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Two blocks on inclined surface

  1. Mar 22, 2015 #1
    1. The problem statement, all variables and given/known data:
    upload_2015-3-23_1-48-25.png
    block M slides down on frictionless incline .Find the minimum co efficient of friction so that m does not slide with respect to M.


    2. Relevant equations:acceleration of the system=total driving force/total mass: upload_2015-3-23_1-49-7.png





    3. The attempt at a solution
    m does not slide with respect to M means there should not be kinetic friction rather static friction.both small and big block will have same acceleration.

    acceleration of the system=total driving force/total mass


    :total driving force=(m+M)g sin theta

    acceleration of the system=(m+M)g sin theta/m+M

    =g sin theta
    force responsible for acceleration of small block would be force of static friction between two blocks.

    Hence force of static friction between two blocks=mass of small block i.e "m" multiplied by g sin theta

    but this force of static friction between two blocks is also equal to or smaller than μ multiplied by normal force on small block i. mg

    force of static friction ≤ μmg


    force of static friction/mg≤ μ

    m× g sin theta= force of static friction

    Hence m× g sin theta/mg ≤ μ

    theta= 37 degrees

    sin theta ≤ μ
    sin 37 degrees ≤ μ
    0.601 ≤ μ
    but the correct answer should be 0.75 ≤ μ
    where am I going wrong?
     
  2. jcsd
  3. Mar 22, 2015 #2

    TSny

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    There are other forces acting on the small block besides friction. What is the direction of the friction force acting on m?
    Draw a good free body diagram for the small mass m.
     
  4. Mar 22, 2015 #3
    You correctly obtained the acceleration of both masses, which is oriented in the same direction as the incline. Can you resolve this acceleration into components in the horizontal and vertical directions? These are the horizontal and vertical components of the acceleration of the smaller mass m. Once you know these, can you do force balances on m in the horizontal and vertical directions? What do you obtain?

    Chet
     
  5. Mar 22, 2015 #4
    I think my diagram was wrong.Here I have corrected myself.
     
  6. Mar 22, 2015 #5
    upload_2015-3-23_7-19-13.png
    I think my diagram was wrong.Here I have corrected myself.
     

    Attached Files:

  7. Mar 22, 2015 #6
    will (m+M)g sin theta act on both the blocks?
     
  8. Mar 22, 2015 #7
    Your diagram is still awful. I thought I understood your original diagram. I'm still trying to figure out how to draw figures with whiteboard that can have straight lines. Meanwhile, please see if you can answer my questions in post #3.

    I still don't know from your figure whether θ = 37° is the angle of the incline with the horizontal, or with the vertical. I assumed it was with the horizontal.

    Chet
     
  9. Mar 22, 2015 #8
    please point out my mistakes.
    θ = 37° is the angle of the incline with the horizontal
     
  10. Mar 22, 2015 #9
    OK. That's all I needed to know. So now, back to post #3.

    Chet
     
  11. Mar 23, 2015 #10

    ehild

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    Is not mass M also a block? If it is a wedge as it was drawn, what are its angles?
     
  12. Mar 23, 2015 #11
    Mass M is also a block.Sorry for my poor drawing.
     
  13. Mar 23, 2015 #12

    ehild

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    Is the set-up that shown in my figure?

    twoblockswedge.jpg
     
  14. Mar 23, 2015 #13
    I want to solve this as soon as I can.I don't have much time.I have a test tomorrow.
     
  15. Mar 23, 2015 #14
    Yes.Absolutely correct.
     
  16. Mar 23, 2015 #15

    ehild

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    And is the problem text as you wrote? Is zero friction between M and the incline?
     
  17. Mar 23, 2015 #16
    Yes.
     
  18. Mar 23, 2015 #17

    ehild

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    Then is friction needed that m accelerate the same as M?
     
  19. Mar 23, 2015 #18
    Sorry.I did not understand.
     
  20. Mar 23, 2015 #19

    ehild

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    What force acts on m along the incline? What acceration does it cause without friction?
     
  21. Mar 23, 2015 #20
    You mean excluding friction between the blocks what other forces are acting on m along the incline?
     
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