# MythBusters Jr. Slinky Drop Stuff

Tonight’s episode (actually there are two episodes tonight) looks at the famous slinky drop problem. Let’s start with the first place I saw this—from Derek Muller (Veritasium) even though he didn’t invent this either.

That’s pretty awesome, right? Of course the first thing I want to do is to make a model of a falling slinky. Here is that first post.

Some important comments.

• It’s important that the slinky itself has mass. You can’t use the normal assumption of a massless spring.
• The best way to model a spring with mass is to have a bunch of smaller masses connected by massless springs.
• When the slinky is dropped, the center of mass falls with a downward acceleration of -9.8 m/s^2.
• However, since the slinky is contracting this makes the bottom of the slinky motionless.

Here is an animation of my python model.

Sorry—this code is older and I don’t have it on some online platform (I will try to update that soon). But here is the important plot. What if you look at the vertical position of the top, bottom and center of mass for this “slinky”? Here’s what that looks like.

The red curve is the bottom mass. Notice how it “hangs” there? Awesome.

But can you just put a mass (like a car) on the end of a spring and drop it? Yes, but it won’t look very cool. The key is the center of mass. You want the center of mass to fall such that the bottom mass stays in place. With a car and a spring, there is no top mass moving down faster than the acceleration due to gravity to make the bottom mass (the car) move up relative to the center of mass.

In the end, you need some type of mass at the top of the spring too. So, that could work. Two large masses separated by a spring. When you hang and then drop, the bottom mass will be stationary.

But wait! You can try this yourself. Get two masses and connect them with rubber bands (even though rubber bands aren’t ideal springs). Hold one mass and let the other hang below. Now drop.

Here’s what that looks like in slow motion. Sorry about the vertical video, when I recorded this I didn’t think I would post it.

Pretty awesome.

But wait! What if you want to make something like the slinky? In that case you can get a bunch of masses and connect them with rubber bands. It will be just like the python animation above, but in real life.

I should have recorded this in slow motion. Oh well.

Just for fun, here are some of my original notes in which I estimate what kind of spring you would need to do this drop thing with two cars.

# MacGyver Season 1 Episode 9 Science Notes: Chisel

There is no introduction, just science.

Lighter and spray can stun thing

MacGyver gets a broken spray can of something (it really could be any aerosol can) and attaches a cigarette lighter to it. He then makes it so the lighter burns while the spray sprays. When he throws it, boom.

Yeah, these spray cans can ignite stuff. This is plausible.

DIY hot air balloon for Jack’s phone

Someone needs to make a super clip of all the times Mac says “Jack, I need your phone”. I think that’s funny.

In this case, the idea is to build a mini hot air balloon to lift up the phone so that they can see a “bird’s eye view” of the city. Here’s how it works.

• Get a thin plastic trash bag.
• Get some fuel—in this case it’s that stuff that burns to keep food hot for a buffet or something. Oh, they put it in aluminum foil.
• Hang the phone and light the fuel.

Boom. That’s it. Yes, it’s real. The basic idea is that the fuel heats up air that fills the bag. Hot air has a lower density than cold air—this means that the weight of the air inside the bag is less than the weight of air outside of the bag. This gives a net upward buoyancy force on the bag.

Here is a more detailed explanation of buoyancy, if you need it.

OK, but would this be enough to lift a phone? It would be tough, but it’s at least plausible. It depends on the weight of the phone and fuel, the size of the bag, the temperature of the inside and outside air. So, it’s possible.

Here is one you can make yourself.

Bullet proof paper

OK, it’s not bullet proof paper. It’s a calculation of how much paper you would need to stop a bullet. I love how well this turned out.

Bullet proof shield

This one is simple. Yes, if you tape a bunch of kevlar vests to a door it will be fairly bulletproof. MacGyver’s calculation is great (I should know). OK, it’s not perfect—but it’s a good example how to make a basic estimation.

Personally, the dialogue gets to the basic point and the animations and graphics are really nice. LOVE IT.

Let’s go over some of the details.

• You need some basic values—like the speed and mass of a bullet from an AK-47. I googled this, but maybe MacGyver just knew it.
• From there, you want to somehow model the interaction between a bullet and paper. The first idea is to think of it like a drag force (just like a bullet going through air or something). Of course this causes a problem because that makes it a velocity dependent force and therefore VERY difficult to deal with.
• But what if there is a constant force on the bullet during the interaction with the paper? In that case, we can use the work-energy principle (which MacGyver says—YAY!).
• With a constant drag force, you can then find the distance over which this force needs to do work to stop the bullet.
• For the constant drag force, I estimated the density of paper (a little bit lower than the density of water) and assumed this was the constant force. Of course this is wrong—but it’s just a place to start. You have to start somewhere.
• Really, the rest is just calculations.

Here is my original estimation.

Oh, I guess there are a few things to point out. First, the MythBusters also looked at using paper to bulletproof a car. It sort of worked. Second, in the end MacGyver reports the paper thickness in inches. I hate imperial units—but I guess that’s just the way things are.

Still, super pumped at the way this turned out.

