For Pi Day, Calculate Pi Yourself Using Two Colliding Balls

This is at least my ninth year of writing about Pi Day—here is my post from 2010. Of course it’s called Pi Day because the date, 3/14, is similar to the first three digits of pi (3.1415 …). At this point I’ve built up a whole library of fun things in honor of Pi Day.

Here is a new one. You can calculate the digits of pi using elastic collisions between two objects of different masses and a wall. Let me explain with this diagram.

Rhett Allain

There are two balls, A and B. Ball A has a larger mass and is initially moving. It collides with ball B such that ball B speeds up and ball A slows down just a little bit (this is a perfectly elastic collision). After this, ball B starts moving toward the wall and eventually bounces off it back toward ball A for another collision. This continues until ball A is moving away from the wall instead of toward it, and there are no longer any collisions.

Now for the pi part. If you know that the mass of ball A is 100 times greater [...]  read more

How Many Times Do You Have to Slap a Chicken to Cook It?

Could you cook a chicken by slapping it? This recent meme may not sound like a good physics question at first glance, but it is, in fact, a great question. In fact, I thought I’d already answered it. Back in 2010, I looked into the possibility of cooking a turkey by dropping it.

But this chicken slap question is still a great physics problem, so let’s get to it.

Cooking is Heating

Let’s say you want to cook a chicken. You could grill it, fry it, broil it, or even microwave it. The point is that you need to increase the temperature of the chicken from, say, room temperature to 165 degrees Fahrenheit (74 degrees Celsius). Cooking the chicken does two things. First, cooked meat is easier for humans to digest (and we get more calories from cooked vs. raw meat). Second, at 165 degrees Fahrenheit the chicken is at a temperature at which all of the bad bacteria have probably been destroyed. So, don’t eat raw chicken.

Even though cooked chicken is not just hot raw meat, I’m [...]  read more

Estimate the Friction Coefficient in That Massive Nascar Pile-Up

I don’t normally watch many NASCAR races, but I do come across some NASCAR videos online. Sometimes these clips become the basis of a great physics problem. In this case, it’s a 21-car crash at the Daytona 500 earlier this week. There are two things I find amazing about it: First, that a tiny collision between two cars can lead to a bunch of cars getting knocked out of the race. Second, that the cars have so much technology that none of the drivers was seriously injured.

But what about the physics? It’s that bird’s-eye view of the race, as seen from the blimp, that gets me thinking about physics. That top view essentially gives us a very expensive physics homework question. You can see the position of each car in different frames of the video. This will allow for a measurement of both velocity and acceleration.

Before the crash, there’s nothing much to analyze. After the crash, the cars are sliding along the track and slowing down due to  [...]  read more

Sorry, Sandra Bullock: A Fire Extinguisher Is a Lousy Thruster

Suppose you are an astronaut out in space. You have nothing with you except your wits and … a fire extinguisher? Why a fire extinguisher? Because that’s what Sandra Bullock’s character has in the movie Gravity. Because a fire extinguisher shoots out gas (normally to put out a fire), it can also be used to produce thrust and help you maneuver in space. But would this really work? That is what the MythBusters, for whom I’m a science consultant, set out to test in a recent episode.

The MythBusters started by trying to create a similar situation on the surface of the Earth. They used a leaf blower to fashion a one-person hovercraft (it’s not too hard to build one yourself). They let it loose on an ice rink, which pretty much eliminated the frictional force. Then they used a fire extinguisher for thrust and tried maneuvering around on the ice.

It turned out that the fire extinguisher wasn’t so great for controlling the motion of the hovercraft. [...]  read more

How to Figure Out a Drone’s Angular Field of View

You know what happens when I get a new toy? Physics happens. I can’t stop myself, it’s just the way I am.

In this case, the toy is a DJI Spark drone (it was a birthday present). I’ve always wanted a drone that could do some cool stuff. The one I had before was basically just a toy. But with this new toy, I am going to determine the angular field of view for the Spark camera.

Sometimes referred to as FOV, the angular field of view is the portion of the world that a camera can see.

Here, maybe this picture will help.

Rhett Allain

Anything within that angle (θ) can be seen by the camera. Who cares? If you know the FOV, you can get the angular size of objects that you see. Angular size depends on both the distance from the camera and the size of the object. If you measure the angular size in radians, then the following relationship holds.

