Re: [Phys-l] October Physics Challenge

[John Mallinckrodt <ajm@csupomona.edu>]

Carl (and anyone else following this thread),

I've put together a small spreadsheet to analyze the three possible cases 

1. Both blocks slip
2. Just m slips
3. Just M slips

for any set of parameters.  It is available at

http://www.csupomona.edu/~ajm/special/SlippingBlocks.xls

It confirms both that the scenario you suggest can occur and that it is "stable" in the sense that M is guaranteed to continue slipping until it reaches the end of the ribbon, or either block reaches the top or bottom of the wedge.  

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Another interesting case occurs for 

M = 2*m
theta = 25 degrees
mu_s = 0.75
mu_k = 0.35

Now, if you start with M slipping, it will eventually stop slipping and when it does the two blocks will thereafter  remain in static contact with the ribbon.  Alternatively, if you start with m, slipping it will continue to slip.

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A research project:  Is it possible to find a case where the large mass can be set slipping but will come to rest at which point the small mass will begin slipping?

John Mallinckrodt
Cal Poly Pomona

On Nov 10, 2010, at 2:44 PM, Carl Mungan wrote:

> To be concrete, try the following values:
>
> M = 2*m
> theta = 30 degrees
> mu_s = 0.75
> mu_k = 0.35
>
> Suppose that it were possible (which it is) to 
> have the heavy block (M) slipping on the ribbon 
> while the light block (m) does not. Compute the 
> magnitude and direction of the acceleration of:
>
> (a) the ribbon (with the light block riding on it)
> (b) the heavy block
>
> relative to the lab frame. Verify explicitly that 
> the static friction holding the light block on 
> the ribbon is less than its maximum value.
>
> Have fun! -Carl