Improvised weapons

In order to fend off the attackers, MacGyver makes some improvised explosives to shoot marble cannon balls. I don’t want to go into the chemistry of explosives so I will just put my normal explanation.

Any time you mix two or more chemicals, it is plausible that it could make an explosion. The end.

Intercept radio transmission

MacGyver wants to figure out what the bad guys are saying on their radios. He uses a yaghi antenna to get a directional signal and then he connects it to an AM/FM radio and picks up the signal.

OK, they probably don’t broadcast on the AM-FM frequency range. However, it’s possible he could modify the tuner in the radio to pick up their frequency. It would help if he knew their frequency. Also it’s hopeful that they aren’t using encrypted radios.

Dish soap to slide a safe

This is basic physics. Dish soap can indeed decrease the frictional force—especially for smooth surfaces. This would make a great physics problem.

Sugar putty bomb

Again with the bomb thing—using sugar for an explosive. Well, you can make a rocket from sugar (again—from the MythBusters)

Radio detonator

In order to detonate the explosives, MacGyver takes apart one radio such that it makes a spark when receiving a signal (instead of making a noise). This is fairly plausible.

There are a couple of other things, but I will stop here.

# MythBusters – a tree is 90% air

Dear Mythbusters. I hope you know that I think you are awesome. I know you are not scientists, but rather master robot builders. I respect that. I envy your robot-building abilities. Please forgive me for pointing this out – but even if a tree is 90% air, that does not mean a ball has a 90% probability of passing through it.

For those of you who are unaware, in the last episode of MythBusters, they explored the idea that a golf ball should pass through a tree 90% of the time. What if they were to test following alternative myth:

*A golf ball has a 90% chance of passing through something that is 90% air.*

Here is my test object:

![Screenshot 05](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-05.jpg)

It is a steel box with air inside. I did not give the dimensions, but you can imagine it would not be difficult to make this 10% steel and 90% air. What would happen if I hit a golf ball at this? I think there were would be a 0.000000000000000000001% percent chance of it going through (smaller than that – but I think you get the idea).

What is really important is the scattering cross-section, not the density.

# Bullets have a lot of kinetic energy (apparently)

I was recently re-watching a MythBusters episode and I found something I had wanted to explore previously (but accidentally deleted the episode). Here is a short clip from the “shooting fish in a barrel” episode:

Did you see what I found interesting? That big barrel of water left the floor from being hit by a bullet.
The question here is: Does a bullet have enough energy to increase the gravitational potential energy of the barrel to that height?

# MythBusters: How small could a lead balloon be?

On a previous episode of The MythBusters, Adam and Jamie made a lead balloon float. I was impressed. Anyway, I decided to give a more detailed explanation on how this happens. Using the thickness of foil they had, what is the smallest balloon that would float? If the one they created were filled all the way, how much could it lift?

First, how does stuff float at all? There are many levels that this question could be answered. I could start with the nature of pressure, but maybe I will save that for another day. So, let me start with pressure. The reason a balloon floats is because the air pressure (from the air outside the balloon) is greater on the bottom of the balloon than on the top. This pressure differential creates a force pushing up that can cause the balloon to float.

**Why is the pressure greater on the bottom?**
Think of air as a whole bunch of small particles (which it basically is). These particles have two interactions. They are interacting with other gas particles and they are being pulled down by the Earth’s gravity. All the particles would like to fall down to the surface of the Earth, but the more particles that are near the surface, the more collisions they will have that will push them back up. Instead of me explaining this anymore, the best thing for you to do is look at a great simulator (that I did not make)
[http://phet.colorado.edu/new/simulations/sims.php?sim=Balloons_and_Buoyancy](http://phet.colorado.edu/new/simulations/sims.php?sim=Balloons_and_Buoyancy)

![Page 0 Blog Entry 14 1](http://blog.dotphys.net/wp-content/uploads/2008/09/page-0-blog-entry-14-1.jpg)

# MythBusters pulling on a phone book: You are doing it wrong.

The MythBusters aren’t really doing it wrong, but they give me a chance to talk about some physics. In the latest show, they tested the myth that two phone books with their pages alternating were indestructible. To test this, they put the two phone books together and then pulled them apart in a sort of tug of war. Here is a diagram:

Looks great, what is wrong with this? The problem is that by pulling this way, the MythBusters produces 320 pounds of force on the book – but they could have done twice that. This really goes back to the old question: Which would produce a greater tension, two horses pulling in opposite directions, or one horse pulling on a rope tied to a tree. The answer is that both tensions are the same. However, many say that the two horses create a greater tension. The likely thinking in this “two horses are more” answer is that TWO things are doing something must be greater than ONE thing doing something. This reasoning fails because if you tie a rope to a tree, it is doing exactly the same thing the other horse doing: not moving.

Why? A force explanation follows:

# Another MythBusters Tie in: zero-g in a plane

Maybe you can tell I am watching the MythBuster’s Moon Special. In the show, the MythBusters go in a plane to reproduce the gravitational forces on the moon. I previously went over this, so here is the link:
[Tutorial on how gravity and weightlessness (zero-g) work](http://dotphys.net/page1/gravity/gravity1.html)