s law, as Kaku outlines, is a problem posed by the quantum theory – the uncertainty principle – which says that you cannot know for certain the location and velocity of any atom or particle. “Today’s Pentium chip may have a layer about thirty atoms thick. By 2020, that layer could be five atoms across, so that the electron’s position is uncertain, and it begins to leak through the layer, causing a short circuit. Thus, there is a quantum limit to how small a silicon transistor can be.”

Moore’s law is a logarithmic scale based on physical quantities. Because the transistor gets smaller and smaller, it will one day get so small, that it can either a. no longer function as a transistor or b. no longer be called a transistor. There really isn’t a lot of thing we can do about this currently. We have some ideas, but engineers really are the ones who are going to have to put their heads together ( like solving the problem with the memristor ).

Unfortunately I’m not a fan of futurism, and this phrase in particular bothers me:

“If each catom is instructed to bind with only a tiny set of neighbouring catoms, then the catoms would magically rearrange themselves into complex structures (much like the neurons of a baby’s brain need to know only how to attach themselves to neighbouring neurons as the brain develops).”

Emphasis mine of course. The idea that this would be a magical process, completely misses the point. We should be investigating more and more, it wouldn’t be a show of magic, but rather it would show our courage to understand the world in a very detailed way.

« Older Entries