Although Angry Birds is a great source for some cool physics, what about Bad Piggies? The nice thing about Bad Piggies is that it is easy to set up your own experiments since you get to build stuff.
Here I will try to find the masses of the different building blocks in Bad Piggies. There are two basic methods I can use. Both of them rely on some real-world physics that might not actually work in Bad Piggies.
Actually, since this post is a little bit longer than I expected, I have made a video showing you the basic idea. If you like, just watch the video and then skip to the end of the post to see the results.
However, if you skip to the end you might miss some awesome physics.
Torque
Take a look at this "contraption" in Bad Piggies.
If you make something like this, you will probably notice that often it will tip over to one side. Sometimes it will stay balanced. I think this is just the random nature of how these blocks interact. In general, if it slowly tips over I am going to say that it is balanced. But why does it balance?
Let me claim that for an object to balance, the counterclockwise torque must be equal to the clockwise torque. Here are a couple of key aspects of torque.
- Yes. Torque is really a vector. However, in this example the masses can only rotate clockwise or counterclockwise. It's still like a vector.
- The magnitude of the torque depends on the product of the force and the distance from the force to point of rotation. The distance and the force have to be perpendicular.
Back to the balancing blocks in Bad Piggies. In that same case from above, let me show the torque from the two blocks on the end.
The block on the left produces a counterclockwise torque (let me just call this a positive torque to make it shorter) with a magnitude of:
Here, mb is the mass of one of the wooden blocks. The perpendicular distance from the point of rotation for this block is 4s where s is the length of one of the blocks. Since there is another wooden block on the other side of the beam, it will have the same torque but with an opposite sign. Really, if I wanted to calculate the total torque on this device I could write it as the following. Oh, Let me call the mass of the metal blocks mm where the "m" subscript stands for "metal".
I probably didn't need to write that out, but I did. The point is that the net torque from this device is zero. That I can ignore the torque from the device and just look at the torque from extra objects. Here is another case with some blocks that balance. I have highlighted the three blocks that don't have a matching block on the other side.
For this, I can write the net torque equation (ignoring the symmetrical elements):
According to the torque model, this should balance and it seems like it mostly does. I guess physics works well enough in this case.
Using the Balance
Now it is time to just play around. With some trial and error, I found an item that has the same mass as a plain wooden block. Check it out.
Try that setup yourself and you should see that the fan is about the same mass as the wooden block. Sure, sometimes it will tilt one way, but sometimes it tilts the other way. Oh, there is something else. Maybe the distance from the point of rotation to the fan is different than the distance to the center of mass of the wooden block on the other side. However, the difference in distance wouldn't be that large.
Another Experiment to Test Mass
I need a backup plan. If the mass of the fan and the mass of the wooden block is indeed the same, then they should move with the same motion vertically when lifted by a balloon. Here is a picture of that.
If you assume the vertical motion of the balloon with a payload depends on the mass of the payload, the motion says something about the mass. For this case, the two object have the same vertical motion - I will assume the fan and the wooden block have the same mass. Of course, there is much more that should be explored with regard to the vertical motion of a balloon - but I will get to that later.
Measuring More Stuff
Let me just pick one more object and go through the process of finding the mass. Since the wooden block seems to be the most common building element, I will use this as the standard mass unit. Thus the mass of the wooden block will be 1 wb (where wb stands for wooden block).
The most obvious element to look at next would be the pig, right? Here is a setup that mostly balances. I have highlighted the non-symmetrical elements.
The pig on the left is 4 blocks from the pivot point and so are the two extra wooden blocks on the right. This would mean that the pig has a mass of 2 wb. But let me check with the balloons also.
Yup. Looks good.
Now for more stuff. I am not going to measure all the elements - but I will try to get the important ones. If you are skipping down to look for the results, THIS IS IT.
For the elements with an asterisk by the mass, I was unable to verify the mass with the balloon method (due to a lack of elements).
I guess the real question seems to be: What will I do with this info? Now I can set up other experiments that depend on mass. Since I have a measure of mass, this can be used for all sorts of cool stuff. Hopefully, I will get another experiment up soon. This has way more opportunities than plain Angry Birds.
Bonus Stuff
Let me do one more object in Bad Piggies. Why? Because the example I chose above turned out to be too easy. How do I come up with a fractional mass? Here I will look at the large metal wheel. If I try to get it to balance, I get something like this - which looks like it mostly balances.
If I just include non-matching elements, I get the following torque equation:
For cases that are difficult to balance, you could add extra wooden blocks to either side of the balance. But if this does have a mass of 7/4th of a wooden block, it would have the same mass as the metal block.
Looks like it works.
