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Re: [Phys-l] October Physics Challenge



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.

Sounds right. I left my analysis at work since today's Veteran's Day, but we can easily enough check it using John's spreadsheet reference below.

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

If *some* initial conditions permit the heavy block to begin slipping, then it will stably continue to do so. The original problem didn't ask us to explain all possible scenarios for how the blocks might initially be held and released. There could presumably be very many possibilities, and some will undoubtedly start with the heavy block slipping. Since the problem *does* say to consider all possible motions, we must include this possibility.

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.

Much thanks, that's great! I've been hoping you or Denker would get interested.

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?

Nice addition to the problem: consider what happens at longer times (assuming the blocks don't run off the ribbon first!). Seems like with your spreadsheet, you're in the best position to answer this research project. (At least you can try finding a numerical case where it does occur, if it can, and then generalizing from there....) -Carl