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Centripetal Motion Question (Two Blocks Stacked)

  1. Oct 21, 2015 #1
    1. The problem statement, all variables and given/known data
    Mass 1 (2.0kg) sits on top of mass 2(5.0kg), which rests on a frictionless surface. The coefficient of static friction between mass 1 and mass 2 is 0.30. A string of length 5.0m is tied to mass 2, and both masses are swung around in a horizontal circle. Calculate:
    a) The maximum speed of the masses
    b) The tension in the string

    2. Relevant equations
    Fc= mv^2/r

    3. The attempt at a solution
    I assumed that since there is no vertical motion, the Fc would be the tension in the string. So, i added both masses to make a system diagram of one block with both masses. Then, when I tried to solve for the maximum speed, I was stuck with 2 unknowns, Fc, and Ftension. I think we should make two equations and subsitute into the other and solve for one variable, but im not sure.

    Can someone please help me, and work through this problem with me?
  2. jcsd
  3. Oct 21, 2015 #2


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    Hello Leaq, welcome to PF :smile: !

    doesn't that eliminate one of the two from
    I see a few variables in your problem statement that don't appear in the relevant equations. What about that friction coefficient ?
  4. Oct 21, 2015 #3

    Mister T

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    So far so good, now if you do the same for the upper object alone, Fc is ...
  5. Oct 21, 2015 #4
    So i'm on the right track. I think the Fc of the upper object would be the same as the bottom block. So what steps do I take, can u please explain im stuck?
  6. Oct 21, 2015 #5
    Im not sure man, I'm not really that great at physics, so I do need some help, and it would be great if u can explain it more clearly, and demonstrate some steps
  7. Oct 21, 2015 #6

    Mister T

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    Think about it this way. The tension force acts on the lower block, keeping it moving in a circle. If that force weren't there (if the string broke, for example) the block would move off in a straight line instead of following the circular path.

    What force is doing the same thing to the upper block? It can't be the tension in the string because the string isn't attached to the upper block.
  8. Oct 21, 2015 #7
    im guessing force normal
  9. Oct 21, 2015 #8
    sorry i mean force of friction, because there is a coefficient of static friction given
  10. Oct 21, 2015 #9

    Mister T

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    There you go! Note that a horizontal force, not a vertical force, is required. Remember, all that's meant by "centripetal force" is a force that points towards the center. For the lower block that force is the tension in the string. For the upper block it's the friction force.

    So, what you originally did for the composite body consisting of the upper and lower blocks, now needs to be done for the upper block alone.
  11. Oct 21, 2015 #10
    so basically i would calculate force of friction of the upper block, and use that to calculate the tension of the string in the bottom block?
  12. Oct 21, 2015 #11
    or would the force of friction of the upper block equal the tension of the bottom block
  13. Oct 21, 2015 #12

    Mister T

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    Show us the work you described in your opening post.
  14. Oct 21, 2015 #13
    how do i show it? like post a picture?
  15. Oct 21, 2015 #14

    Mister T

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    You could either post a picture or type it.
  16. Oct 22, 2015 #15
  17. Oct 22, 2015 #16
    I posted a picture
  18. Oct 22, 2015 #17


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    Yes. Give that a go.
    The two blocks are capable of moving independently, so you can obtain equations for the forces on each. If you treat them as a single unit only then you are denying yourself enough equations.
  19. Oct 22, 2015 #18

    Mister T

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    Let's start by looking at what you did for the composite body of mass ##m_1+m_2##. In your first post you said you had two equations, but were stuck with two unknowns, ##F_c## and ##F_T##, but for this composite body those two forces are actually not any different. ##F_T## is the centripetal force. So the last equation on your paper is

    ##F_T=\displaystyle \frac{mv^2}{r}##,

    where ##m## is the mass of the composite body.

    Now do the same thing for the upper body.

    Let's review the process:

    Start with Newton's Second Law: ##F_{net}=ma##,

    where ##F_{net}## is the net force exerted on some object,
    ##m## is the mass of that object, and
    ##a## is the acceleration of that object.

    You need to first understand that process for the composite body, and then again for the upper body. That will give you your solution.
    Last edited: Oct 22, 2015
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