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Newton's 2nd Law - Trimming a Stack of Discs Down to Size

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You have probably seen the demonstration of a tablecloth pulled out from underneath dishes. If you pull the tablecloth quickly enough the dishes stay there. This demonstration is similar to that but instead of dishes we have a stack of wooden disks and instead of a table cloth we have a stick and the goal is to remove the dishes from the stack, there are eight of them, one at a time from the bottom up without making the stack topple over. Now here's how to go about doing it: to get the bottom disc out: just hit it very quickly with the stick. Now I could hit it slowly but if I did that the whole stack moves. Or a little bit faster and the stack may topple over. What's happening here is that when I hit the stick I am hitting it with a fairly large force and that force is acting on that disc on the bottom. So I have a large force acting on a fairly small mass. Now you know that acceleration = force/mass and so we have a large force over small mass = large acceleration. When I have the whole stack there let's talk about the force and acceleration of the stack above the bottom disk why does that stack move at all? If I move slowly you can see that it does move. It moves because the bottom disk is exerting a force of friction on the stack. Now that's a relatively small force compared to the force I exert on the stick. That small force is accelerating a fairly large mass. So in that case we have acceleration = small force/large mass so we get a small acceleration. So the result is when I hit quickly the bottom disc acquires a large acceleration while the stack of discs above it acquires a small acceleration. The acceleration, the forces act for the same period of time for both. As a result the bottom disc speeds up much more than the top does. And we are able to get the bottom disc out, and we can just keep going back and forth and get rid of the whole stack that way.

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