Mechanics - inclined plane with friction and finding max M

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Homework Statement


A block with mass M is on an inclined plane having an angle of [itex]\theta[/itex] with respect to the horizontal. The coefficient of friction is [itex]\mu[/itex]. Find the maximum mass that the block can have before sliding down.

Homework Equations



[itex]\mu_{s}[/itex]= tan([itex]\theta[/itex]) - I derived this and tried to force it back into the problem with no luck.

The Attempt at a Solution



This is for an upper division mechanics class, so I've run across problems similar before. I'm not going to get crazy here, because I've attempted this problem several different ways, but I'm starting to think there is a typo in the problem.

After several attempts, I came to the same conclusion each time that no matter the mass, static friction with not convert to kinetic since increases the mass increases the static friction at a directly proportional rate. It shows up clearly in the math when I write the net force equations for both X and Y, and solving ends up cancelling out the M's, which tells me there is no dependency on the mass.

Is there something I'm missing here? Because I cannot for the life of me figure out this problem with cancelling the M's in the force equations. Any suggestions/incite?
 

Answers and Replies

  • #2
gneill
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So your conclusion would be that the mass is irrelevant since the friction force scales with the mass; if a light block doesn't slide, then neither will a heavy one so long as the friction coefficient remains the same. You haven't missed a thing :smile: There is no maximum mass according to theory.
 

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