Rhett Allain

In this expression, r is the distance to the object and L is the length of the object. But here’s the real [...]  read more

The Way Superman Picks Up a Building Is a Physics Travesty

You can’t really use standard physics principles to explain how Superman can be so strong or fly or have x-ray vision. Pretty much everything he does is impossible. But hey—that’s OK. I’m fine with this stretching of reality. It’s what makes superheroes interesting. They don’t have to be completely realistic to be entertaining.

But sometimes things just cross the line for me. Let’s take a look at a scene from Justice League (the movie). Don’t worry about all the details (also because I don’t want to spoil the plot), but at some point Flash and Superman are trying to save a bunch of people in a town that is going to get destroyed. Flash, being the Flash, ends up pushing a pickup truck with some people in it. He goes super fast and they reach safety. Yay! Oh but wait. Superman is better. Instead of saving just a couple of people, he flies out of town carrying a whole building.

This is where I have a problem. I don’t [...]  read more

This Fearsome *Titan Games* Event Reveals the Value of Torque

I’m oddly attracted to The Titan Games. I think we can all agree that this is the newest incarnation of the popular ’90s show American Gladiators. It’s not the theatrics that I enjoy, it’s the crazy competitions. As you can imagine, there’s a bunch of cool physics to talk about for some of these events. Actually, if you use a little bit of physics you might be able to get an advantage over your opponent.

In this case, the event is the Herculean Pull. The main idea is to pull some horizontal poles out of a giant wedge. The two contestants are trying to pull the poles out from different sides. There’s a chance you could reach a pole before the other person and win the easy way. But if you’re both pulling on the same pole, you need to use some physics. Here, check out this clip from the show.


p class=”paywall”>The physics trick is to not just pull out on the pole—but also UP! Yes, pull out and up. This is especially true if you are [...]  read more

Thank the Old-Timey Telegraph for Your Garage Door Opener

I remember the first time I had to deal with a faulty relay. My garage door opener had stopped working, and my kids were tired of going out in the rain to open the garage door manually (it’s my job as the dad to control the car). It turned out that our 20-year-old opener had a bad relay.

But what the heck is a relay? How do they work? Why do you need one? Yes, I am going to answer these questions for you.

It appears that the first relays were created for the telegraph system. A telegraph is a fairly simple technology. Essentially, it’s a battery and a switch on one end and an electromagnet on the other end. When a human presses the switch at the transmitting side of the telegraph, electric current runs down a wire and activates an electromagnetic switch on the receiving side to produce a “click.” These clicks can then be timed to generate a pattern that can be mapped to letters—you know this as Morse Code.

But there’s a problem. If you have [...]  read more

A Flying Tesla? Sure! We Calculate the Power Demands

Elon Musk isn’t afraid to play around on Twitter. In a recent tweet, Musk suggested that a future Tesla would look like the flying car from Back to the Future.


p class=”paywall”>Ha ha. Funny. But could it really work? What would it take to make a flying Tesla that converts from driving to flying mode with the thrust coming out of the wheels? Time for some physics.

I can think of a couple options for getting a flying Telsa off the ground. The first method would be rocket propulsion. This seems to be what Elon wants to use (a natural choice because of the connection with SpaceX). In fact, it appears he’s not even joking.

I’m not a rocket expert, but it seems like you would have to keep refueling the rockets. It would be a nice stunt, but not for everyday use.

However, there is another way to make a car fly—some type of air thruster. It doesn’t matter if you use some type of jet engine or a rotor, the physics is mostly the same. In [...]  read more

A Magic Wand? Nope, Just Good Ol’ Fashioned Physics

Check this out. It looks like a magic wand that makes things float, but it’s just plain physics. I guess that’s what makes these kinds of toys so cool. They do things that go against our everyday experiences. Normally stuff doesn’t just hang in the air like this.

But how does it work? The answer is a fundamental interaction in nature—the Coulomb force (also called the electrostatic force). The Coulomb force is an interaction between any two electric charges. It’s sort of a circular definition, since you still have to define an electric charge. I will just say that the two most common electric charges are everywhere—they are the electron (negative charge) and the proton (positive charge). Along with the neutron, these three particles make up pretty much everything you see in everyday life.

For the Coulomb force, if the two charges are opposite in sign (negative vs. positive), there is an attractive force between them. If the two charges have the [...]  read more