# MacGyver Season 3 Episode 22 Science Notes: Mason + Cable + Choices

Season 3 finale—but don’t worry, MacGyver has been renewed for a 4th season. Boom. Now for some science.

Descender Device

MacGyver needs to get down an elevator cable—to do this, he builds a descender. The basic idea is to “grab” hold of the cable to produce enough friction that it supports a human. That keeps you from falling. Of course you also want to move down, there needs to be some method to “inch” your way down. The one MacGyver builds looks like this.

Here is an early sketch for a type of descender

Of course the problem is that the elevator cable is under tension and very thick. It’s really more like a pole than a rope. That’s why the design in the episode would work better.

These aren’t bad hacks—they are hacks from the Bad MacGyver (Mason). First, there is the cable cutter. This is just a bolt cutter connected to an electric motor. That should work.

The other one is the hydrochloric acid in the basement of a building around support pillars. So, would this work? Well, hydrochloric acid does indeed dissolve concrete and cement—it’s not super fast though. Everyone likes to think of acid as being that kind in the movie Alien. It’s not like that.

Of course a pillar isn’t just cement. It has steel rods in there too. But acid will eat through steel as well—again, it just takes a while. But you don’t have to completely dissolve the pillars to cause destruction. Just making them weak could do the job.

Oh, it’s a good thing the hydrochloric acid is in plastic barrels. It would melt steel barrels.

Atwood Machine

MacGyver’s plan is to connect one elevator to the one next to it. When the cable is cut, the two elevators will create an Atwood machine. This is of course a real physics problem.

The idea is to have two different masses connected by a string. This string then runs over a pulley. If the masses are different, the two masses will accelerate (one up and one down) with a constant acceleration. The key is that this acceleration will be much smaller than the acceleration of a free falling object. That’s a good thing since waaaaay back in the day, it was very difficult to measure the motion of an object with a large acceleration.

I think I will save the physics of an “Atwood Machine Problem” (no one really calls it that) for a later post. Instead, here is my calculation.

But wait! There’s more! This calculation would give you the tension in the cable, but once there is a tension the cable would stretch. How much the cable stretches depends on:

• Tension
• Cable length
• Cable diameter
• Type of material

So you see that the stretch really depends on two things—the material and the size of the cable. For the material dependence on stretch, we call this Young’s Modulus.

There is one more thing—maximum tension before a cable breaks. This also depends on the type of material and the shape of the cable. Here is a sample calculation.

Too bad MacGyver never got a chance to put these calculations into practice. Of course it’s Mason’s fault.

Recover Serial Number

It is possible to recover a serial number that’s scratched off a metal. Essentially, when the number is stamped into the metal there is a more than just a surface effect. The deeper metal is also changed in some way. Using acid, it’s possible show these differences and find this number. Yes, this is real.

For a circuit chip, the serial number is not likely to be stamped—it will be printed. Still, it’s entirely plausible that you could still recover some type of artifact.

# Video Analysis of Soyuz MS-10

There should be a grave yard for blog posts that start, but never get published.  Fortunately, I have this site.  Here I can share with you my failed posts.  Get ready.

It starts with this epic video from the Soyuz MS-10 failed launch.

That’s pretty awesome.  It’s doubly awesome that the astronauts survived.

Ok, so what is the blog post?  The idea is to use video analysis to track the angular size of stuff on the ground and from that get the vertical position of the rocket as a function of time.  It’s not completely trivial, but it’s fun.  Also, it’s a big news event, so I could get a little traffic boost from that.

How do you get the position data?  Here are the steps (along with some problems).

The key idea is the relationship between angular size, actual size and distance.  If the angular size is measured in radians (as it should be), the following is true $L = r\theta$ where L is the length (actual length), theta is the angular size, and r is the distance.

Problem number 1 – find the actual distance of stuff on the ground.  This is sort of fun.  You can get snoop around with Google maps until you find stuff.  I started by googling the launch site.  The first place I found wasn’t it.  Then after some more searching, I found Gagarin’s Start.  That’s the place.  Oh, Google maps lets you measure the size of stuff.  Super useful.

Finding the angular size is a little bit more difficult.  I can use video analysis to mark the location of stuff (I use Tracker Video Analysis because it’s both free and awesome).  However, to get the angular distance between two points I need to know the angular field of view—the angular size of the whole camera view.  This usually depends on the camera, which  I don’t know.

How do you find the angular field of view for the camera?  One option is to start with a known distance and a known object. Suppose I start off with the base of the Soyuz rocket.  If I know the size of the bottom thruster and the distance to the thruster, I can calculate the correct angular size and use that value to scale the video.  But I don’t the exact location of the camera.  I could only guess.

As Yoda says, “there is another”.  OK, he was talking about another person that could become a Jedi (Leia)—but it’s the same idea here.  The other way to get position time data from some other source and then match that up to the position-time data from the angular size.  Oh, I’m in luck.  Here is another video.

