Season 5 Episode 6.
I normally just jump right into the science stuff for these episodes, but I need to add some additional comments. This episode takes place during the pandemic shut down — and it’s one of the best of all the MacGyver shows. It’s just so good. Here are some of the things that makes it awesome.
I’m currently reading Randall Munroe’s book, How To (Penguin Random House). Personally, I love anything from Randall Munroe — you might know him from his awesome xkcd comics.
The basic idea of the book is to take some crazy (or even normal) questions and explain how to do them. For instance, this question was “how to jump high”. Of course, it’s just a book — and with that, he has to skip over some of the details. But that’s why I’m here. I’m going to fill in all the missing details of some of these equations.
Here is the one I want to start with. The idea is that if you are moving with some speed, you can redirect that velocity upward and send yourself into the air. This would be the case of running on a skateboard and then hitting a vertical ramp. Munroe then gives the following equation (which I have reproduced with LaTeX). …
Season 5 Episode 5
Skee Ball Physics
This not really a MacGyver hack, but it’s still physics. Mac and Riley are playing skee ball. His explanation for why he’s going to do better at the game goes like this:
Well, that’s because last time we were here, my kinematic equation scalar and vector variables — but when I compensate for rotational motion…
The basic idea is that a skee ball is a lot like a projectile motion problem. Once it leaves the ramp, the only force acting on it is the downward gravitational force. However, while it’s rolling things are more complicated. …
In this modern society, cables are pretty much everywhere. It’s not just the stuff that connects your computer and monitor, but data and power cables need to be run all over the place. Often these cables are suspended between poles to keep them out of the way of cars and pedestrians.
Some of these overhead lines might look like they are straight from one pole to the next, but they aren’t. There is always some bit of sag. You can really notice this when the cable mounting points are quite a distance away.
But now we get to the physics of this. What shape does a cable make as it is supported between two points? The answer is a catenary curve. No, it’s not a parabola — even though it sort of looks like one. …
Season 5 Episode 4
A quick comment. I really liked this episode. It has:
Now for the science.
Breaking Glass With a Temperature Difference
I’m working through some examples of physics problems that use Lagrangian Mechanics. Oh, what’s that? You aren’t sure about this whole Lagrangian thing? Well, here you go — my introduction to this physics method. Also, here is a more basic example finding the motion of a half-Atwood machine.
The Moving Wedge Problem
OK, so here is the problem:
A 100 gram block starts from rest on top of a frictionless wedge. The wedge can also slide. It has a mass of 431 grams (see how I used an unexpected value) with an incline of 34 degrees. The distance from the block down the incline is 14 cm. …
I’m in the process of working through some mechanics examples that use the Lagrangian to find a solution. In case you missed it, here is my introduction to Lagrangian Mechanics.
For this physics example, I’m going to look at a half Atwood machine. That’s just a fancy name for two blocks connected by a string. One block (mass 1) sits on a horizontal frictionless table. The other block (mass 2) hangs vertically off the table and is connected to mass 1 with a string. Oh, the pulley at the edge of the table is massless and frictionless. …
In the past, I’ve posted my top 10 blog posts for the year. I think I’m going to do it a little bit different this time — I mean, 2020 wasn’t a normal year. So, how about I break the top into the following categories.
Oh, I’m very happy if you disagree with my choices — it just means there is more awesome stuff out there.
Best Superhero Physics
I’ll be honest. There is a lot of stuff to talk about when we are talking about the Lagrangian. It’s not super simple — but it is super powerful.
Before jumping into Lagrangian mechanics, let’s think about Newtonian mechanics. At the most basic level, this uses the momentum principle and the work-energy principle:
This is a story. I’m telling it in the form of a script for a play.
SCENE: A house. Your typical house. It could be your house. It could be my house. The owner is a human. I’m just going to call the owner — OWNER. There is another human, a guest. I’ll call this human GUEST.
OWNER: Hello! Welcome to my house. It’s nice to see you. Will you please remove your shoes? We don’t wear shoes in the house here.
GUEST: Hello to you as well. It’s quite a lovely day and I’m excited to visit you.
OWNER: Great. Just don’t forget about the shoes. …