Hat tip to Frank for sending me a link to this video:
If you have never done a demo like this (without the motorcycle), you should. It really isn’t too difficult. Here is a video of my version:
So, the question is: is the motorcycle thing real or fake?
First, let me talk about the key aspect of this demo. Why don’t the glasses move? Well, they move – but just not very far. The demo is supposed to be an example of Newton’s Second law, or you could say it is the momentum principle (which is what I will use). If a force is applied for a short time interval, the momentum will not change too much. Here is the momentum principle:
And here is a diagram of a glass on a table with the cloth being pulled out.
Ok, so I know the demo works – I have done it. However, let me look at some of the parameters involved.
Static vs. kinetic friction
If the glass is moving with the same speed as the tablecloth, then there would be static friction between the two objects. This is bad because 1) the glass would be moving and 2) the static friction can have a greater value than the kinetic friction. The key is to make the table cloth have a high enough acceleration so that the static friction force is not enough to keep the glass at the same speed as the cloth. So, the magnitude of the max static friction force is:
Where N is the force the tablecloth pushes up on the glass (the normal force). Since the glass is not accelerating in the vertical direction:
Where m is the mass of the glass. So, the maximum horizontal acceleration for static friction would be:
And, this is why I put some slack in the cloth before pulling it out. I can get a huge acceleration that way.
So, suppose it is sliding. No need to worry about the static friction force. The force diagram would essentially look the same except that the friction force would be a bit smaller. The next key thing is the time interval. You want this friction force to be on the glass for as short of a time as possible. The momentum principle says:
I guess I could put in the model for friction. In this case, I could get the scalar equation (for the horizontal direction)
Now for some measurements
This video has something very useful. First, the demo is done as a normal demo. If I assume this first part is real (and why wouldn’t it be – since I can do this myself?), then I can assume that the parameters are the same for both cases. Using my uber-tracker video skills (Tracker Video), I can get the time for the cloth to leave and maybe an estimate for the motion of the glass.
I know this is really a rough measurement, but from that video – the cloth is moving under the glass for about 0.12 seconds. If I had a good measurement of the final velocity of the glass, I could get an estimate for the coefficient of friction. This is my best shot:
So, if I assume a change in velocity 0.19 m/s and a delta t of 0.12 seconds, then:
Measuring the BMW version
Whoever made this video hasn’t paid attention to what I have said about video analysis. The camera is not on a tripod AND they zoom out. Well, let me first get the time. Going through frame by frame, it looks like it took about 0.6 seconds. I will give it a value of 0.5 seconds just to be safe.
So IF I assume that the coefficient of friction is the same, then how fast would the glasses be moving after the tablecloth is pulled out?
That gives a speed that is about 4 times faster than the other dishes. Those dishes do move, but it seems like they should move more than that.
Is it fake
So, here are the options:
- It is fake. Don’t know how they did it, but they did something. Whatever they did, it looks convincing enough. The dishes do move some.
- It is not fake and the model I was using for friction does not apply in this case because the tablecloth is moving so fast (remember, friction is actually pretty complicated).
- It is not fake and I just made an error somewhere – perhaps with my measurements.
It seems like The Blog of Phyz posted this before I finished my analysis.