This video shows the same launch from the side.  I can use normal video analysis in this case to get the position as a function of time.  I just need to scale the video in terms of size.  Assuming this site is legit, I have the dimensions of a Soyuz rocket.  Boom, that’s it (oh, I need to correct for the motion of the camera—but that’s not too difficult).  Here is the plot of vertical position as a function of time.

Yes, that does indeed look like a parabola—which indicates that it has a constant acceleration (at least for this first part of the flight).  The term in front of t2 is 1.73 m/s2 which is half of the acceleration.  This puts the launch acceleration at around 2.46 m/s2.  Oh, that’s not good.  Not nearly good enough.  I’m pretty sure a rocket has an acceleration of at least around 3 g’s—this isn’t even 1 g.  I’m not sure what went wrong.

OK, one problem won’t stop me.  Let’s just go to the other video and see what we can get.  Here is what the data looks like for a position of one object on the ground.

You might not see the problem (but it sticks out when you are doing an analysis).  Notice the position stays at the same value for multiple time steps?  This is because the video was edited and exported to some non-native frame rate.  What happens is that you get repeating frames.  You can see this if you step through the video frame by frame.

It was at this point that I said “oh, forget it”.  Maybe it would turn out ok, but it was going to be a lot of work.  Not only would I still have to figure out the angular field of view for the camera, but I need to export the data for two points on the ground to a spreadsheet so that I can find the absolute distance between them (essentially using the magnitude of the vector from point A to point B). Oh, but that’s not all.  When the rocket gets high enough, the object I was using is too small to see.  I need to switch to a larger object.

Finally, as the rocket turns to enter low Earth orbit, it no longer points straight up.  The stuff in the camera is much farther away than the altitude of the rocket.

OK, that’s no excuse.  I should have kept calm and carried on.  But I bailed.  The Soyuz booster failure was quite some time ago and this video analysis wouldn’t really add much to the story.  It’s still a cool analysis—I’ve started it here so you can finish it for homework.

Also, you can see what happens when I kill a post (honestly, this doesn’t happen very often).

Actually, there is one other reason to not continue with this analysis.  I have another blog post that I’m working that deals with angular size (ok, I haven’t started it—but I promise I will).  That post will be much better and I didn’t want two angular size posts close together.

The end.

# Basics: Making graphs with kinematics stuff part II

**pre-reqs**: [kinematics](http://blog.dotphys.net/2008/09/basics-kinematics/) *I don’t think you need [part I of this](http://blog.dotphys.net/2008/09/basics-making-graphs-with-kinematics-stuff/) if you don’t want*

So, you still want to make a graph with that kinematics data? You think that graphs on paper are too barbaric? Well, if you are ready, you can use a spreadsheet. But be careful. If you don’t know what you are doing, you can cause some damage (much like flying a 747 after reading a blog about it). Speadsheets allow you to do a couple of things.

• make pretty graphs
• fit mathematical functions to data

Of course they actually do much more – but you need [“clippy”](http://en.wikipedia.org/wiki/Clippy) to help you with that.

First, what software do you use? I think most people will immediately go for Microsoft Excel. I have to admit, this is what I use because I am so familiar with it. Many people already have this also. Truthfully, it is a good spreadsheet program (but not perfect). There are some free alternatives:

• Open Office – I use the Mac OS X variant Neo Office
• Online spreadsheet like Zoho) or Google Docs. Both of these are fairly useable.
• Other – like Apple’s spreadsheet or other non-free stuff.
• A final excellent option is Vernier’s Logger Pro. Although it is not free (nor perfect) it is not too expensive and can be covered by a school site license

For this tutorial, I will show explicitly how to make graphs using MS Excel. I was going to use open office, but in order to fit a polynomial to data, you have to do some more serious stuff. The basic idea is the same no matter what you use.

# Physics of Linerider Part II: Scale

Scale of the Line Rider

First, we assume that the line rider is on Earth and for low speeds will have a free-falling acceleration of 9.8 m/s2. Next, an arbitrary distance is selected. In this case the length of the sled is chosen to be 1 LU (Linerider Unit).

The goal will be to put the linerider in a free fall (where air resistance should be able to be ignored) and determine his (it could be a she, it is difficult to tell) acceleration in LU/s2. Then we can determine the conversion factor from LU/s2 to m/s2.

# Basics: Kinematics

**pre reqs:** *none*

Often I will do some type of analysis that I think is quite cool. But there is a problem. I keep having to make a choice. Either go into all the little details, or skip over them. My goal for this blog is to make each post such that someone could learn some physics, but I also don’t want it to go too long. So, instead of continually describing different aspects of basic physics – I will just do it once. Then, when there is a future post using those ideas, I can just refer to this post. Get it?

Fine. On with the first idea – kinematics. Kinematics typically means a description of motion (not what causes that motion). In particular, kinematics looks at position, velocity, and acceleration. In this post, I will try to stay in one dimension. This will make things look simpler without really losing too much. Later, when I talk about vectors, I will make it all better.