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I get: a = gsin() - mu_k * 2gcos(), which is -1.06 m/s^2 (up the ramp).
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-(b) the heavy block
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I get just less than 2 m/s^2 towards the bottom of the ramp.
relative to the lab frame. Verify explicitly that
the static friction holding the light block on
the ribbon is less than its maximum value.It is, by a bit.
So... where's the issue in our analysis? In what regime does this apply?
jg
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.
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.
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?