Maximum Resting Mass and Acceleration in a Friction System

[drsl92]

Homework Statement

block 1 of mass m1 is placed on block 2 of mass m2 which is then placed on a table. A string connecting block 2 to a hanging mass M passes over a pulley attached to one end of the table. The mass and friction of the pulley are negligible. The coefficient of friction between blocks 1 and 2 and between block 2 and the tabletop are nonzero.

A) Determine the largest value of M for which the blocks can remain at rest
B) Now suppose that M is large enough that the hanging block descends when the block are released. No slippage. Determine the magnitude a of their acceleration
C) With slippage find the acceleration of block 1
D) The acceleration of block 2

Homework Equations

The Attempt at a Solution

Tried to solve it but no success

 

[Delphi51]

I'm stuck, too! I don't think there is enough information to get a numerical answer. For A, the blocks will stay at rest until the Mg of the hanging mass exceeds the friction force holding m1 and m2 on the table. We don't know the coefficient of friction, so we're stuck. You could, of course write an expression for the answer that has a mu (coefficient of friction) in it. Perhaps that is what you are supposed to do.

In B, I'm trying to wrap my mind around "no slippage". How can M descend without making m2 slip on the table? Once again we need the coefficient of friction to find the answer.

 

[drsl92]

I'm stuck, too! I don't think there is enough information to get a numerical answer. For A, the blocks will stay at rest until the Mg of the hanging mass exceeds the friction force holding m1 and m2 on the table. We don't know the coefficient of friction, so we're stuck. You could, of course write an expression for the answer that has a mu (coefficient of friction) in it. Perhaps that is what you are supposed to do.

In B, I'm trying to wrap my mind around "no slippage". How can M descend without making m2 slip on the table? Once again we need the coefficient of friction to find the answer.

i think your right that i have to find an expression, but i still have a hard time solving the problem

 

[Hannisch]

I reckon what they want in a) is an expression for M containing m₁, m₂ and μ (coefficient of friction).

The best way to go around this is to draw FBDs, one for the two masses on the table and one for the mass hanging off the string. Not moving means that the net force has to be zero, right?

For b) and c) I'm rather confused - what on Earth is slippage? (I'm Swedish, never heard the term before.)

Edit: Oh! I get it! "No slippage" means that m₁ and m₂ don't move relative to each other, right? Never heard it being said as slippage before, even though I go to an English speaking school (my Physics teachers aren't English speakers from the beginning either, so you never really know).

 

[drsl92]

ya the F=0
slippage is to fall, to lose balance

 

[Delphi51]

Force of gravity on M = force of friction
u(m1+m2)g = Mg
Cancel the g's and you have A done.
There is an assumption here that m1 doesn't slide on m2. That should be okay for A because the acceleration will be very small, therefore little force m1*a working to overcome the friction u*m1*g.

 

[drsl92]

thank
your answer seems to make sense, and it really helps to solve the rest of the question