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A pulley system with two objects stacked on each other

  1. Mar 27, 2014 #1
    1. The problem statement, all variables and given/known data

    Block B, with mass 5.00kg, rests on block A, with mass 8.00kg , which in turn is on a horizontal tabletop. There is no friction between block A and the tabletop, but the coefficient of static friction between block A and block B is 0.750. A light string attached to block A passes over a frictionless, massless pulley, and block C is suspended from the other end of the string. What is mass of block C?

    2. Relevant equations
    F=ma
    FFriction = μmg

    3. The attempt at a solution
    I made equations for all 3 masses:

    box C:
    mCa=mcg-T.


    box B:
    mBa=FS


    box A:
    mAa=T-FS


    added all three equations, the internal forces (tension and friction) cancel and I get:

    mCg = a(mA+mB+mC)

    However I still have 2 unknowns ([itex]a[/itex] and mc)
    I attempted to figure out acceleration using the equation for box B:

    mBa=FS
    mBa=μmBg
    a = μg
    a = (0.750)(9.8)
    a = 7.35 m/s^2
    but that seems to be a sketchy way to do it?
     

    Attached Files:

  2. jcsd
  3. Mar 27, 2014 #2
    As written, the problem statement is incomplete. Without knowing how the system is moving, there is no way to determine the mass of C (as evidenced by the fact that you have 3 equations and 4 unknowns - T, FS, a, mC).

    The last part of your solution is incorrect because FS will depend on the acceleration of the blocks, which is unknown.
     
  4. Mar 27, 2014 #3
    no when you add the 3 equations together you only have 2 unknowns. Then if you find the acceleration (7.35) and solve for mC you get 39 kg, which seems to be the correct answer.
     
  5. Mar 27, 2014 #4

    jbunniii

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    You seem to be making an implicit assumption here. The friction force is at most ##\mu mg## but it can be less. For example, if mass ##C## was zero and there was no movement, then the friction force would be zero.
     
  6. Mar 27, 2014 #5

    haruspex

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    To get that acceleration, you had to assume that the frictional force between A and B was at its maximum value. This is presumably the missing piece of information.
    The question as stated does not provide any basis for such an assumption. If the normal force is N and the coefficient of friction is μ then the frictional force is anything from -μN to +μN.
     
  7. Mar 27, 2014 #6
    You have a set of 3 equations and 4 unknowns. Adding them together is a good way to isolate the variables you want, but you still are under-constrained.

    Regardless, the problem is incomplete and there needs to be another piece of information (most likely about the acceleration of the blocks) to determine the mass of block C.
     
  8. Mar 27, 2014 #7

    haruspex

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    No, most likely that it is the maximum mass for which the system remains static.
     
  9. Mar 28, 2014 #8
    Because the horizontal surface is frictionless, there is no static configuration for this system. The acceleration is mCg/(mA+mB+mC), which can only be zero if mC is zero or mA+mB is infinite.
     
  10. Mar 28, 2014 #9

    haruspex

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    Sorry, I should have said, for which the blocks do not slide on each other.
     
  11. Mar 28, 2014 #10
    Gotcha. So you're assuming that the question is asking for the maximum mass of block C such that block B doesn't slip. That would make sense.

    Who knew physics question forensics would be so much fun?!
     
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