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Conquering the Physics GRE Section 1.1 Prob. 3

  1. Aug 20, 2014 #1
    1. The problem statement, all variables and given/known data
    Two blocks of masses M and m are oriented as shown in the diagram. The block M moves on a surface with coefficient of kinetic friction μ_1, and the coefficient of static friction between two blocks is μ_2. What is the minimum force F which must be applied to M such that m remains stationary relative to M?

    The diagram essentially looks like Utah rotated 90 degrees clockwise.

    2. Relevant equations
    F_f = F_N * μ

    3. The attempt at a solution

    I drew force diagrams for both objects and summed up the forces, as is standard with these problems. My answer was:

    g * (μ_1 * M + (m / μ_2))

    The book tells you the correct answer and this is not it. I have triple checked my diagrams but I can't find my error.

    Any help is greatly appreciated!
  2. jcsd
  3. Aug 20, 2014 #2


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    Did you mean to say "What is the maximum force ...?" (Or am I misunderstanding the problem?)

    Ahh, that diagram makes more sense as to why they asked for the minimum (I was imagining utah rotated 90 degrees in the other direction)
    Last edited: Aug 20, 2014
  4. Aug 20, 2014 #3


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    Hello, coca-cola.

    To help you find your error, we'll need to see the details of your work. You might start by describing the force diagrams.

    How many forces do you have acting on M? Can you describe the nature of each force and the direction of each force?

    Same questions for the forces acting on m.

    Does the attached diagram correctly show the configuration?

    Attached Files:

  5. Aug 20, 2014 #4
    The attached diagram is a correct representation and it states "...minimum force F..." in the problem. I have three forces on the smaller block:

    Force to the right exerted by the bigger block
    Gravity downwards
    The frictional force that keeps the block up upwards

    On the larger block, 5 forces:

    Gravity downwards
    Normal force upwards
    Applied force to the right
    Force from the smaller block to the left
    Frictional force to the left
  6. Aug 20, 2014 #5


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    I think there is one more force on the larger block. Can you identify it?
  7. Aug 20, 2014 #6
    The only one that I can think of is a frictional force exerted downward on the larger block. Is this correct?
  8. Aug 20, 2014 #7


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    Yes. Good.
  9. Aug 20, 2014 #8
    Haha yes! Thank you very much!
  10. Aug 20, 2014 #9


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    You're welcome. That's a nice exercise.
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