I don't recall where I first read about an idea like this (but I am pretty sure I did not come up with this). There was this article that describe a similar situation. They said they had one of these wireless circuit board cameras that they mounted in a box and dropped and recorded the video. The idea was that they could show some toys floating around like they were in space. Awesome, I thought. Too bad I did not have a circuit board camera. Alas, I had other things to worry about.
Then, about a year ago, I read about the CVS "disposable" video camera. This would be perfect for the zero g box (and many other cool uses). My first attempt was a complete failure. I dropped the box 1 story and the video was really disappointing. Next I tried placing the toys on something that would be springy enough to "launch" them into the air when it fell. This still was a failure. Finally, I decided to throw the box up (instead of dropping it). This was better, but still not that great.
What was the problem? Was there too much air resistance on the box? To answer this question, I made a video of me throwing the box.
From this, I used Tracker Video Analysis (great free program) to get position and time data of the box while it was in the air. Plotting the vertical velocity as a function of time, I get:
The key thing to look at here is the slope of the line. While the box is going up, the acceleration is -10.25 m/s2 and going down, it is -9.19 m/s2. This is what one would expect when air resistance is present. While the box is moving upward, gravity pulls down and so does the air resistance (opposite direction of motion). These force combine to give an acceleration greater than gravity alone. On the way down, the air resistance is now up, but gravity is still down. This gives a lower acceleration. This change in acceleration explains why the action figure goes up and then down the first movie.
I can reduce this change in acceleration by increasing the mass of the box. Can I calculate this? Yes, I can. I am not going to repeat the physics behind this - I already described this as part of my Line Rider Project. Here is the info I need:
- Size of box (cross sectional area) = .28 m2
- Mass of box = 2.1 kg
- Initial y-velocity = 7 m/s (approximately)
- Coefficient of drag for a flat plate = 1.28
I started to do this calculation in zoho spreadsheets, but it was too slow for my patience level. Here is what I started (if you want to look at it). After that, I finished it in Excel. Here is a plot of the velocity as a function of time (similar to above)
This gives an acceleration on the way up and on the way down similar to the data from the video. Close enough for me. What I want is for the acceleration up and down to be as close to -9.8 m/s2 as possible. If I made the mass of the box 2000 kg, this would probably work, but then it might be a little difficult to throw. What if I just doubled the mass?
| Mass of box | acceleration up (m/s2) | acceleration down (m/s2) |
| 2.1 kg | -10.86 | -9.01 |
| 4 kg | -10.44 | -9.45 |
| 8 kg | -10.14 | -9.65 |
| 10 kg | -10.08 | -9.68 |
| 15 kg | -9.99 | -9.72 |
| 20 kg | -9.95 | -9.74 |
If the box had a mass of 20 kg, that should give pretty good results. I think I might have a difficult time throwing a 20 kg box. A student instantly suggested building a trebuchet. Yes, a good idea but maybe another day. I think I should try a 10 kg box and get someone to help me throw it.
Can I throw a 10 kg box? - (obviously, I can - but can I throw it 3 meters high?)
Lets do a simple calculation to see if I can even throw this box the way I want it to go. In the acceleration test video, I threw the box about 3 meters high. The best way to approach this is using the work-energy theorem. This says that the work done on an object is equal to its change in energy. For this box, its change in energy will just be gravitational (actually it is the change in energy of the Earth-box system). The change in gravitational energy for a 10 kg box moving up 3 meters would be:
Clearly I can do 294 Joules of work, no big deal. But I don't want to move the box up 3 meters, I want to throw the box up three meters. These means that I will have to do this 294 Joules of work in a short distance. Looking at the video, I move the box about 1 meter while throwing it. In this case, the work done on the box would be:
Solving this for F (the force exerted by me):
I am no muscle-man, but I think I can do this. I could very likely do this with my legs. Close enough for me to give it a try.
So, I finally got the nerve to throw my increased mass box. Here is a picture of the beast:
Notice the wooden frame on the bottom. The plastic bags hold the scuba weights (I didn't want duck tape stuck to the weights). I don't know the exact mass of the box (yet), but I estimate it to be around 12 or 13 kg.
I threw the sucker twice. Not the best results, but good enough to post (really, I have pretty low standards).
I particularly like the ending of this movie (looking up at the sky). I kept that part in for artistic effect.
Here is the second throw.
I also videoed from outside the box so that I could get a measurement of the acceleration. Here are the two throws (actually in reverse order). Notice the GREAT data I will get from run 2.
Was Air Resistance a Factor?
Just as before, I analyzed the acceleration of the box on the way up and down while it was in free fall. Here is the data (from the movie shown above).
This gives an acceleration on the way up of -9.48 m/s2 and -10.58 m/s2 on the way down. The acceleration on the way up should be greater because gravity and air resistance are both pointing down. However, in this data the downward acceleration is larger. ERR??? One possible reason this could happen is because of the rotation of the box. I used the center of the box as the point to mark in each frame of the video and the box was slightly rotating. Since the outside center of the box is not the center of mass of the box, this could possibly make the accelerations off. Nonetheless, I think the added mass makes a difference. If you look at the videos from inside the box, the toys basically stay on the ground (where before they came way off).
My next step is to try and throw this thing higher. But that would be silly. I have realized that I am doing this the wrong way. Why is my box so big? There is no reason except to make my life more difficult (you can see that during this time, my life revolved around this stupid box).
If I make a much smaller box with smaller toy, it will have less air resistance and need less mass. Here is my version 2 box:
- Have a significant "zero-g" time. 2 seconds would be ok. 1 second is not enough.
- Reduce the effect of air resistance.
Where the initial velocity is zero m/s
and the final position is zero meters, so:
If I want it to fall for 2 seconds, I
would have to drop it from:
If I throw it (note: throw it
vertically, not eat it then vomit it) it will take
half the time going up and half the time going down.
So it would be like twice the time for dropping for 1
second. This would be:
(also note that I am calling
y0 as just y - just to add a pinch of
confusion).
This will give it just as much time, but have a much lower impact speed.
Needless to say, this box did not produce great results. It was still too heavy and it suffered significant damage from dropping it from a large height.
Zero g Box Version 3:
At first, I made the V2 box that size because of the focus of the video camera. If objects were too close to the camera, it would be out of focus. It turns out that the focus of the camera is adjustable (it was just glued in a fix position). This means that I can make the box even smaller. Another change I made was to use a longer box so that the objects inside would always be in the field of view of the camera. Here is what I came up with:
This box is actually made of three plastic cups. The top cup has the bottom cut out to hold the video camera and a window for light. Below that is the cup to hold the "astronaut". I drew some lines inside so it would be easier to see movement. A third cup is connected to the compartment cup with the only function of holding a weight (in this case, a two lbs scuba weight). Also pictured is my astronaut. I needed something small that would wiggle around in zero g. I made this guy out of rubber bands and clay.
This box still has its problems. The biggest problem is that it is difficult to throw without having it spin. Anyway, here are some results: