2. July 2017
Speed limits are a subject that sometimes causes a lot of stir in the minds of speed devils. Personally, I don’t think the subject is that exciting – drive the km/h (or mph, if you don’t use the metric system) you are allowed to and you won’t get any speeding tickets or risk killing yourself or anyone else. But where I do find the idea of speed limits interesting is the amount of energy involved when traveling at a high speed; more accurate, the amount of kinetic energy involved. Whenever the speed limit is raised it’s often only by a few kilometers (or miles) per hour. Why not raise the speed limit from, lets say, 120 km/h to 200 km/h (75 mph to 124 mph), instead of raising it to “only” 130 km/h (80 mph)? Well, in order to explain why, let’s simulate it and do some (simple, don’t worry) math. I’m gonna walk you through it with images while I explain.
Algodoo is a program used to simulate various physics. It’s great for simulating and visualizing physics, for building simple virtual machines, and to learn everything from engineering to optics. Download the program from the official site here. This isn’t a tutorial for Algodoo itself (there are plenty of YouTube videos for that purpose) but I will walk you through the steps of simulating the kinetic energy of moving objects.
Now that you’ve installed Algodoo it’s time to open the program. It should look something like this:
Click on “file” in the top left corner and select “New Scene”
A menu pops up prompting you to select a palette. Just choose “Default”.
Now you should see a new, blank scene. Scenes are basically project files. An empty scene is an empty project file.
As I explained earlier Algodoo is great for building simple machines in. So, therefore, we’re gonna build our own car.
Start by selecting the box icon in the Tools menu at the left (or press X on the keyboard).
Now left-click and drag with your mouse somewhere on the screen and create a rectangle. When you have the desired size, release the mousebutton.
Now select the Circle tool in the Tools menu or press C on the keyboard. Drag as before to create two circles. These are gonna be our wheels.
Right-click on of the wheels and navigate to Geometric Actions –> Add Center Axle in the popup menu. Do this for both of the wheels. This will add a hinge to the wheels that will allow them to rotate.
Now right-click on the hinge itself on one of the wheels and navigate to Axles in the popup menu.
Check the box that says “Motor”. Two new controls should popup.
Change the motor speed of the hinge to 100 by sliding the slider up or down.
Now do the same thing for the other hinge as well.
Zoom out with the scroll wheel on your mouth and create a big box a little away from the car on it’s right side. This will act as the wall our car will hit.
In order to actually show the kinetic energy involved when traveling at high speeds, we need to open the plotter for the car. Do this by right-clicking on the body of the car and selecting Show plot in the popup menu.
You should see a new window pop up on the screen. This window can be moved so it isn’t in the way of the car. Just drag it to the site like so it isn’t in the way of the car.
In this popup window, you’re gonna click on “Y-Axis: Speed”. In the popup-menu, deselect speed and instead select Kinetic energy (sum) at the bottom.
When this is done, just close down the “Y-axis” menu popup in the top right corner. Now you’re ready to actually run the simulation.
You either press the spacebar or the big green play button at the bottom of the screen. This will make the car drive towards the big box while at the same time showing the time and kinetic energy of the car. The kinetic energy should rise steadily with the acceleration of the car, and then level out once the cars top speed has been reached. If you see some jitter in the beginning, it’s probably because the car isn’t placed perfectly on the ground but just above it. This means that the car will drop when the simulation is run, and the jitter is just the visualization of this.
Once the car hits the wall, the Kinetic energy of the car will drop dramatically.
So why is this such a big deal? Well, energy doesn’t just disappear it has to go somewhere. All the energy is displaced throughout the body of the car and YOU. What this basically means is that you’re gonna get a lot of damage. But what has this to do with raising the speed limits of the road only a tiny amount? To answer this, pause the simulation with the spacebar and press Ctrl + Z to go back to the start of the path of the car. Now right-click on the hinges and raise the speed from 100mph to 200mph.
So what do you think will happen now? Twice the speed means twice the kinetic energy, right? Well, run the simulation and we will see.
The bottom line shows the kinetic energy while driving 100 mph while the top line shows the kinetic energy when driving at 200 mph. The time it took to hit the wall was more or less half the time which makes sense since we’re driving twice as fast. But even though the speed is only twice as fast, the kinetic energy is more than twice that of when we were driving at 100 mph. This is the reason why the speed limits only gets raised a small amount.
In order to understand why the amount of kinetic energy is multiplied by multitudes rather than just doubled when moving twice as fast, we need to look at the equation for calculating kinetic energy. The equation is relatively simple and looks like this:
KE = 0,5 * mv2
KE means “Kinetic Energy”, m is the mass of the object (how much it weighs) and v is the velocity of the object (how fast an object is moving in one direction) in m/s (meters per second). The result is stated in Joules (J).
As you can see velocity is to the power of 2. Let’s say that we have a car that has a mass of 1500 kg and is moving at 100 km/h – that is 27 m/s. let’s plot it into the equation
KE = 0,5 * 1500kg * (27 m/s)^2
This would equal to 546.750 J, or 546,7 KJ (Kilo Joules).
If we look at the equation where we plot in the velocity: (27 m/s)^2. What is going on here is, that we are basically saying 27*27. If double the speed from 100 km/h to 200 Km/h (which would be 54 m/s) the equation is gonna look like this: (54 m/s)^2. This means that we are saying 54*54. This means that the result is more than twice that of (25 m/s)^2.
When raising the speed limits it’s often just raised by a tiny amount. The reason behind this is, that raising the speed limit just a tiny amount will more than double the amount of kinetic energy resulting in greater damage should you crash.
I hope this may have helped you in some way or at least have introduced you to Algodoo. I can’t stress enough how much I recommend checking out Algodoo since it’s a GREAT tool for all sorts of experiments. And besides being a great tool it’s also tons of fun!